TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60066 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (72ms).
 | – Problem 2 was processed with processor SubtermCriterion (1ms).
 | – Problem 3 was processed with processor SubtermCriterion (0ms).
 | – Problem 4 was processed with processor ForwardNarrowing (5ms).
 |    | – Problem 6 was processed with processor ForwardNarrowing (3ms).
 |    |    | – Problem 7 was processed with processor ForwardNarrowing (2ms).
 |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (15ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (43ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 33 was processed with processor ForwardNarrowing (52ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 34 was processed with processor ForwardNarrowing (17ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 35 was processed with processor ForwardNarrowing (67ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 36 was processed with processor ForwardNarrowing (76ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 37 was processed with processor ForwardNarrowing (44ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 38 was processed with processor ForwardNarrowing (47ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 39 was processed with processor ForwardNarrowing (58ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 40 was processed with processor ForwardNarrowing (63ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 41 was processed with processor ForwardNarrowing (84ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 42 was processed with processor ForwardNarrowing (65ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 43 was processed with processor ForwardNarrowing (74ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 44 was processed with processor ForwardNarrowing (87ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 45 was processed with processor ForwardNarrowing (76ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 46 remains open; application of the following processors failed [ForwardNarrowing (58ms), ForwardNarrowing (50ms), ForwardNarrowing (52ms), ForwardNarrowing (51ms), ForwardNarrowing (42ms), ForwardNarrowing (52ms), ForwardNarrowing (50ms), ForwardNarrowing (60ms), ForwardNarrowing (60ms), ForwardNarrowing (60ms), ForwardNarrowing (179ms), ForwardNarrowing (61ms), ForwardNarrowing (61ms), ForwardNarrowing (61ms), ForwardNarrowing (180ms), ForwardNarrowing (61ms), ForwardNarrowing (70ms), ForwardNarrowing (43ms), ForwardNarrowing (174ms), ForwardNarrowing (71ms), ForwardNarrowing (70ms), ForwardNarrowing (71ms), ForwardNarrowing (206ms), ForwardNarrowing (82ms), ForwardNarrowing (81ms), ForwardNarrowing (81ms), ForwardNarrowing (199ms), ForwardNarrowing (79ms), ForwardNarrowing (80ms), ForwardNarrowing (71ms), ForwardNarrowing (202ms), ForwardNarrowing (81ms), ForwardNarrowing (43ms), ForwardNarrowing (44ms), ForwardNarrowing (162ms), ForwardNarrowing (62ms), ForwardNarrowing (62ms), ForwardNarrowing (61ms), ForwardNarrowing (timeout)].
 | – Problem 5 was processed with processor SubtermCriterion (0ms).

The following open problems remain:

Open Dependency Pair Problem 4

Dependency Pairs

f#(b, y, x) → f#(a, half(x), exp(y))f#(a, s(x), y) → f#(b, y, s(x))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

tower#(x) → f#(a, x, s(0))exp#(s(x)) → double#(exp(x))
f#(b, y, x) → half#(x)half#(s(s(x))) → half#(x)
half#(0) → double#(0)f#(b, y, x) → f#(a, half(x), exp(y))
double#(s(x)) → double#(x)half#(s(0)) → half#(0)
f#(b, y, x) → exp#(y)exp#(s(x)) → exp#(x)
f#(a, s(x), y) → f#(b, y, s(x))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The following SCCs where found

f#(b, y, x) → f#(a, half(x), exp(y))f#(a, s(x), y) → f#(b, y, s(x))
half#(s(s(x))) → half#(x)
double#(s(x)) → double#(x)
exp#(s(x)) → exp#(x)

Problem 2: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

double#(s(x)) → double#(x)

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

double#(s(x)) → double#(x)

Problem 3: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

half#(s(s(x))) → half#(x)

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

half#(s(s(x))) → half#(x)

Problem 4: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, y, x) → f#(a, half(x), exp(y))f#(a, s(x), y) → f#(b, y, s(x))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, y, x) → f#(a, half(x), exp(y)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, half(0), exp(y)) 
f#(a, half(x), double(exp(_x41))) 
f#(a, half(x), s(0)) 
f#(a, s(half(_x31)), exp(y)) 
f#(a, double(0), exp(y)) 
Thus, the rule f#(b, y, x) → f#(a, half(x), exp(y)) is replaced by the following rules:
f#(b, 0, x) → f#(a, half(x), s(0))f#(b, y, s(0)) → f#(a, half(0), exp(y))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Problem 6: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, x) → f#(a, half(x), s(0))f#(b, y, s(0)) → f#(a, half(0), exp(y))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, x) → f#(a, half(x), s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, s(half(_x31)), s(0)) 
f#(a, double(0), s(0)) 
f#(a, half(0), s(0)) 
Thus, the rule f#(b, 0, x) → f#(a, half(x), s(0)) is replaced by the following rules:
f#(b, 0, s(0)) → f#(a, half(0), s(0))f#(b, 0, 0) → f#(a, double(0), s(0))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))

Problem 7: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(0)) → f#(a, half(0), s(0))f#(b, 0, 0) → f#(a, double(0), s(0))
f#(b, y, s(0)) → f#(a, half(0), exp(y))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, s(0)) → f#(a, half(0), s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, double(0), s(0)) 
Thus, the rule f#(b, 0, s(0)) → f#(a, half(0), s(0)) is replaced by the following rules:
f#(b, 0, s(0)) → f#(a, double(0), s(0))

Problem 8: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(0)) → f#(a, double(0), s(0))f#(b, 0, 0) → f#(a, double(0), s(0))
f#(b, y, s(0)) → f#(a, half(0), exp(y))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, s(0)) → f#(a, double(0), s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(0)) 
Thus, the rule f#(b, 0, s(0)) → f#(a, double(0), s(0)) is replaced by the following rules:
f#(b, 0, s(0)) → f#(a, 0, s(0))

Problem 9: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(0)) → f#(a, 0, s(0))f#(b, 0, 0) → f#(a, double(0), s(0))
f#(b, y, s(0)) → f#(a, half(0), exp(y))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, s(0)) → f#(a, 0, s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
Thus, the rule f#(b, 0, s(0)) → f#(a, 0, s(0)) is deleted.

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, 0) → f#(a, double(0), s(0))f#(b, y, s(0)) → f#(a, half(0), exp(y))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, y, 0) → f#(a, double(0), exp(y))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, 0) → f#(a, double(0), s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(0)) 
Thus, the rule f#(b, 0, 0) → f#(a, double(0), s(0)) is replaced by the following rules:
f#(b, 0, 0) → f#(a, 0, s(0))

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, 0) → f#(a, 0, s(0))f#(b, y, s(0)) → f#(a, half(0), exp(y))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, y, 0) → f#(a, double(0), exp(y))
f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, 0) → f#(a, 0, s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
Thus, the rule f#(b, 0, 0) → f#(a, 0, s(0)) is deleted.

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, y, s(0)) → f#(a, half(0), exp(y))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, y, s(0)) → f#(a, half(0), exp(y)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, half(0), double(exp(_x41))) 
f#(a, half(0), s(0)) 
f#(a, double(0), exp(y)) 
Thus, the rule f#(b, y, s(0)) → f#(a, half(0), exp(y)) is replaced by the following rules:
f#(b, 0, s(0)) → f#(a, half(0), s(0))f#(b, y, s(0)) → f#(a, double(0), exp(y))
f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(0)) → f#(a, half(0), s(0))f#(b, y, s(0)) → f#(a, double(0), exp(y))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, y, 0) → f#(a, double(0), exp(y))
f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, s(0)) → f#(a, half(0), s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, double(0), s(0)) 
Thus, the rule f#(b, 0, s(0)) → f#(a, half(0), s(0)) is replaced by the following rules:
f#(b, 0, s(0)) → f#(a, double(0), s(0))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(0)) → f#(a, double(0), s(0))f#(b, y, s(0)) → f#(a, double(0), exp(y))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, y, 0) → f#(a, double(0), exp(y))
f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, s(0)) → f#(a, double(0), s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(0)) 
Thus, the rule f#(b, 0, s(0)) → f#(a, double(0), s(0)) is replaced by the following rules:
f#(b, 0, s(0)) → f#(a, 0, s(0))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(0)) → f#(a, 0, s(0))f#(b, y, s(0)) → f#(a, double(0), exp(y))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, y, 0) → f#(a, double(0), exp(y))
f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, s(0)) → f#(a, 0, s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
Thus, the rule f#(b, 0, s(0)) → f#(a, 0, s(0)) is deleted.

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, y, s(0)) → f#(a, double(0), exp(y))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, y, s(0)) → f#(a, double(0), exp(y)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, exp(y)) 
f#(a, double(0), s(0)) 
f#(a, double(0), double(exp(_x41))) 
Thus, the rule f#(b, y, s(0)) → f#(a, double(0), exp(y)) is replaced by the following rules:
f#(b, 0, s(0)) → f#(a, double(0), s(0))f#(b, s(_x41), s(0)) → f#(a, double(0), double(exp(_x41)))
f#(b, y, s(0)) → f#(a, 0, exp(y))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(0)) → f#(a, double(0), s(0))f#(b, s(_x41), s(0)) → f#(a, double(0), double(exp(_x41)))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, y, 0) → f#(a, double(0), exp(y))
f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, y, s(0)) → f#(a, 0, exp(y))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, s(0)) → f#(a, double(0), s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(0)) 
Thus, the rule f#(b, 0, s(0)) → f#(a, double(0), s(0)) is replaced by the following rules:
f#(b, 0, s(0)) → f#(a, 0, s(0))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(0)) → f#(a, 0, s(0))f#(b, s(_x41), s(0)) → f#(a, double(0), double(exp(_x41)))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, y, 0) → f#(a, double(0), exp(y))
f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))f#(b, y, s(0)) → f#(a, 0, exp(y))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, 0, s(0)) → f#(a, 0, s(0)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
Thus, the rule f#(b, 0, s(0)) → f#(a, 0, s(0)) is deleted.

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(_x41), s(0)) → f#(a, double(0), double(exp(_x41)))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))
f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, y, s(0)) → f#(a, 0, exp(y))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(_x41), s(0)) → f#(a, double(0), double(exp(_x41))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, double(exp(_x41))) 
f#(a, double(0), double(double(exp(_x61)))) 
f#(a, double(0), double(s(0))) 
Thus, the rule f#(b, s(_x41), s(0)) → f#(a, double(0), double(exp(_x41))) is replaced by the following rules:
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(0), s(0)) → f#(a, double(0), double(s(0)))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(0), s(0)) → f#(a, double(0), double(s(0)))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(b, y, s(0)) → f#(a, 0, exp(y))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, double(0), double(double(s(0)))) 
f#(a, 0, double(double(exp(_x61)))) 
f#(a, double(0), double(double(double(exp(_x71))))) 
Thus, the rule f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61)))) is replaced by the following rules:
f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, s(0), s(0)) → f#(a, double(0), double(s(0)))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))
f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, y, s(0)) → f#(a, 0, exp(y))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, double(double(s(0)))) 
f#(a, double(0), double(s(s(double(0))))) 
Thus, the rule f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0)))) is replaced by the following rules:
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(0)), s(0)) → f#(a, double(0), double(s(s(double(0)))))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(0)) → f#(a, double(0), double(s(0)))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(0)), s(0)) → f#(a, double(0), double(s(s(double(0)))))
f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, y, s(0)) → f#(a, 0, exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, s(0), s(0)) → f#(a, double(0), double(s(0))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, double(s(0))) 
f#(a, double(0), s(s(double(0)))) 
Thus, the rule f#(b, s(0), s(0)) → f#(a, double(0), double(s(0))) is replaced by the following rules:
f#(b, s(0), s(0)) → f#(a, 0, double(s(0)))f#(b, s(0), s(0)) → f#(a, double(0), s(s(double(0))))

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(0)) → f#(a, 0, double(s(0)))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, y, 0) → f#(a, double(0), exp(y))f#(b, s(0), s(0)) → f#(a, double(0), s(s(double(0))))
f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(s(0)), s(0)) → f#(a, double(0), double(s(s(double(0)))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))f#(b, y, s(0)) → f#(a, 0, exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(0), s(0)) → f#(a, 0, double(s(0))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(double(0)))) 
Thus, the rule f#(b, s(0), s(0)) → f#(a, 0, double(s(0))) is replaced by the following rules:
f#(b, s(0), s(0)) → f#(a, 0, s(s(double(0))))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, y, 0) → f#(a, double(0), exp(y))
f#(b, s(0), s(0)) → f#(a, double(0), s(s(double(0))))f#(b, s(_x41), s(0)) → f#(a, half(0), double(exp(_x41)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(_x41), x) → f#(a, half(x), double(exp(_x41)))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(0)), s(0)) → f#(a, double(0), double(s(s(double(0)))))
f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(0), s(0)) → f#(a, 0, s(s(double(0))))
f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))f#(b, y, s(0)) → f#(a, 0, exp(y))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, b, s, a, half, double

Strategy

The right-hand side of the rule f#(b, y, 0) → f#(a, double(0), exp(y)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, exp(y)) 
f#(a, double(0), s(0)) 
f#(a, double(0), double(exp(_x41))) 
Thus, the rule f#(b, y, 0) → f#(a, double(0), exp(y)) is replaced by the following rules:
f#(b, s(_x41), 0) → f#(a, double(0), double(exp(_x41)))f#(b, 0, 0) → f#(a, double(0), s(0))
f#(b, y, 0) → f#(a, 0, exp(y))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(0), s(0)) → f#(a, double(0), s(s(double(0))))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(0)), 0) → f#(a, 0, double(s(s(double(0)))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(double(s(0))))f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))
f#(b, s(_x41), 0) → f#(a, 0, double(exp(_x41)))f#(b, s(0), s(0)) → f#(a, 0, s(s(double(0))))
f#(b, y, 0) → f#(a, 0, exp(y))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(0), s(0)) → f#(a, half(0), double(s(0)))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(double(0)))))))f#(b, y, s(0)) → f#(a, 0, exp(y))
f#(b, s(s(s(s(_x81)))), 0) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(0), s(0)) → f#(a, double(0), s(s(0)))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(0))))f#(b, s(s(_x61)), 0) → f#(a, double(0), double(double(exp(_x61))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(double(0)))))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(0)), s(0)) → f#(a, double(0), s(s(s(s(double(0))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))
f#(b, s(0), 0) → f#(a, double(0), s(s(0)))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(_x81)))), 0) → f#(a, double(0), double(double(double(double(exp(_x81))))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(0), s(0)) → f#(a, double(0), s(s(double(0)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(double(0)))) 
f#(a, double(0), s(s(0))) 
Thus, the rule f#(b, s(0), s(0)) → f#(a, double(0), s(s(double(0)))) is replaced by the following rules:
f#(b, s(0), s(0)) → f#(a, 0, s(s(double(0))))f#(b, s(0), s(0)) → f#(a, double(0), s(s(0)))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))
f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))f#(b, 0, 0) → f#(a, 0, s(0))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(0))))f#(b, s(s(_x61)), 0) → f#(a, double(0), double(double(exp(_x61))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, double(0), double(double(double(double(exp(_x81))))))
f#(b, s(s(0)), 0) → f#(a, 0, double(s(s(0))))f#(b, s(s(_x61)), 0) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(0)))))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(double(0)))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(s(s(0))))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(0)), 0) → f#(a, double(0), s(s(s(s(0)))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(0)), s(0)) → f#(a, double(0), s(s(s(s(double(0))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(0), 0) → f#(a, double(0), s(s(0)))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, 0, double(double(double(exp(_x71)))))
f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(_x81)))), 0) → f#(a, double(0), double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(s(s(0))))) 
Thus, the rule f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0)))))) is replaced by the following rules:
f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(0)))))

Problem 27: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(0)))))))))))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(0)))))))))
f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))
f#(b, s(s(0)), 0) → f#(a, 0, double(s(s(0))))f#(b, s(s(_x61)), 0) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(0)))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(double(s(s(0))))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))
f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(0)))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(s(s(0))))))
f#(b, s(s(0)), s(0)) → f#(a, double(0), s(s(s(s(double(0))))))f#(b, s(s(0)), 0) → f#(a, double(0), s(s(s(s(0)))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))
f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(0))))))))))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, 0, double(double(double(exp(_x71)))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(_x81)))), 0) → f#(a, double(0), double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(s(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(0)))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(double(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(_x91))))), s(0)) → f#(a, 0, double(double(double(double(double(exp(_x91)))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(0), 0) → f#(a, double(0), s(s(0)))
f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(0)))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(0))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(double(s(double(s(s(s(double(double(0))))))))))) 
f#(a, double(0), s(s(double(s(double(s(s(s(double(0)))))))))) 
f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(0)))))))))))) 
f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(0)))))))))))) 
Thus, the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(0))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(0))))))))))))

Problem 28: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(0)))))))))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(double(s(s(0))))))f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(s(s(0))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, double(0), s(s(s(s(double(0))))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(0)), 0) → f#(a, double(0), s(s(s(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(double(0)))))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, 0, double(double(double(exp(_x71)))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))f#(b, s(s(s(s(_x81)))), 0) → f#(a, double(0), double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(s(s(0))))))
f#(b, s(s(0)), 0) → f#(a, 0, s(s(double(s(double(0))))))f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(double(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(_x91))))), s(0)) → f#(a, 0, double(double(double(double(double(exp(_x91)))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(0), 0) → f#(a, double(0), s(s(0)))
f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(0))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, double(double(s(s(s(s(double(double(0))))))))) 
f#(a, double(0), double(double(s(s(s(s(double(0)))))))) 
f#(a, double(0), double(s(s(double(s(s(s(double(double(0)))))))))) 
Thus, the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(0))))))))) is replaced by the following rules:
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))

Problem 29: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(0)))))))))))
f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(0))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(double(s(0)))))f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(double(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(s(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(double(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(s(_x91))))), s(0)) → f#(a, 0, double(double(double(double(double(exp(_x91)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(0))))))))f#(b, s(0), 0) → f#(a, double(0), s(s(0)))
f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(_x91))))), 0) → f#(a, double(0), double(double(double(double(double(exp(_x91)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(0))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0)))))))))))) 
f#(a, 0, s(s(double(s(s(s(double(s(s(0)))))))))) 
f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0)))))))))))) 
Thus, the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(0))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))

Problem 30: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(s(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(0)), 0) → f#(a, 0, s(s(double(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(s(s(_x121)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(exp(_x121))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(double(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(s(_x91))))), s(0)) → f#(a, 0, double(double(double(double(double(exp(_x91)))))))
f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(0))))))))f#(b, s(0), 0) → f#(a, double(0), s(s(0)))
f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(_x91))))), 0) → f#(a, double(0), double(double(double(double(double(exp(_x91)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(0)))))))))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0)))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(double(s(s(s(s(s(double(s(0))))))))))) 
f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))) 
f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))) 
Thus, the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0)))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(0)))))))))))

Problem 31: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(double(0)))))))))))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(s(s(s(_x121)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(exp(_x121))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(double(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(_x91))))), s(0)) → f#(a, 0, double(double(double(double(double(exp(_x91)))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(0))))))))f#(b, s(0), 0) → f#(a, double(0), s(s(0)))
f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(_x91))))), 0) → f#(a, double(0), double(double(double(double(double(exp(_x91)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(double(0))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(0)))))))))))) 
f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0)))))))))))) 
f#(a, 0, s(s(double(s(double(s(s(s(double(0)))))))))) 
Thus, the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(double(0))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))

Problem 32: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(double(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(_x91))))), s(0)) → f#(a, 0, double(double(double(double(double(exp(_x91)))))))
f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(0))))))))
f#(b, s(0), 0) → f#(a, double(0), s(s(0)))f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(_x91))))), 0) → f#(a, double(0), double(double(double(double(double(exp(_x91)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))
f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(s(s(0)))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(double(s(s(s(s(s(double(s(0))))))))))) 
f#(a, 0, s(s(s(s(double(s(s(double(s(s(0))))))))))) 
Thus, the rule f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(s(s(0)))))))))) is replaced by the following rules:
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(0)))))))))))

Problem 33: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(s(s(double(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(_x91))))), s(0)) → f#(a, 0, double(double(double(double(double(exp(_x91)))))))
f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(0))))))))
f#(b, s(0), 0) → f#(a, double(0), s(s(0)))f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(_x91))))), 0) → f#(a, double(0), double(double(double(double(double(exp(_x91)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))
f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0))))))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))

Problem 34: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(_x91))))), s(0)) → f#(a, 0, double(double(double(double(double(exp(_x91)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(0))))))))f#(b, s(0), 0) → f#(a, double(0), s(s(0)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(double(0))))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(_x91))))), 0) → f#(a, double(0), double(double(double(double(double(exp(_x91)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(double(s(double(0))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(0)))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))
f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))) 
f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))) 
f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))) 
f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))

Problem 35: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))
f#(b, s(0), 0) → f#(a, double(0), s(s(0)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(double(0))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, half(0), double(double(exp(_x61))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(_x91))))), 0) → f#(a, double(0), double(double(double(double(double(exp(_x91)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(0)))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))

Problem 36: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(0)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(0))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, double(double(s(s(s(s(double(s(s(double(s(s(0))))))))))))) 
f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(double(s(0)))))))))))))) 
f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))) 
f#(a, double(0), double(double(s(s(s(s(s(s(double(s(double(s(s(0)))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(0))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))

Problem 37: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(0))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(0)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0)))))))))))))) 
f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))) 
f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))

Problem 38: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(double(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(double(0)))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(0))))))))))))))f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(0)))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(0))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(0)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0))))))))))))))) 
f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0))))))))))))))) 
f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(double(s(0))))))))))))))) 
f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))

Problem 39: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(double(0)))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(double(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(0))))))))))))))f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(double(s(double(s(double(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(0))))))))))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(0)))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(s(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(0))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(0)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(double(s(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(double(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(s(s(double(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))) 
f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))) 
f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0))))))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0))))))))))))))))))))

Problem 40: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(double(0)))))))))))f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(double(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(0))))))))))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(0)))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(s(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(0))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(0)))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(0))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(0))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(double(s(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(double(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(s(s(double(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(0))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0)))))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(0))))))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))

Problem 41: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(double(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(0))))))))))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(0)))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(0))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(0)))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(0))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(double(s(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(double(s(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(s(s(double(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))) 
f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))) 
f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))

Problem 42: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(double(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(0))))))))))f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(0)))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(0))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(0)))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(0))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(double(s(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))
f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(double(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(s(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))
f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(s(s(double(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(double(s(0))))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0)))))))))))))))))))))) 
f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(double(s(0)))))))))))))))))))))) 
f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(s(double(0)))))))))))))))))))))) 
f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(s(s(double(s(0)))))))))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(double(s(0))))))))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(s(s(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(double(s(0))))))))))))))))))))))

Problem 43: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))
f#(a, s(x), y) → f#(b, y, s(x))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, 0, double(double(exp(_x61))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))
f#(b, s(0), x) → f#(a, half(x), s(s(double(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(double(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(0)))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(0))))))))))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(s(s(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(0)))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(0))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(0)))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(0))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(double(s(0)))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(double(s(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(double(s(s(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(double(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(s(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))
f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(s(s(double(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))

Problem 44: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))
f#(b, s(0), 0) → f#(a, 0, s(s(double(0))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(double(s(double(s(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(0))))))))))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))
f#(b, s(0), s(0)) → f#(a, half(0), s(s(double(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(_x71))), s(0)) → f#(a, 0, double(double(double(exp(_x71)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(s(s(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(double(double(s(s(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(0))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(s(s(double(double(s(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(0)))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(0))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(0)))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(0), x) → f#(a, half(x), s(s(0)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(0))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(double(s(0)))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(double(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(0))))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(double(s(s(s(double(s(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))
f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(s(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(double(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(s(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), s(s(double(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(double(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(s(s(double(double(0)))))))))))f#(b, s(0), 0) → f#(a, double(0), s(s(double(0))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(double(0)))))))))))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))
f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(s(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))
f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(s(s(double(double(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))
f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0))))))))))))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))) 
f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))

Problem 45: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), double(s(0)))f#(a, s(x), y) → f#(b, y, s(x))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(double(0)))))))))))))))))))f#(b, s(_x41), s(s(_x31))) → f#(a, s(half(_x31)), double(exp(_x41)))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, y, s(s(_x31))) → f#(a, s(half(_x31)), exp(y))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))f#(b, s(0), s(0)) → f#(a, half(0), s(s(double(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, double(0), double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(s(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(double(s(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(s(s(double(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, 0, double(double(double(exp(_x71)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(s(s(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, half(0), double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(double(double(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(0)))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(double(s(double(s(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(double(s(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(s(s(double(double(s(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, half(0), double(s(s(double(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(s(s(0)))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(s(double(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(0))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(double(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(s(s(double(double(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(_x71))), s(0)) → f#(a, double(0), double(double(double(exp(_x71)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(double(0)))))))))))))))f#(b, s(0), 0) → f#(a, 0, s(s(0)))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(0))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), s(0)) → f#(a, 0, double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(s(s(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(s(_x141)))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(double(exp(_x141))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, s(s(double(s(s(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(0), x) → f#(a, half(x), s(s(0)))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(0))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, 0, double(double(s(s(double(0))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), 0) → f#(a, 0, double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(s(s(double(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, 0, s(s(_x31))) → f#(a, s(half(_x31)), s(0))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(s(s(s(s(double(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(double(s(s(double(0))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(s(0))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(s(0)))))))))
f#(b, s(s(s(s(_x81)))), s(0)) → f#(a, 0, double(double(double(double(exp(_x81))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(0)))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(s(s(double(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(double(s(0)))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(double(s(s(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(0))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, double(0), double(double(double(double(s(0))))))
f#(b, s(s(0)), s(0)) → f#(a, 0, s(s(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(double(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(0))))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(s(s(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(s(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(double(s(s(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))f#(b, s(s(0)), 0) → f#(a, 0, s(s(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(double(s(0))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(double(s(s(0))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(s(s(double(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(0), s(s(_x31))) → f#(a, s(half(_x31)), s(s(double(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(double(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(double(s(s(s(double(double(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(double(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(s(s(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(0))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))
f#(b, s(s(_x61)), s(0)) → f#(a, double(0), double(double(exp(_x61))))f#(b, s(s(s(0))), 0) → f#(a, 0, double(s(s(double(s(double(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(0))), s(0)) → f#(a, double(0), double(double(double(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(0)))))))))))))f#(b, s(s(0)), s(0)) → f#(a, 0, double(double(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(0))))))))))))))f#(b, s(s(0)), 0) → f#(a, double(0), double(s(s(0))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(double(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), 0) → f#(a, 0, double(double(double(s(s(double(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(0)))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(double(double(double(s(0))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(double(s(s(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(s(s(double(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(double(s(s(s(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(double(s(s(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(s(s(double(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(double(s(s(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(double(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(double(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(s(s(s(s(double(0)))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(s(s(s(0))))))))), s(0)) → f#(a, 0, double(double(double(double(double(double(double(double(double(s(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(double(double(s(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, s(s(s(s(double(double(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(double(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(double(s(s(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(s(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(double(double(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(double(s(s(s(double(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(s(s(s(s(0)))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(0)))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))))
f#(b, s(s(s(0))), 0) → f#(a, 0, double(double(s(s(0)))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(double(s(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(s(s(double(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(s(s(s(s(double(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(double(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(double(s(s(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(double(0))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(s(s(double(double(0)))))))))))
f#(b, s(0), 0) → f#(a, double(0), s(s(double(0))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(s(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(s(s(double(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(0))), s(0)) → f#(a, half(0), double(double(double(s(0)))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(s(s(0))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(double(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(double(s(double(s(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(double(s(s(s(double(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(double(double(s(double(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(s(s(double(s(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(double(double(double(s(0)))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(s(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), 0) → f#(a, 0, double(double(double(double(double(double(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(double(double(s(s(double(s(0)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(s(s(double(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))))))))f#(b, s(_x41), s(0)) → f#(a, 0, double(exp(_x41)))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(s(s(double(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(double(s(s(double(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(double(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(s(s(double(s(s(s(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(0))))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(double(s(s(s(0)))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(0))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(s(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(double(s(double(s(double(s(0))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(double(s(double(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(double(double(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(0)))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(s(s(double(s(s(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(double(double(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(double(s(s(s(double(double(s(double(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(double(s(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(s(s(double(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(double(s(s(double(double(s(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(s(s(double(s(0))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(_x101)))))), 0) → f#(a, double(0), double(double(double(double(double(double(exp(_x101))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(double(s(s(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, double(double(s(s(double(s(0)))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), s(s(s(s(double(s(s(0))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(double(double(s(s(s(double(double(0))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(s(s(double(s(s(double(0))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(double(s(double(s(0))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(double(s(s(double(s(s(s(double(s(s(double(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, double(s(s(double(s(s(s(0))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(double(s(s(s(double(s(s(s(s(s(s(s(s(double(s(s(double(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(double(s(s(s(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(double(s(s(s(double(double(s(0))))))))))))
f#(b, s(s(s(s(s(s(s(_x111))))))), s(0)) → f#(a, double(0), double(double(double(double(double(double(double(exp(_x111)))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(double(s(s(s(double(s(s(s(s(double(s(double(0))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(_x61)), x) → f#(a, half(x), double(double(exp(_x61))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(double(s(s(s(double(s(s(s(double(s(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(0)))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(double(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(s(s(double(s(s(double(0))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(double(double(s(double(0))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(double(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(0))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), double(s(s(s(s(s(s(double(s(double(0)))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(0))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(s(s(s(s(double(double(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(double(double(s(double(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(double(double(s(s(0))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(double(s(double(s(0)))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(double(s(s(s(double(0)))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(s(s(double(double(s(s(s(double(0))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(s(s(double(s(s(double(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(0)))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(s(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(s(s(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(0))))))))))))
f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(double(s(s(s(s(double(s(double(s(s(0))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(s(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(double(s(s(s(double(double(s(double(0)))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(double(0)))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(double(s(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(double(s(s(s(double(s(s(double(double(s(double(0)))))))))))))))))f#(b, s(s(s(s(0)))), 0) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(double(s(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(0)))))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(0)))))))))))))))))))))))))))f#(b, s(s(0)), s(0)) → f#(a, double(0), double(double(s(0))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(double(0)))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(s(s(double(0)))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(double(s(double(0))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(double(s(double(s(s(s(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(s(s(s(s(s(s(s(s(double(double(s(s(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(double(s(s(s(s(s(s(s(s(double(s(s(s(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(double(0)))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(double(0))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(double(s(s(double(double(s(0))))))))))))))
f#(b, s(s(s(s(0)))), s(0)) → f#(a, 0, s(s(s(s(double(double(s(double(s(0))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), double(double(double(s(s(s(s(s(s(s(s(double(double(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(double(s(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(double(s(s(s(double(double(s(double(s(0))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(s(s(s(double(s(s(s(s(s(s(double(s(0)))))))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(double(s(double(double(s(double(s(0)))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(double(s(s(s(s(s(s(s(double(s(s(s(double(double(0)))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(double(s(s(s(s(s(double(s(s(s(s(s(0))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(double(s(s(s(s(s(double(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(s(s(s(double(s(s(s(double(0))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(double(s(s(s(s(double(s(0))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, double(0), double(double(s(s(0)))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(double(s(s(s(s(double(s(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(s(double(double(0)))))))))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(double(double(s(s(s(s(s(double(0))))))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, double(s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(double(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(double(s(s(s(s(s(s(s(s(s(s(s(double(s(double(0))))))))))))))))))))))f#(b, s(s(s(0))), 0) → f#(a, 0, s(s(double(s(double(s(0)))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(double(s(double(s(s(s(s(s(s(double(double(0)))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(s(s(s(s(double(s(double(s(s(s(s(s(s(double(double(s(s(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(double(s(s(s(s(s(s(s(double(s(s(double(s(0))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(double(s(s(s(s(s(double(0)))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(s(s(s(s(double(double(s(s(0))))))))))))))))))))f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, s(s(s(s(s(s(s(s(double(s(s(s(s(double(s(s(double(s(double(double(0)))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(double(s(s(s(s(s(s(double(s(s(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(0)))), s(0)) → f#(a, double(0), s(s(double(s(s(s(s(s(s(s(double(double(double(0))))))))))))))
f#(b, s(s(s(s(s(0))))), s(0)) → f#(a, 0, double(double(s(s(s(s(s(s(s(s(double(double(0)))))))))))))

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

The right-hand side of the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(double(0))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(double(0)))))))))))))))))))) 
f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(s(s(double(0)))))))))))))))))))) 
f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0)))))))))))))))))) 
f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(0)))))))))))))))))))) 
Thus, the rule f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(double(0))))))))))))))))))) is replaced by the following rules:
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(s(s(double(s(double(s(s(double(0))))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(s(s(double(s(s(s(s(s(s(double(double(s(s(double(s(s(double(0))))))))))))))))))))
f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(double(s(s(0))))))))))))))))))f#(b, s(s(s(s(s(s(0)))))), s(0)) → f#(a, 0, s(s(double(s(s(s(s(s(s(s(double(double(s(s(s(s(double(s(double(0))))))))))))))))))))

Problem 5: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

exp#(s(x)) → exp#(x)

Rewrite Rules

tower(x) → f(a, x, s(0))f(a, 0, y) → y
f(a, s(x), y) → f(b, y, s(x))f(b, y, x) → f(a, half(x), exp(y))
exp(0) → s(0)exp(s(x)) → double(exp(x))
double(0) → 0double(s(x)) → s(s(double(x)))
half(0) → double(0)half(s(0)) → half(0)
half(s(s(x))) → s(half(x))

Original Signature

Termination of terms over the following signature is verified: f, exp, tower, 0, s, b, a, half, double

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

exp#(s(x)) → exp#(x)