TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60005 ms.

The following DP Processors were used

Problem 1 was processed with processor DependencyGraph (210ms).
 | – Problem 2 was processed with processor SubtermCriterion (1ms).
 |    | – Problem 5 was processed with processor ReductionPairSAT (415ms).
 |    |    | – Problem 7 was processed with processor ReductionPairSAT (256ms).
 |    |    |    | – Problem 9 was processed with processor ReductionPairSAT (176ms).
 |    |    |    |    | – Problem 10 was processed with processor ReductionPairSAT (90ms).
 | – Problem 3 was processed with processor SubtermCriterion (1ms).
 | – Problem 4 was processed with processor ReductionPairSAT (3111ms).
 |    | – Problem 6 was processed with processor ReductionPairSAT (2793ms).
 |    |    | – Problem 8 was processed with processor ForwardNarrowing (8ms).
 |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (15ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (18ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (22ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (120ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (57ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 was processed with processor ForwardNarrowing (129ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 33 was processed with processor ForwardNarrowing (128ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 34 remains open; application of the following processors failed [ForwardNarrowing (45ms), ForwardNarrowing (49ms), ForwardNarrowing (39ms), ForwardNarrowing (46ms), ForwardNarrowing (46ms), ForwardNarrowing (44ms), ForwardNarrowing (50ms), ForwardNarrowing (45ms), ForwardNarrowing (38ms), ForwardNarrowing (45ms), ForwardNarrowing (50ms), ForwardNarrowing (44ms), ForwardNarrowing (45ms), ForwardNarrowing (44ms), ForwardNarrowing (39ms), ForwardNarrowing (51ms), ForwardNarrowing (45ms), ForwardNarrowing (38ms), ForwardNarrowing (45ms), ForwardNarrowing (timeout)].

The following open problems remain:

Open Dependency Pair Problem 8

Dependency Pairs

active^#(f(X))	→	mark^#(if(X, c, f(true)))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(f(X))	→	mark^#(X)	mark^#(if(X1, X2, X3))	→	active^#(if(mark(X1), mark(X2), X3))
mark^#(f(X))	→	active^#(f(mark(X)))	active^#(if(true, X, Y))	→	mark^#(X)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

mark^#(false)	→	active^#(false)	mark^#(true)	→	active^#(true)
active^#(if(false, X, Y))	→	mark^#(Y)	f^#(active(X))	→	f^#(X)
if^#(X1, active(X2), X3)	→	if^#(X1, X2, X3)	mark^#(f(X))	→	mark^#(X)
if^#(X1, X2, active(X3))	→	if^#(X1, X2, X3)	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(X1, X2, X3))	→	active^#(if(mark(X1), mark(X2), X3))	if^#(active(X1), X2, X3)	→	if^#(X1, X2, X3)
active^#(if(true, X, Y))	→	mark^#(X)	mark^#(c)	→	active^#(c)
active^#(f(X))	→	f^#(true)	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(X1, X2, X3))	→	mark^#(X2)	if^#(X1, mark(X2), X3)	→	if^#(X1, X2, X3)
if^#(X1, X2, mark(X3))	→	if^#(X1, X2, X3)	if^#(mark(X1), X2, X3)	→	if^#(X1, X2, X3)
mark^#(if(X1, X2, X3))	→	mark^#(X1)	active^#(f(X))	→	if^#(X, c, f(true))
mark^#(if(X1, X2, X3))	→	if^#(mark(X1), mark(X2), X3)	mark^#(f(X))	→	f^#(mark(X))
f^#(mark(X))	→	f^#(X)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The following SCCs where found

f^#(active(X)) → f^#(X)

f^#(mark(X)) → f^#(X)

if^#(X1, mark(X2), X3) → if^#(X1, X2, X3)	if^#(X1, X2, mark(X3)) → if^#(X1, X2, X3)
if^#(mark(X1), X2, X3) → if^#(X1, X2, X3)	if^#(X1, active(X2), X3) → if^#(X1, X2, X3)
if^#(X1, X2, active(X3)) → if^#(X1, X2, X3)	if^#(active(X1), X2, X3) → if^#(X1, X2, X3)

active^#(f(X)) → mark^#(if(X, c, f(true)))	mark^#(false) → active^#(false)
mark^#(if(X1, X2, X3)) → mark^#(X2)	active^#(if(false, X, Y)) → mark^#(Y)
mark^#(true) → active^#(true)	mark^#(if(X1, X2, X3)) → mark^#(X1)
mark^#(f(X)) → mark^#(X)	mark^#(f(X)) → active^#(f(mark(X)))
mark^#(if(X1, X2, X3)) → active^#(if(mark(X1), mark(X2), X3))	mark^#(c) → active^#(c)
active^#(if(true, X, Y)) → mark^#(X)

Problem 2: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

if^#(X1, mark(X2), X3)	→	if^#(X1, X2, X3)	if^#(X1, X2, mark(X3))	→	if^#(X1, X2, X3)
if^#(mark(X1), X2, X3)	→	if^#(X1, X2, X3)	if^#(X1, active(X2), X3)	→	if^#(X1, X2, X3)
if^#(X1, X2, active(X3))	→	if^#(X1, X2, X3)	if^#(active(X1), X2, X3)	→	if^#(X1, X2, X3)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

Projection

The following projection was used:

π (if#): 1

Thus, the following dependency pairs are removed:

if^#(mark(X1), X2, X3)

→

if^#(X1, X2, X3)

if^#(active(X1), X2, X3)

→

if^#(X1, X2, X3)

Problem 5: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

if^#(X1, mark(X2), X3)	→	if^#(X1, X2, X3)		if^#(X1, X2, mark(X3))	→	if^#(X1, X2, X3)
if^#(X1, active(X2), X3)	→	if^#(X1, X2, X3)		if^#(X1, X2, active(X3))	→	if^#(X1, X2, X3)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

Function Precedence

active < mark < f = c = if = false = true = if#

Argument Filtering

f: all arguments are removed from f
c: all arguments are removed from c
if: collapses to 3
false: all arguments are removed from false
true: all arguments are removed from true
active: collapses to 1
if#: collapses to 2
mark: 1

Status

f: multiset
c: multiset
false: multiset
true: multiset
mark: multiset

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

if^#(X1, mark(X2), X3) → if^#(X1, X2, X3)

Problem 7: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

if^#(X1, X2, mark(X3))	→	if^#(X1, X2, X3)		if^#(X1, active(X2), X3)	→	if^#(X1, X2, X3)
if^#(X1, X2, active(X3))	→	if^#(X1, X2, X3)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

Function Precedence

active = mark < f = c = if = false = true = if#

Argument Filtering

f: collapses to 1
c: all arguments are removed from c
if: 3
false: all arguments are removed from false
true: all arguments are removed from true
active: 1
if#: collapses to 2
mark: all arguments are removed from mark

Status

c: multiset
if: lexicographic with permutation 3 → 1
false: multiset
true: multiset
active: multiset
mark: multiset

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

if^#(X1, active(X2), X3) → if^#(X1, X2, X3)

Problem 9: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

if^#(X1, X2, mark(X3))

→

if^#(X1, X2, X3)

if^#(X1, X2, active(X3))

→

if^#(X1, X2, X3)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

Function Precedence

active = mark < f = c = if = false = true = if#

Argument Filtering

Status

f: multiset
c: multiset
if: multiset
false: multiset
true: multiset
if#: lexicographic with permutation 1 → 1 3 → 2
mark: multiset

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

if^#(X1, X2, mark(X3)) → if^#(X1, X2, X3)

Problem 10: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

if^#(X1, X2, active(X3))

→

if^#(X1, X2, X3)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

Function Precedence

active < f = c = if = false = true = if# = mark

Argument Filtering

f: all arguments are removed from f
c: all arguments are removed from c
if: 2 3
false: all arguments are removed from false
true: all arguments are removed from true
active: 1
if#: collapses to 3
mark: 1

Status

f: multiset
c: multiset
if: lexicographic with permutation 2 → 2 3 → 1
false: multiset
true: multiset
active: multiset
mark: lexicographic with permutation 1 → 1

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

if^#(X1, X2, active(X3)) → if^#(X1, X2, X3)

Problem 3: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

f^#(active(X))

→

f^#(X)

f^#(mark(X))

→

f^#(X)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

Projection

The following projection was used:

π (f#): 1

Thus, the following dependency pairs are removed:

f^#(active(X))

→

f^#(X)

f^#(mark(X))

→

f^#(X)

Problem 4: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

active^#(f(X))	→	mark^#(if(X, c, f(true)))	mark^#(false)	→	active^#(false)
mark^#(if(X1, X2, X3))	→	mark^#(X2)	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(true)	→	active^#(true)	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(f(X))	→	mark^#(X)	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(X1, X2, X3))	→	active^#(if(mark(X1), mark(X2), X3))	mark^#(c)	→	active^#(c)
active^#(if(true, X, Y))	→	mark^#(X)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

Function Precedence

f = if = active = mark = mark# < c = false = true = active#

Argument Filtering

f: all arguments are removed from f
c: all arguments are removed from c
if: all arguments are removed from if
false: all arguments are removed from false
true: all arguments are removed from true
active: collapses to 1
mark: all arguments are removed from mark
active#: collapses to 1
mark#: all arguments are removed from mark#

Status

f: multiset
c: multiset
if: multiset
false: multiset
true: multiset
mark: multiset
mark#: multiset

Usable Rules

if(X1, active(X2), X3) → if(X1, X2, X3)	if(mark(X1), X2, X3) → if(X1, X2, X3)
mark(if(X1, X2, X3)) → active(if(mark(X1), mark(X2), X3))	mark(c) → active(c)
active(if(false, X, Y)) → mark(Y)	if(active(X1), X2, X3) → if(X1, X2, X3)
mark(true) → active(true)	if(X1, mark(X2), X3) → if(X1, X2, X3)
if(X1, X2, active(X3)) → if(X1, X2, X3)	mark(false) → active(false)
if(X1, X2, mark(X3)) → if(X1, X2, X3)	f(active(X)) → f(X)
active(if(true, X, Y)) → mark(X)	mark(f(X)) → active(f(mark(X)))
f(mark(X)) → f(X)	active(f(X)) → mark(if(X, c, f(true)))

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

mark^#(true) → active^#(true)

mark^#(c) → active^#(c)

Problem 6: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

mark^#(false)	→	active^#(false)	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(X1, X2, X3))	→	mark^#(X2)	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(f(X))	→	mark^#(X)
mark^#(if(X1, X2, X3))	→	active^#(if(mark(X1), mark(X2), X3))	mark^#(f(X))	→	active^#(f(mark(X)))
active^#(if(true, X, Y))	→	mark^#(X)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

Function Precedence

c = active# < active = mark < true < f = if = false = mark#

Argument Filtering

f: all arguments are removed from f
c: all arguments are removed from c
if: all arguments are removed from if
false: all arguments are removed from false
true: all arguments are removed from true
active: all arguments are removed from active
mark: all arguments are removed from mark
active#: collapses to 1
mark#: all arguments are removed from mark#

Status

f: multiset
c: multiset
if: multiset
false: multiset
true: multiset
active: multiset
mark: multiset
mark#: multiset

Usable Rules

if(X1, active(X2), X3) → if(X1, X2, X3)	if(mark(X1), X2, X3) → if(X1, X2, X3)
mark(if(X1, X2, X3)) → active(if(mark(X1), mark(X2), X3))	mark(c) → active(c)
active(if(false, X, Y)) → mark(Y)	if(active(X1), X2, X3) → if(X1, X2, X3)
mark(true) → active(true)	if(X1, mark(X2), X3) → if(X1, X2, X3)
if(X1, X2, active(X3)) → if(X1, X2, X3)	mark(false) → active(false)
if(X1, X2, mark(X3)) → if(X1, X2, X3)	f(active(X)) → f(X)
active(if(true, X, Y)) → mark(X)	mark(f(X)) → active(f(mark(X)))
f(mark(X)) → f(X)	active(f(X)) → mark(if(X, c, f(true)))

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

mark^#(false) → active^#(false)

Problem 8: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

active^#(f(X))	→	mark^#(if(X, c, f(true)))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(f(X))	→	mark^#(X)	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(X1, X2, X3))	→	active^#(if(mark(X1), mark(X2), X3))	active^#(if(true, X, Y))	→	mark^#(X)

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(X1, X2, X3)) → active^#(if(mark(X1), mark(X2), X3)) 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 Terms	Irrelevant Terms
active^#(if(mark(X1), _x22, _x23))
active^#(if(active(true), mark(X2), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))
active^#(if(mark(X1), mark(X2), _x23))
active^#(if(active(f(mark(_x31))), mark(X2), X3))
active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
active^#(if(active(c), mark(X2), X3))
active^#(if(mark(X1), active(false), X3))
active^#(if(_x21, mark(X2), _x23))
active^#(if(mark(X1), active(true), X3))
active^#(if(mark(X1), active(f(mark(_x41))), X3))
active^#(if(active(false), mark(X2), X3))
active^#(if(mark(X1), active(c), X3))

Thus, the rule mark^#(if(X1, X2, X3)) → active^#(if(mark(X1), mark(X2), X3)) is replaced by the following rules:

mark^#(if(c, X2, X3)) → active^#(if(active(c), mark(X2), X3))	mark^#(if(_x21, X2, _x23)) → active^#(if(_x21, mark(X2), _x23))
mark^#(if(X1, c, X3)) → active^#(if(mark(X1), active(c), X3))	mark^#(if(X1, _x22, _x23)) → active^#(if(mark(X1), _x22, _x23))
mark^#(if(if(_x31, _x32, _x33), X2, X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(false, X2, X3)) → active^#(if(active(false), mark(X2), X3))
mark^#(if(X1, f(_x41), X3)) → active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(X1, true, X3)) → active^#(if(mark(X1), active(true), X3))
mark^#(if(f(_x31), X2, X3)) → active^#(if(active(f(mark(_x31))), mark(X2), X3))	mark^#(if(X1, if(_x41, _x42, _x43), X3)) → active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(X1, false, X3)) → active^#(if(mark(X1), active(false), X3))	mark^#(if(true, X2, X3)) → active^#(if(active(true), mark(X2), X3))
mark^#(if(X1, X2, active(_x23))) → active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(X1, X2, mark(_x23))) → active^#(if(mark(X1), mark(X2), _x23))

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, X2, X3))	→	active^#(if(active(c), mark(X2), X3))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(X1, c, X3))	→	active^#(if(mark(X1), active(c), X3))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))
mark^#(f(X))	→	active^#(f(mark(X)))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(X1, X2, X3))	→	mark^#(X2)	mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))
mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(c, X2, X3)) → active^#(if(active(c), mark(X2), X3)) 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 Terms	Irrelevant Terms
active^#(if(active(c), _x22, _x23))
active^#(if(active(c), mark(X2), _x23))
active^#(if(active(c), active(false), X3))
active^#(if(active(c), active(c), X3))
active^#(if(active(c), active(true), X3))
active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
active^#(if(c, mark(X2), _x23))
active^#(if(active(c), active(f(mark(_x41))), X3))

Thus, the rule mark^#(if(c, X2, X3)) → active^#(if(active(c), mark(X2), X3)) is replaced by the following rules:

mark^#(if(c, X2, _x23)) → active^#(if(c, mark(X2), _x23))	mark^#(if(c, X2, active(_x23))) → active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, false, X3)) → active^#(if(active(c), active(false), X3))	mark^#(if(c, c, X3)) → active^#(if(active(c), active(c), X3))
mark^#(if(c, X2, mark(_x23))) → active^#(if(active(c), mark(X2), _x23))	mark^#(if(c, if(_x41, _x42, _x43), X3)) → active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, true, X3)) → active^#(if(active(c), active(true), X3))	mark^#(if(c, f(_x41), X3)) → active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, _x22, _x23)) → active^#(if(active(c), _x22, _x23))

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, X2, active(_x23)))	→	active^#(if(active(c), mark(X2), _x23))	mark^#(if(c, X2, _x23))	→	active^#(if(c, mark(X2), _x23))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(X1, c, X3))	→	active^#(if(mark(X1), active(c), X3))	mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
active^#(if(true, X, Y))	→	mark^#(X)	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(X1, X2, X3))	→	mark^#(X2)	mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))
mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(f(X))	→	mark^#(X)
mark^#(f(X))	→	active^#(f(mark(X)))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(c, X2, _x23)) → active^#(if(c, mark(X2), _x23)) 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 Terms	Irrelevant Terms
active^#(if(c, active(f(mark(_x51))), _x23))
active^#(if(c, _x32, _x33))
active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
active^#(if(c, active(true), _x23))
active^#(if(c, active(false), _x23))
active^#(if(c, active(c), _x23))
active^#(if(c, mark(X2), _x33))

Thus, the rule mark^#(if(c, X2, _x23)) → active^#(if(c, mark(X2), _x23)) is replaced by the following rules:

mark^#(if(c, c, _x23)) → active^#(if(c, active(c), _x23))	mark^#(if(c, f(_x51), _x23)) → active^#(if(c, active(f(mark(_x51))), _x23))
mark^#(if(c, true, _x23)) → active^#(if(c, active(true), _x23))	mark^#(if(c, _x32, _x33)) → active^#(if(c, _x32, _x33))
mark^#(if(c, if(_x51, _x52, _x53), _x23)) → active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, X2, mark(_x33))) → active^#(if(c, mark(X2), _x33))
mark^#(if(c, X2, active(_x33))) → active^#(if(c, mark(X2), _x33))	mark^#(if(c, false, _x23)) → active^#(if(c, active(false), _x23))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, X2, active(_x23)))	→	active^#(if(active(c), mark(X2), _x23))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(c, _x32, _x33))	→	active^#(if(c, _x32, _x33))	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(X1, c, X3))	→	active^#(if(mark(X1), active(c), X3))	mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))	active^#(if(true, X, Y))	→	mark^#(X)
active^#(f(X))	→	mark^#(if(X, c, f(true)))	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(f(X))	→	mark^#(X)	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(c, X2, active(_x23))) → active^#(if(active(c), mark(X2), _x23)) 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 Terms	Irrelevant Terms
active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))
active^#(if(active(c), mark(X2), _x33))
active^#(if(active(c), active(c), _x23))
active^#(if(active(c), active(true), _x23))
active^#(if(active(c), active(f(mark(_x51))), _x23))
active^#(if(active(c), active(false), _x23))
active^#(if(active(c), _x32, _x33))
active^#(if(c, mark(X2), _x33))

Thus, the rule mark^#(if(c, X2, active(_x23))) → active^#(if(active(c), mark(X2), _x23)) is replaced by the following rules:

mark^#(if(c, X2, active(active(_x33)))) → active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, false, active(_x23))) → active^#(if(active(c), active(false), _x23))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23))) → active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, true, active(_x23))) → active^#(if(active(c), active(true), _x23))
mark^#(if(c, c, active(_x23))) → active^#(if(active(c), active(c), _x23))	mark^#(if(c, f(_x51), active(_x23))) → active^#(if(active(c), active(f(mark(_x51))), _x23))
mark^#(if(c, X2, active(mark(_x33)))) → active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, X2, active(_x33))) → active^#(if(c, mark(X2), _x33))
mark^#(if(c, _x32, active(_x33))) → active^#(if(active(c), _x32, _x33))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, _x32, _x33))	→	active^#(if(c, _x32, _x33))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(X1, c, X3))	→	active^#(if(mark(X1), active(c), X3))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), active(f(mark(_x51))), _x23))	mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
active^#(if(true, X, Y))	→	mark^#(X)	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(f(X))	→	mark^#(X)	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(c, _x32, _x33)) → active^#(if(c, _x32, _x33)) 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 Terms	Irrelevant Terms
active^#(if(c, _x22, _x23))

Thus, the rule mark^#(if(c, _x32, _x33)) → active^#(if(c, _x32, _x33)) is replaced by the following rules:

mark^#(if(c, mark(_x22), _x23)) → active^#(if(c, _x22, _x23))	mark^#(if(c, _x22, mark(_x23))) → active^#(if(c, _x22, _x23))
mark^#(if(c, _x22, active(_x23))) → active^#(if(c, _x22, _x23))	mark^#(if(c, active(_x22), _x23)) → active^#(if(c, _x22, _x23))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(X1, c, X3))	→	active^#(if(mark(X1), active(c), X3))	mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), active(f(mark(_x51))), _x23))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))
mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
active^#(if(true, X, Y))	→	mark^#(X)	mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))
active^#(f(X))	→	mark^#(if(X, c, f(true)))	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(f(X))	→	mark^#(X)
mark^#(f(X))	→	active^#(f(mark(X)))	mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))	mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(c, c, X3)) → active^#(if(active(c), active(c), X3)) 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 Terms	Irrelevant Terms
active^#(if(active(c), active(c), _x23))
active^#(if(active(c), c, _x23))
active^#(if(c, active(c), _x23))

Thus, the rule mark^#(if(c, c, X3)) → active^#(if(active(c), active(c), X3)) is replaced by the following rules:

mark^#(if(c, c, _x23)) → active^#(if(active(c), c, _x23))	mark^#(if(c, c, _x23)) → active^#(if(c, active(c), _x23))
mark^#(if(c, c, active(_x23))) → active^#(if(active(c), active(c), _x23))	mark^#(if(c, c, mark(_x23))) → active^#(if(active(c), active(c), _x23))

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(X1, c, X3))	→	active^#(if(mark(X1), active(c), X3))
mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), active(f(mark(_x51))), _x23))
mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))
mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))	active^#(if(true, X, Y))	→	mark^#(X)
active^#(f(X))	→	mark^#(if(X, c, f(true)))	mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))
mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(f(X))	→	mark^#(X)	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(X1, c, X3)) → active^#(if(mark(X1), active(c), X3)) 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 Terms	Irrelevant Terms
active^#(if(_x21, active(c), _x23))
active^#(if(active(f(mark(_x31))), active(c), X3))
active^#(if(active(c), active(c), X3))
active^#(if(mark(X1), c, _x23))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
active^#(if(active(true), active(c), X3))
active^#(if(mark(X1), active(c), _x23))
active^#(if(active(false), active(c), X3))

Thus, the rule mark^#(if(X1, c, X3)) → active^#(if(mark(X1), active(c), X3)) is replaced by the following rules:

mark^#(if(X1, c, mark(_x23))) → active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, c, X3)) → active^#(if(active(c), active(c), X3))
mark^#(if(false, c, X3)) → active^#(if(active(false), active(c), X3))	mark^#(if(X1, c, active(_x23))) → active^#(if(mark(X1), active(c), _x23))
mark^#(if(_x21, c, _x23)) → active^#(if(_x21, active(c), _x23))	mark^#(if(if(_x31, _x32, _x33), c, X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
mark^#(if(true, c, X3)) → active^#(if(active(true), active(c), X3))	mark^#(if(f(_x31), c, X3)) → active^#(if(active(f(mark(_x31))), active(c), X3))
mark^#(if(X1, c, _x23)) → active^#(if(mark(X1), c, _x23))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(false, c, X3))	→	active^#(if(active(false), active(c), X3))	mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), active(f(mark(_x51))), _x23))	mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))
mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))	mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))
active^#(f(X))	→	mark^#(if(X, c, f(true)))	mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))
mark^#(if(X1, X2, X3))	→	mark^#(X2)	mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))
mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))	mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))	mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(f(X))	→	mark^#(X)	mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
mark^#(f(X))	→	active^#(f(mark(X)))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(false, c, X3)) → active^#(if(active(false), active(c), X3)) 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 Terms	Irrelevant Terms
active^#(if(active(false), c, _x23))
active^#(if(active(false), active(c), _x23))
active^#(if(false, active(c), _x23))

Thus, the rule mark^#(if(false, c, X3)) → active^#(if(active(false), active(c), X3)) is replaced by the following rules:

mark^#(if(false, c, _x23)) → active^#(if(false, active(c), _x23))	mark^#(if(false, c, _x23)) → active^#(if(active(false), c, _x23))
mark^#(if(false, c, mark(_x23))) → active^#(if(active(false), active(c), _x23))	mark^#(if(false, c, active(_x23))) → active^#(if(active(false), active(c), _x23))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), active(f(mark(_x51))), _x23))
mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))
active^#(if(true, X, Y))	→	mark^#(X)	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))	mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))
mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))
mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))
mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))
mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(c, _x22, mark(_x23))) → active^#(if(c, _x22, _x23)) 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 Terms	Irrelevant Terms
active^#(if(c, _x32, _x33))

Thus, the rule mark^#(if(c, _x22, mark(_x23))) → active^#(if(c, _x22, _x23)) is replaced by the following rules:

mark^#(if(c, mark(_x32), mark(_x33))) → active^#(if(c, _x32, _x33))	mark^#(if(c, active(_x32), mark(_x33))) → active^#(if(c, _x32, _x33))
mark^#(if(c, _x32, mark(mark(_x33)))) → active^#(if(c, _x32, _x33))	mark^#(if(c, _x32, mark(active(_x33)))) → active^#(if(c, _x32, _x33))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, mark(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), active(f(mark(_x51))), _x23))
mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))
mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))
mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))
mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))
mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))	mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(c, mark(_x32), mark(_x33))) → active^#(if(c, _x32, _x33)) 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 Terms	Irrelevant Terms
active^#(if(c, _x22, _x23))

Thus, the rule mark^#(if(c, mark(_x32), mark(_x33))) → active^#(if(c, _x32, _x33)) is replaced by the following rules:

mark^#(if(c, mark(active(_x22)), mark(_x23))) → active^#(if(c, _x22, _x23))	mark^#(if(c, mark(_x22), mark(mark(_x23)))) → active^#(if(c, _x22, _x23))
mark^#(if(c, mark(_x22), mark(active(_x23)))) → active^#(if(c, _x22, _x23))	mark^#(if(c, mark(mark(_x22)), mark(_x23))) → active^#(if(c, _x22, _x23))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), active(f(mark(_x51))), _x23))	mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))
active^#(if(true, X, Y))	→	mark^#(X)	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))
mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))	mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))
mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))
mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))	mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(c, f(_x51), active(_x23))) → active^#(if(active(c), active(f(mark(_x51))), _x23)) 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 Terms	Irrelevant Terms
active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))
active^#(if(active(c), active(f(active(true))), _x23))
active^#(if(active(c), active(f(active(c))), _x23))
active^#(if(active(c), active(f(active(false))), _x23))
active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
active^#(if(c, active(f(mark(_x51))), _x33))
active^#(if(active(c), active(f(_x71)), _x23))
active^#(if(active(c), f(mark(_x51)), _x33))
active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
active^#(if(active(c), active(f(mark(_x51))), _x33))

Thus, the rule mark^#(if(c, f(_x51), active(_x23))) → active^#(if(active(c), active(f(mark(_x51))), _x23)) is replaced by the following rules:

mark^#(if(c, f(_x51), active(active(_x33)))) → active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, f(false), active(_x23))) → active^#(if(active(c), active(f(active(false))), _x23))
mark^#(if(c, f(_x71), active(_x23))) → active^#(if(active(c), active(f(_x71)), _x23))	mark^#(if(c, f(f(_x81)), active(_x23))) → active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
mark^#(if(c, f(c), active(_x23))) → active^#(if(active(c), active(f(active(c))), _x23))	mark^#(if(c, f(_x51), active(_x23))) → active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))
mark^#(if(c, f(_x51), active(_x33))) → active^#(if(active(c), f(mark(_x51)), _x33))	mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23))) → active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
mark^#(if(c, f(_x51), active(mark(_x33)))) → active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, f(true), active(_x23))) → active^#(if(active(c), active(f(active(true))), _x23))
mark^#(if(c, f(_x51), active(_x33))) → active^#(if(c, active(f(mark(_x51))), _x33))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(active(c), active(f(_x71)), _x23))	mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(active(c), f(mark(_x51)), _x33))
mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))	mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))
mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))
mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))	mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))	mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(c, f(_x71), active(_x23))) → active^#(if(active(c), active(f(_x71)), _x23)) 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 Terms	Irrelevant Terms
active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))
active^#(if(active(c), active(f(_x61)), _x23))
active^#(if(active(c), f(_x71), _x33))
active^#(if(c, active(f(_x71)), _x33))
active^#(if(active(c), active(f(_x71)), _x33))

Thus, the rule mark^#(if(c, f(_x71), active(_x23))) → active^#(if(active(c), active(f(_x71)), _x23)) is replaced by the following rules:

mark^#(if(c, f(active(_x61)), active(_x23))) → active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(c, f(_x71), active(_x33))) → active^#(if(active(c), f(_x71), _x33))
mark^#(if(c, f(mark(_x61)), active(_x23))) → active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(c, f(_x71), active(active(_x33)))) → active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(c, f(_x71), active(mark(_x33)))) → active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(c, f(_x51), active(_x23))) → active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))
mark^#(if(c, f(_x71), active(_x33))) → active^#(if(c, active(f(_x71)), _x33))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(active(c), f(mark(_x51)), _x33))	mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(active(c), f(_x71), _x33))
mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))	mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))	mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))	mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))
mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))	mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))	mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(f(X))	→	mark^#(X)	mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
mark^#(f(X))	→	active^#(f(mark(X)))	mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))	mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))	mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))
mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(c, f(_x51), active(_x33))) → active^#(if(active(c), f(mark(_x51)), _x33)) 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 Terms	Irrelevant Terms
active^#(if(active(c), f(active(c)), _x33))
active^#(if(c, f(mark(_x51)), _x23))
active^#(if(active(c), f(active(true)), _x33))
active^#(if(active(c), f(active(false)), _x33))
active^#(if(active(c), f(active(f(mark(_x61)))), _x33))
active^#(if(active(c), f(_x41), _x33))
active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x33))
active^#(if(active(c), f(mark(_x51)), _x23))

Thus, the rule mark^#(if(c, f(_x51), active(_x33))) → active^#(if(active(c), f(mark(_x51)), _x33)) is replaced by the following rules:

mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33))) → active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x33))	mark^#(if(c, f(true), active(_x33))) → active^#(if(active(c), f(active(true)), _x33))
mark^#(if(c, f(false), active(_x33))) → active^#(if(active(c), f(active(false)), _x33))	mark^#(if(c, f(_x51), active(_x23))) → active^#(if(c, f(mark(_x51)), _x23))
mark^#(if(c, f(f(_x61)), active(_x33))) → active^#(if(active(c), f(active(f(mark(_x61)))), _x33))	mark^#(if(c, f(c), active(_x33))) → active^#(if(active(c), f(active(c)), _x33))
mark^#(if(c, f(_x41), active(_x33))) → active^#(if(active(c), f(_x41), _x33))	mark^#(if(c, f(_x51), active(active(_x23)))) → active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(c, f(_x51), active(mark(_x23)))) → active^#(if(active(c), f(mark(_x51)), _x23))

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(active(c), f(_x71), _x33))	mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x33))	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))
mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))	mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))	mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))
mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))	mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))
mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))	mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))	mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(c, f(_x71), active(_x33))) → active^#(if(active(c), f(_x71), _x33)) 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 Terms	Irrelevant Terms
active^#(if(active(c), f(_x71), _x23))
active^#(if(active(c), f(_x41), _x33))
active^#(if(c, f(_x71), _x23))

Thus, the rule mark^#(if(c, f(_x71), active(_x33))) → active^#(if(active(c), f(_x71), _x33)) is replaced by the following rules:

mark^#(if(c, f(active(_x41)), active(_x33))) → active^#(if(active(c), f(_x41), _x33))	mark^#(if(c, f(_x71), active(active(_x23)))) → active^#(if(active(c), f(_x71), _x23))
mark^#(if(c, f(mark(_x41)), active(_x33))) → active^#(if(active(c), f(_x41), _x33))	mark^#(if(c, f(_x71), active(mark(_x23)))) → active^#(if(active(c), f(_x71), _x23))
mark^#(if(c, f(_x71), active(_x23))) → active^#(if(c, f(_x71), _x23))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(if(_x31, _x32, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x33))	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))
mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))	mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))
mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))	mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))	mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))
mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))	mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(f(X))	→	mark^#(X)	mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
mark^#(f(X))	→	active^#(f(mark(X)))	mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))	mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))
mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))	mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(if(_x31, _x32, _x33), X2, X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3)) 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 Terms	Irrelevant Terms
active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))
active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))
active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))
active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))
active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))
active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))
active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))
active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))
active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))
active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))

Thus, the rule mark^#(if(if(_x31, _x32, _x33), X2, X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), X3)) is replaced by the following rules:

mark^#(if(if(false, _x32, _x33), X2, X3)) → active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(_x31, c, _x33), X2, X3)) → active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))
mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3)) → active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3)) → active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))
mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(if(_x31, _x32, _x33), false, X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))
mark^#(if(if(_x31, false, _x33), X2, X3)) → active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), X3))	mark^#(if(if(_x31, _x52, _x53), X2, X3)) → active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))
mark^#(if(if(_x31, _x32, _x33), c, X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(if(if(_x31, _x32, _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(_x31, true, _x33), X2, X3)) → active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))
mark^#(if(if(_x31, f(_x71), _x33), X2, X3)) → active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))	mark^#(if(if(_x31, _x32, _x33), X2, _x23)) → active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))
mark^#(if(if(_x31, _x32, _x33), X2, active(_x23))) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(if(c, _x32, _x33), X2, X3)) → active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(_x31, _x32, active(_x53)), X2, X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(true, _x32, _x33), X2, X3)) → active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(_x51, _x32, _x53), X2, X3)) → active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(_x31, _x32, _x33), _x22, _x23)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))
mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23))) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(if(f(_x61), _x32, _x33), X2, X3)) → active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(_x31, _x32, _x33), true, X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(if(_x31, false, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), X3))	mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(if(_x31, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x33))
mark^#(if(if(_x31, true, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))	mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))
mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))	mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))
mark^#(if(if(_x31, _x32, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))	mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))
mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))	mark^#(if(if(_x31, _x32, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))
mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))	mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X2)	mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))
mark^#(if(if(_x31, f(_x71), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))	mark^#(if(if(_x31, _x32, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))
mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))
mark^#(if(if(false, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))	mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))
mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(if(f(_x61), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))
mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))
mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
active^#(if(true, X, Y))	→	mark^#(X)	mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(if(_x31, c, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))
mark^#(if(if(_x31, _x32, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(if(c, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(_x31, _x32, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(if(_x51, _x32, _x53), X2, X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))
mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(_x31, _x52, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))	mark^#(f(X))	→	mark^#(X)
mark^#(f(X))	→	active^#(f(mark(X)))	mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))
mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))	mark^#(if(if(true, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(if(_x31, _x32, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))
mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(if(_x31, false, _x33), X2, X3)) → active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), X3)) 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 Terms	Irrelevant Terms
active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))
active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))
active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))
active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))
active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))
active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))
active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))
active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))
active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))
active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))
active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))
active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))
active^#(if(active(if(active(true), active(false), _x33)), mark(X2), X3))
active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), X3))

Thus, the rule mark^#(if(if(_x31, false, _x33), X2, X3)) → active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), X3)) is replaced by the following rules:

mark^#(if(if(_x31, false, _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, false, _x33), c, X3)) → active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))
mark^#(if(if(_x31, false, mark(_x53)), X2, X3)) → active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(if(_x31, false, _x53), X2, X3)) → active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), true, X3)) → active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))	mark^#(if(if(c, false, _x33), X2, X3)) → active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), X2, _x23)) → active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))	mark^#(if(if(_x31, false, _x33), X2, mark(_x23))) → active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))
mark^#(if(if(true, false, _x33), X2, X3)) → active^#(if(active(if(active(true), active(false), _x33)), mark(X2), X3))	mark^#(if(if(_x31, false, _x33), if(_x41, _x42, _x43), X3)) → active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(if(_x61, _x62, _x63), false, _x33), X2, X3)) → active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))	mark^#(if(if(_x31, false, active(_x53)), X2, X3)) → active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))
mark^#(if(if(f(_x61), false, _x33), X2, X3)) → active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))	mark^#(if(if(false, false, _x33), X2, X3)) → active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), _x22, _x23)) → active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))	mark^#(if(if(_x51, false, _x53), X2, X3)) → active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), false, X3)) → active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))	mark^#(if(if(_x31, false, _x33), X2, active(_x23))) → active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(if(_x31, false, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), X3))	mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(if(_x31, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(true, false, _x33), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), X3))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x33))	mark^#(if(if(_x31, true, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))
mark^#(if(if(_x31, false, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))
mark^#(if(if(_x31, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))
mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(if(_x31, _x32, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))	mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))
mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))	mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))
mark^#(if(if(_x31, _x32, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))	mark^#(if(if(_x31, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(if(_x31, f(_x71), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))	mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))
mark^#(if(X1, X2, X3))	→	mark^#(X2)	mark^#(if(if(false, false, _x33), X2, X3))	→	active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))
mark^#(if(if(_x31, _x32, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(_x31, false, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))
mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))
mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))
mark^#(if(if(false, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(if(_x31, false, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))	mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))	mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))	mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))
mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(if(f(_x61), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))	mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))	mark^#(if(if(c, false, _x33), X2, X3))	→	active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))
mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
active^#(if(true, X, Y))	→	mark^#(X)	mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(if(if(_x61, _x62, _x63), false, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(if(_x31, false, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(if(_x31, c, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))
mark^#(if(if(_x31, _x32, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(if(_x31, false, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))
mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))
active^#(f(X))	→	mark^#(if(X, c, f(true)))	mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))
mark^#(if(if(_x31, _x32, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(if(c, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(_x51, false, _x53), X2, X3))	→	active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))	mark^#(if(if(_x51, _x32, _x53), X2, X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))
mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(_x31, false, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(if(_x31, _x52, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))
mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, false, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))
mark^#(if(if(_x31, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))
mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(f(_x61), false, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))	mark^#(if(if(true, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(if(_x31, _x32, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))	mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(if(_x31, false, _x53), X2, X3)) → active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), X3)) 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 Terms	Irrelevant Terms
active^#(if(active(if(active(f(mark(_x71))), false, _x53)), mark(X2), X3))
active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), false, _x53)), mark(X2), X3))
active^#(if(active(if(active(c), false, _x53)), mark(X2), X3))
active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))
active^#(if(active(if(_x61, false, _x63)), mark(X2), X3))
active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
active^#(if(active(if(mark(_x31), false, _x53)), active(c), X3))
active^#(if(active(if(active(true), false, _x53)), mark(X2), X3))
active^#(if(active(if(mark(_x31), false, _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), false, _x53)), _x22, _x23))
active^#(if(active(if(mark(_x31), false, _x53)), active(true), X3))
active^#(if(active(if(active(false), false, _x53)), mark(X2), X3))
active^#(if(active(if(mark(_x31), false, _x53)), active(if(mark(_x41), mark(_x42), _x43)), X3))
active^#(if(active(if(mark(_x31), false, _x53)), active(false), X3))
active^#(if(if(mark(_x31), false, _x53), mark(X2), _x23))

Thus, the rule mark^#(if(if(_x31, false, _x53), X2, X3)) → active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), X3)) is replaced by the following rules:

mark^#(if(if(_x31, false, _x53), X2, _x23)) → active^#(if(if(mark(_x31), false, _x53), mark(X2), _x23))	mark^#(if(if(_x31, false, _x53), if(_x41, _x42, _x43), X3)) → active^#(if(active(if(mark(_x31), false, _x53)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(_x31, false, _x53), _x22, _x23)) → active^#(if(active(if(mark(_x31), false, _x53)), _x22, _x23))	mark^#(if(if(_x31, false, _x53), c, X3)) → active^#(if(active(if(mark(_x31), false, _x53)), active(c), X3))
mark^#(if(if(if(_x71, _x72, _x73), false, _x53), X2, X3)) → active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), false, _x53)), mark(X2), X3))	mark^#(if(if(_x31, false, active(_x63)), X2, X3)) → active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))
mark^#(if(if(_x31, false, _x53), false, X3)) → active^#(if(active(if(mark(_x31), false, _x53)), active(false), X3))	mark^#(if(if(f(_x71), false, _x53), X2, X3)) → active^#(if(active(if(active(f(mark(_x71))), false, _x53)), mark(X2), X3))
mark^#(if(if(false, false, _x53), X2, X3)) → active^#(if(active(if(active(false), false, _x53)), mark(X2), X3))	mark^#(if(if(_x61, false, _x63), X2, X3)) → active^#(if(active(if(_x61, false, _x63)), mark(X2), X3))
mark^#(if(if(_x31, false, mark(_x63)), X2, X3)) → active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(if(true, false, _x53), X2, X3)) → active^#(if(active(if(active(true), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, _x53), X2, active(_x23))) → active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))	mark^#(if(if(c, false, _x53), X2, X3)) → active^#(if(active(if(active(c), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, _x53), X2, mark(_x23))) → active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))	mark^#(if(if(_x31, false, _x53), true, X3)) → active^#(if(active(if(mark(_x31), false, _x53)), active(true), X3))
mark^#(if(if(_x31, false, _x53), f(_x41), X3)) → active^#(if(active(if(mark(_x31), false, _x53)), active(f(mark(_x41))), X3))

Problem 27: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(c, X2, mark(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(if(_x31, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(true, false, _x33), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), X3))	mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x33))
mark^#(if(if(_x31, true, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))	mark^#(if(if(_x31, false, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))
mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))	mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))
mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))	mark^#(if(if(_x31, false, _x53), _x22, _x23))	→	active^#(if(active(if(mark(_x31), false, _x53)), _x22, _x23))
mark^#(if(if(_x31, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, false, _x53), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))	mark^#(if(if(_x31, false, _x53), true, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(true), X3))
mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))	mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))
mark^#(if(if(_x31, _x32, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))
mark^#(if(if(_x31, _x32, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))	mark^#(if(if(f(_x71), false, _x53), X2, X3))	→	active^#(if(active(if(active(f(mark(_x71))), false, _x53)), mark(X2), X3))
mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(if(_x61, false, _x63), X2, X3))	→	active^#(if(active(if(_x61, false, _x63)), mark(X2), X3))	mark^#(if(if(_x31, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))	mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))
mark^#(if(if(_x31, false, mark(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(active(true), false, _x53)), mark(X2), X3))
mark^#(if(X1, X2, X3))	→	mark^#(X2)	mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))
mark^#(if(if(_x31, f(_x71), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))	mark^#(if(if(false, false, _x33), X2, X3))	→	active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))	mark^#(if(if(_x31, _x32, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))
mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))
mark^#(if(if(false, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(if(_x31, false, _x53), c, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(c), X3))	mark^#(if(if(_x31, false, active(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))	mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))	mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))	mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))
mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(if(f(_x61), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))	mark^#(if(if(_x31, false, _x53), X2, _x23))	→	active^#(if(if(mark(_x31), false, _x53), mark(X2), _x23))
mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(if(_x71, _x72, _x73), false, _x53), X2, X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))	mark^#(if(if(false, false, _x53), X2, X3))	→	active^#(if(active(if(active(false), false, _x53)), mark(X2), X3))
mark^#(if(if(c, false, _x33), X2, X3))	→	active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))	mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(if(if(_x61, _x62, _x63), false, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(if(_x31, false, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))
mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))	mark^#(if(if(_x31, false, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(f(mark(_x41))), X3))
mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(if(_x31, c, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(if(if(_x31, false, _x53), false, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(false), X3))
mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))
mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))	mark^#(if(if(c, false, _x53), X2, X3))	→	active^#(if(active(if(active(c), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, _x53), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))	mark^#(if(if(_x31, _x32, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))	mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(if(_x31, false, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))
mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(if(_x51, false, _x53), X2, X3))	→	active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))
mark^#(if(if(c, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(_x31, _x32, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))
mark^#(if(if(_x51, _x32, _x53), X2, X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(_x31, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))
mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, false, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))	mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))
mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))
mark^#(if(if(_x31, false, _x53), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(_x31, _x52, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))	mark^#(if(if(_x31, false, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))
mark^#(f(X))	→	mark^#(X)	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(if(_x31, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))
mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(f(_x61), false, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))
mark^#(if(if(true, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(if(_x31, _x32, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))	mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(c, X2, mark(_x33))) → active^#(if(c, mark(X2), _x33)) 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 Terms	Irrelevant Terms
active^#(if(c, active(true), _x33))
active^#(if(c, active(if(mark(_x41), mark(_x42), _x43)), _x33))
active^#(if(c, active(f(mark(_x41))), _x33))
active^#(if(c, active(c), _x33))
active^#(if(c, mark(X2), _x23))
active^#(if(c, active(false), _x33))
active^#(if(c, _x22, _x23))

Thus, the rule mark^#(if(c, X2, mark(_x33))) → active^#(if(c, mark(X2), _x33)) is replaced by the following rules:

mark^#(if(c, true, mark(_x33))) → active^#(if(c, active(true), _x33))	mark^#(if(c, c, mark(_x33))) → active^#(if(c, active(c), _x33))
mark^#(if(c, X2, mark(mark(_x23)))) → active^#(if(c, mark(X2), _x23))	mark^#(if(c, f(_x41), mark(_x33))) → active^#(if(c, active(f(mark(_x41))), _x33))
mark^#(if(c, false, mark(_x33))) → active^#(if(c, active(false), _x33))	mark^#(if(c, if(_x41, _x42, _x43), mark(_x33))) → active^#(if(c, active(if(mark(_x41), mark(_x42), _x43)), _x33))
mark^#(if(c, _x22, mark(_x23))) → active^#(if(c, _x22, _x23))	mark^#(if(c, X2, mark(active(_x23)))) → active^#(if(c, mark(X2), _x23))

Problem 28: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(if(_x31, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(true, false, _x33), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), X3))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x33))	mark^#(if(if(_x31, true, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))
mark^#(if(if(_x31, false, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))
mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))	mark^#(if(c, false, mark(_x33)))	→	active^#(if(c, active(false), _x33))
mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))	mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))
mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))	mark^#(if(if(_x31, false, _x53), _x22, _x23))	→	active^#(if(active(if(mark(_x31), false, _x53)), _x22, _x23))
mark^#(if(if(_x31, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, false, _x53), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))	mark^#(if(if(_x31, false, _x53), true, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(true), X3))
mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(if(_x31, _x32, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))	mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))
mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, X2, mark(mark(_x23))))	→	active^#(if(c, mark(X2), _x23))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))
mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))	mark^#(if(if(f(_x71), false, _x53), X2, X3))	→	active^#(if(active(if(active(f(mark(_x71))), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, _x32, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))	mark^#(if(if(_x61, false, _x63), X2, X3))	→	active^#(if(active(if(_x61, false, _x63)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(active(true), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, mark(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))
mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))	mark^#(if(if(_x31, f(_x71), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(if(false, false, _x33), X2, X3))	→	active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))	mark^#(if(if(_x31, _x32, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))	mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))	mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))	mark^#(if(if(false, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(if(_x31, false, _x53), c, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(c), X3))
mark^#(if(if(_x31, false, active(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(if(_x31, false, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))	mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))
mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(if(f(_x61), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))
mark^#(if(c, true, mark(_x33)))	→	active^#(if(c, active(true), _x33))	mark^#(if(if(_x31, false, _x53), X2, _x23))	→	active^#(if(if(mark(_x31), false, _x53), mark(X2), _x23))
mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(if(_x71, _x72, _x73), false, _x53), X2, X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))	mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(false, false, _x53), X2, X3))	→	active^#(if(active(if(active(false), false, _x53)), mark(X2), X3))	mark^#(if(if(c, false, _x33), X2, X3))	→	active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))
mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
active^#(if(true, X, Y))	→	mark^#(X)	mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(if(if(_x61, _x62, _x63), false, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(if(_x31, false, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(if(_x31, false, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(f(mark(_x41))), X3))	mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(if(_x31, c, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))	mark^#(if(c, f(_x41), mark(_x33)))	→	active^#(if(c, active(f(mark(_x41))), _x33))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(if(if(_x31, false, _x53), false, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(false), X3))
mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))
mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))	mark^#(if(if(_x31, false, _x53), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(if(c, false, _x53), X2, X3))	→	active^#(if(active(if(active(c), false, _x53)), mark(X2), X3))	mark^#(if(if(_x31, _x32, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))
mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))	mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))
mark^#(if(if(_x31, false, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(if(_x31, _x32, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))
mark^#(if(if(c, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(_x51, false, _x53), X2, X3))	→	active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))
mark^#(if(if(_x51, _x32, _x53), X2, X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))	mark^#(if(c, if(_x41, _x42, _x43), mark(_x33)))	→	active^#(if(c, active(if(mark(_x41), mark(_x42), _x43)), _x33))
mark^#(if(if(_x31, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))
mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(_x31, false, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(if(_x31, false, _x53), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))
mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))	mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(if(_x31, _x52, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))	mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(f(X))	→	mark^#(X)	mark^#(if(if(_x31, false, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))
mark^#(f(X))	→	active^#(f(mark(X)))	mark^#(if(c, X2, mark(active(_x23))))	→	active^#(if(c, mark(X2), _x23))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))
mark^#(if(if(_x31, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))
mark^#(if(c, c, mark(_x33)))	→	active^#(if(c, active(c), _x33))	mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(if(f(_x61), false, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))
mark^#(if(if(true, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(if(_x31, _x32, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))
mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(if(_x31, _x32, _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), X3)) 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 Terms	Irrelevant Terms
active^#(if(active(if(active(c), mark(_x32), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))
active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(active(false), mark(_x32), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(active(true), mark(_x32), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), _x52, _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(if(mark(_x41), c, f(true))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(false))), X3))
active^#(if(if(mark(_x31), mark(_x32), _x33), active(f(mark(_x41))), _x23))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), f(mark(_x41)), _x23))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(true))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(_x61)), X3))
active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), active(true), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(c))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(f(mark(_x71))))), X3))
active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), active(c), _x33)), active(f(mark(_x41))), X3))

Thus, the rule mark^#(if(if(_x31, _x32, _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), X3)) is replaced by the following rules:

mark^#(if(if(_x31, c, _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(c), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, true, _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(true), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x52, _x53), f(_x41), X3)) → active^#(if(active(if(mark(_x31), _x52, _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(if(mark(_x41), c, f(true))), X3))	mark^#(if(if(_x31, _x32, _x33), f(false), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(false))), X3))
mark^#(if(if(true, _x32, _x33), f(_x41), X3)) → active^#(if(active(if(active(true), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(_x51, _x32, _x53), f(_x41), X3)) → active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), mark(_x23))) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23)) → active^#(if(if(mark(_x31), mark(_x32), _x33), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, f(_x71), _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, false, _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), f(mark(_x41)), _x23))	mark^#(if(if(_x31, _x32, _x33), f(c), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(c))), X3))
mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), f(_x41), X3)) → active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(false, _x32, _x33), f(_x41), X3)) → active^#(if(active(if(active(false), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, _x33), f(f(_x71)), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(c, _x32, _x33), f(_x41), X3)) → active^#(if(active(if(active(c), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x61), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(_x61)), X3))	mark^#(if(if(_x31, _x32, _x33), f(true), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(true))), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), active(_x23))) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, _x33), f(if(_x71, _x72, _x73)), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))
mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(f(_x61), _x32, _x33), f(_x41), X3)) → active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, mark(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3))

Problem 29: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(true, false, _x33), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), X3))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x33))	mark^#(if(if(_x31, true, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))
mark^#(if(if(_x31, _x32, _x33), f(false), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(false))), X3))	mark^#(if(if(_x31, false, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))
mark^#(if(f(_x31), X2, X3))	→	active^#(if(active(f(mark(_x31))), mark(X2), X3))	mark^#(if(c, false, X3))	→	active^#(if(active(c), active(false), X3))
mark^#(if(c, false, mark(_x33)))	→	active^#(if(c, active(false), _x33))	mark^#(if(true, X2, X3))	→	active^#(if(active(true), mark(X2), X3))
mark^#(if(if(_x51, _x32, _x53), f(_x41), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))
mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))	mark^#(if(if(_x31, false, _x53), _x22, _x23))	→	active^#(if(active(if(mark(_x31), false, _x53)), _x22, _x23))
mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))
mark^#(if(if(_x31, _x32, _x33), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, false, _x53), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(if(c, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))
mark^#(if(if(_x31, false, _x53), true, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(true), X3))	mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), active(f(mark(_x41))), X3))
mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))	mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))
mark^#(if(if(_x31, _x32, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, X2, mark(mark(_x23))))	→	active^#(if(c, mark(X2), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))	mark^#(if(if(_x31, _x32, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))
mark^#(if(if(f(_x71), false, _x53), X2, X3))	→	active^#(if(active(if(active(f(mark(_x71))), false, _x53)), mark(X2), X3))	mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))
mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))	mark^#(if(if(_x61, false, _x63), X2, X3))	→	active^#(if(active(if(_x61, false, _x63)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(if(_x31, false, mark(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))
mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(active(true), false, _x53)), mark(X2), X3))	mark^#(if(if(_x31, f(_x71), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(if(true, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(false, false, _x33), X2, X3))	→	active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))
mark^#(if(if(_x31, _x32, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(_x31, false, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))
mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))
mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), active(f(mark(_x41))), _x23))
mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))	mark^#(if(if(false, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(if(_x31, _x32, _x33), f(c), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(c))), X3))
mark^#(if(if(_x31, false, _x53), c, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(c), X3))	mark^#(if(if(_x31, false, active(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))
mark^#(if(if(_x31, false, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))	mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))	mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))	mark^#(if(if(_x31, _x32, _x33), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))	mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))
mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(if(f(_x61), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))
mark^#(if(c, true, mark(_x33)))	→	active^#(if(c, active(true), _x33))	mark^#(if(if(_x31, false, _x53), X2, _x23))	→	active^#(if(if(mark(_x31), false, _x53), mark(X2), _x23))
mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(if(_x71, _x72, _x73), false, _x53), X2, X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))	mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(if(mark(_x41), c, f(true))), X3))	mark^#(if(if(false, false, _x53), X2, X3))	→	active^#(if(active(if(active(false), false, _x53)), mark(X2), X3))
mark^#(if(if(c, false, _x33), X2, X3))	→	active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))	mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(if(if(_x61, _x62, _x63), false, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(if(_x31, false, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))	mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(if(_x31, false, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, _x33), f(_x41), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, c, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))	mark^#(if(c, f(_x41), mark(_x33)))	→	active^#(if(c, active(f(mark(_x41))), _x33))
mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), f(mark(_x41)), _x23))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(if(if(_x31, false, _x53), false, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(false), X3))	mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(if(false, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))
mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))	mark^#(if(if(c, false, _x53), X2, X3))	→	active^#(if(active(if(active(c), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, _x53), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))	mark^#(if(if(_x31, _x32, _x33), f(_x61), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(_x61)), X3))
mark^#(if(if(_x31, _x32, _x33), f(if(_x71, _x72, _x73)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))	mark^#(if(if(_x31, _x32, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))	mark^#(if(if(_x31, _x32, mark(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(if(_x31, c, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), active(f(mark(_x41))), X3))
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(if(_x31, false, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))
mark^#(if(if(_x31, true, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x52, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(if(_x51, false, _x53), X2, X3))	→	active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))
mark^#(if(if(c, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(_x31, _x32, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))
mark^#(if(if(_x51, _x32, _x53), X2, X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))	mark^#(if(c, if(_x41, _x42, _x43), mark(_x33)))	→	active^#(if(c, active(if(mark(_x41), mark(_x42), _x43)), _x33))
mark^#(if(if(_x31, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))
mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(_x31, f(_x71), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, false, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))	mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))
mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))
mark^#(if(if(_x31, false, _x53), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(_x31, _x52, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))	mark^#(if(if(_x31, false, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))
mark^#(f(X))	→	mark^#(X)	mark^#(if(c, X2, mark(active(_x23))))	→	active^#(if(c, mark(X2), _x23))
mark^#(f(X))	→	active^#(f(mark(X)))	mark^#(if(if(_x31, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))
mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))	mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))	mark^#(if(c, c, mark(_x33)))	→	active^#(if(c, active(c), _x33))
mark^#(if(if(_x31, _x32, _x33), f(true), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(true))), X3))	mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(f(_x61), false, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))	mark^#(if(if(true, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(if(_x31, _x32, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))
mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))	mark^#(if(if(f(_x61), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), active(f(mark(_x41))), X3))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, false, active, true, mark

Strategy

The right-hand side of the rule mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3)) 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 Terms	Irrelevant Terms
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x23))
active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x23))
active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), X3))
active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), X3))
active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), X3))
active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(_x41))), X3))
active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x61)), X3))
active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))
active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(_x41))), X3))
active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(_x41))), X3))

Thus, the rule mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3)) is replaced by the following rules:

mark^#(if(if(_x31, false, active(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23)) → active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, true, active(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x23))
mark^#(if(if(false, _x32, active(_x53)), f(_x41), X3)) → active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(true, _x32, active(_x53)), f(_x41), X3)) → active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(c, _x32, active(_x53)), f(_x41), X3)) → active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(_x41), X3)) → active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x23))) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(false), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), X3))	mark^#(if(if(_x31, _x62, active(_x63)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(_x41))), X3))
mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(_x41), X3)) → active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, c, active(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), mark(_x23))) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(c), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x61), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x61)), X3))	mark^#(if(if(_x31, _x32, active(active(_x63))), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(mark(_x63))), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(if(_x71, _x72, _x73)), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))	mark^#(if(if(f(_x71), _x32, active(_x53)), f(_x41), X3)) → active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), X3))	mark^#(if(if(_x31, f(_x81), active(_x53)), f(_x41), X3)) → active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(true), X3)) → active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), X3))

Problem 30: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(active(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(_x31, if(true, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x71, _x32, active(mark(_x73))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(c, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(mark(f(_x41)))), f(f(_x71)), X3))	→	active^#(if(active(f(mark(_x41))), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
mark^#(if(if(mark(_x71), true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x81), _x82, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, _x82, _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(true, false, _x33), c, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(c), X3))	mark^#(if(true, if(if(_x71, _x72, _x73), _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x42), _x43)), X3))
mark^#(if(true, if(false, if(_x71, _x72, _x73), _x43), _x23))	→	active^#(if(active(true), if(active(false), active(if(mark(_x71), mark(_x72), _x73)), _x43), _x23))	mark^#(if(true, if(c, _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(c), mark(_x42), _x43)), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), mark(if(active(f(mark(_x71))), c, f(true))), X3))	mark^#(if(if(_x31, true, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(true, if(_x41, _x42, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x43)), _x23))	mark^#(if(true, if(_x61, _x42, _x63), X3))	→	active^#(if(active(true), active(if(_x61, mark(_x42), _x63)), X3))
mark^#(if(if(_x31, false, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(if(_x111, _x112, _x113), true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(f(_x71), false, _x53), X2, X3))	→	active^#(if(active(if(active(f(mark(_x71))), false, _x53)), mark(X2), X3))	mark^#(if(if(false, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(f(_x31), f(_x41), X3))	→	active^#(if(active(f(mark(_x31))), active(f(mark(_x41))), X3))	mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))
mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(f(mark(_x71)))), X3))
mark^#(if(if(_x31, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(if(mark(_x61), mark(_x62), _x63)), _x33))	mark^#(if(if(mark(true), _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(mark(_x32)), active(f(mark(_x41))), _x23))
mark^#(if(if(false, false, _x33), X2, X3))	→	active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(mark(_x53))))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x53))
mark^#(if(if(false, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))
mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))	mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x101, _x82, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(f(_x71), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(false, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, false, _x43), _x23))	→	active^#(if(true, active(if(active(false), active(false), _x43)), _x23))	mark^#(if(if(_x81, false, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(false), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(if(_x61, _x72, _x73)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), _x72, _x73))), _x33))	mark^#(if(if(_x31, _x32, active(active(_x63))), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(if(_x61, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x112, mark(_x113)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(_x41, c, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(c), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(if(_x91, _x92, _x93), _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(if(mark(_x91), mark(_x92), _x93)), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(false, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(if(f(_x61), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))	mark^#(if(c, true, mark(_x33)))	→	active^#(if(c, active(true), _x33))
mark^#(if(true, if(false, _x42, _x53), _x23))	→	active^#(if(active(true), if(false, mark(_x42), _x53), _x23))	mark^#(if(f(_x31), true, X3))	→	active^#(if(active(f(mark(_x31))), active(true), X3))
mark^#(if(if(_x31, false, _x53), X2, _x23))	→	active^#(if(if(mark(_x31), false, _x53), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(f(_x71), if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(true), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(true))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))
mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))	mark^#(if(true, if(false, false, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(false), _x43), _x23))
mark^#(if(if(true, false, _x33), _x22, _x23))	→	active^#(if(active(if(active(true), active(false), _x33)), _x22, _x23))	mark^#(if(true, if(false, f(_x81), _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(f(mark(_x81))), _x43)), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(if(mark(_x41), c, f(true))), X3))	mark^#(if(if(_x81, true, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(true), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(true, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(active(f(mark(_x71))), c, f(true))), X3))
mark^#(if(if(mark(mark(_x41)), _x32, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), mark(if(mark(_x41), c, f(true))), _x23))	mark^#(if(c, f(_x41), mark(_x33)))	→	active^#(if(c, active(f(mark(_x41))), _x33))
mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), f(mark(_x41)), _x23))	mark^#(if(true, f(_x41), X3))	→	active^#(if(active(true), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x61), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x61)), X3))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(if(true, if(false, _x42, active(_x53)), _x23))	→	active^#(if(active(true), if(active(false), mark(_x42), _x53), _x23))	mark^#(if(if(_x31, false, _x53), false, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(false), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))
mark^#(if(if(c, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x61), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(_x61)), X3))	mark^#(if(if(_x31, false, _x53), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(f(_x91)), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(f(mark(_x91))))), _x23))	mark^#(if(if(mark(_x81), true, active(mark(_x43))), f(f(_x81)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(if(f(_x71), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(mark(false), true, active(mark(_x53))), f(f(false)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(true), c, f(true))))), _x23))
mark^#(if(if(mark(true), true, active(f(true))), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(if(mark(active(true)), mark(c), f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, false, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))	mark^#(if(if(_x31, true, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), active(f(mark(_x41))), X3))
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(c, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x53))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(if(mark(mark(if(mark(_x71), c, f(true)))), mark(c), f(true))), X3))	mark^#(if(if(_x81, if(_x91, _x92, _x93), active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(if(mark(_x91), mark(_x92), _x93)), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x43))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(_x41, true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(if(_x31, _x62, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x61, if(_x81, true, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))
mark^#(if(if(_x51, _x32, _x53), X2, X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23))	→	active^#(if(if(_x51, active(true), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(true, true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(true, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, if(_x81, _x82, _x83), _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x43)), X3))	mark^#(if(if(_x31, false, _x53), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(c, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(_x81)))), X3))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(_x81, _x32, active(_x83)), f(if(_x91, _x92, _x93)), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(if(mark(_x91), mark(_x92), _x93)))), _x23))	mark^#(if(if(_x31, true, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(if(true, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(true), mark(_x62), _x63))), _x33))	mark^#(if(true, if(_x41, _x42, mark(_x63)), X3))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x63)), X3))
mark^#(if(if(_x31, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(true, if(false, false, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(active(false), active(false), _x43)), _x23))
mark^#(if(if(mark(_x71), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(f(_x91)), true, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(true), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(true))), X3))	mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(true, if(_x41, f(_x81), _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(f(mark(_x81))), _x43)), X3))	mark^#(if(if(mark(_x71), true, active(mark(mark(_x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(f(_x91)), true, active(mark(_x53))), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))
mark^#(if(true, if(false, true, _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(true), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(true), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(f(f(_x61)), X2, X3))	→	active^#(if(active(f(active(f(mark(_x61))))), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(c))), f(f(_x71)), X3))	→	active^#(if(active(c), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x51), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(f(mark(_x71)))), X3))
mark^#(if(if(_x31, _x32, active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(mark(_x53))))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x53))
mark^#(if(if(_x31, true, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))	mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, false, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(true, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(false, _x32, active(_x41)), f(f(_x71)), X3))	→	active^#(if(mark(_x41), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, false, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(false), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x53)), mark(X2), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(false), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(false))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x91), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x91)), _x23))
mark^#(if(if(_x31, if(_x81, active(_x112), _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, _x32, active(_x41)), f(f(_x71)), X3))	→	active^#(if(mark(mark(_x32)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x61, if(_x81, _x102, _x103), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(mark(_x53)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, if(f(_x111), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))
mark^#(if(if(_x31, false, _x53), _x22, _x23))	→	active^#(if(active(if(mark(_x31), false, _x53)), _x22, _x23))	mark^#(if(if(_x61, false, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(false), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(mark(_x81), true, active(mark(_x53))), f(f(_x81)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(true, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, _x53), true, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(true), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(c), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(c))), _x23))	mark^#(if(f(_x31), _x22, _x23))	→	active^#(if(active(f(mark(_x31))), _x22, _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(false, c, _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(c), _x43)), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(_x53)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), f(mark(_x41)), _x53))	mark^#(if(if(_x31, if(c, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))	mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(mark(_x81)), _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))
mark^#(if(if(true, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, true, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(f(mark(_x91))))))), X3))	mark^#(if(if(_x41, true, active(active(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, true, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x111, _x112, _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x111, _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(false), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), _x23))
mark^#(if(if(_x31, _x32, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))	mark^#(if(true, if(_x41, _x42, _x43), _x23))	→	active^#(if(true, active(if(mark(_x41), mark(_x42), _x43)), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(false))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x53)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), f(mark(_x41)), _x53))
mark^#(if(if(_x61, false, _x63), X2, X3))	→	active^#(if(active(if(_x61, false, _x63)), mark(X2), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(true, if(false, f(_x71), _x43), _x23))	→	active^#(if(active(true), if(active(false), active(f(mark(_x71))), _x43), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), _x102, _x103), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(false), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(false))), _x23))	mark^#(if(if(_x31, false, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))
mark^#(if(true, X2, _x23))	→	active^#(if(true, mark(X2), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))	mark^#(if(if(mark(false), true, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23))	→	active^#(if(active(if(_x51, active(true), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, f(if(_x61, false, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(false), _x63))), _x33))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), mark(_x82), _x83), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(false, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(true, active(false), _x53)), mark(X2), X3))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(true, if(false, false, mark(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), active(false), _x63)), X3))
mark^#(if(if(_x31, _x32, _x33), f(c), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(c))), X3))	mark^#(if(f(_x31), X2, mark(_x23)))	→	active^#(if(active(f(mark(_x31))), mark(X2), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(if(active(true), c, f(true)))), X3))
mark^#(if(true, X2, active(_x23)))	→	active^#(if(active(true), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(mark(_x71), false, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(false), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(active(f(mark(_x71)))), _x23))	mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(_x61, c, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(c), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, if(_x101, _x102, _x103), active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x101), mark(_x102), _x103)), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(true, _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(mark(_x32)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, if(c, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(mark(if(active(true), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(true), true, active(mark(_x53))), f(f(true)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(c, false, _x33), X2, X3))	→	active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(if(true, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(active(_x53))))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x53))
mark^#(if(if(if(_x61, _x62, _x63), false, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(if(_x31, if(false, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, false, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))
mark^#(if(if(_x31, if(true, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x81), _x32, active(active(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, _x22, _x23))	→	active^#(if(active(true), _x22, _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(f(mark(_x91))))))), X3))
mark^#(if(if(f(_x71), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(false, true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(mark(false), true, active(mark(_x43))), f(f(false)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(mark(c), true, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(_x31, c, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))	mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(c))))), X3))	mark^#(if(if(false, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(_x53)))	→	active^#(if(if(_x71, mark(_x32), _x73), active(f(mark(_x41))), _x53))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(true), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(true))), _x23))	mark^#(if(if(_x81, _x32, active(_x83)), f(c), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(c))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(active(f(mark(_x71))), c, f(true))), X3))	mark^#(if(c, f(if(if(_x81, _x82, _x83), _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(if(mark(_x81), mark(_x82), _x83)), mark(_x62), _x63))), _x33))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(f(_x91)), true, active(mark(_x43))), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(true, if(false, _x42, _x43), active(_x23)))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x43)), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(if(_x31, if(if(_x111, _x112, _x113), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(active(_x41), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(true, if(_x41, if(_x81, _x82, _x83), _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(if(mark(_x81), mark(_x82), _x83)), _x43)), X3))
mark^#(if(if(_x31, f(_x81), active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(_x41))), X3))	mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(if(mark(false), _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(_x61), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x63)))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x63))
mark^#(if(if(_x31, if(_x81, _x82, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, false, _x23))	→	active^#(if(active(c), false, _x23))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, f(if(_x61, _x62, mark(_x73))), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x73))), _x33))
mark^#(if(if(mark(_x71), c, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(c), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, c, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), active(f(mark(_x41))), X3))
mark^#(if(true, if(false, _x42, _x43), active(_x33)))	→	active^#(if(active(true), if(active(false), mark(_x42), _x43), _x33))	mark^#(if(true, true, X3))	→	active^#(if(active(true), active(true), X3))
mark^#(if(if(false, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), mark(if(mark(_x41), c, f(true))), _x23))
mark^#(if(if(_x31, if(_x81, c, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(mark(if(active(true), c, f(true)))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(true))))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(true), c, f(true))))), _x23))	mark^#(if(if(_x51, false, _x53), X2, X3))	→	active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, _x62, active(_x63)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), f(active(f(mark(_x71)))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(f(true))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(if(mark(_x71), c, f(true)), c, f(true))), X3))	mark^#(if(if(_x31, false, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(active(_x63))))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x63))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(f(_x111), true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(f(_x31), if(_x41, _x42, _x43), X3))	→	active^#(if(active(f(mark(_x31))), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, false, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))	mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))	mark^#(if(if(_x31, if(_x81, c, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(c), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(f(_x91)), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(f(mark(_x91))))), _x23))	mark^#(if(c, false, mark(active(_x23))))	→	active^#(if(c, active(false), _x23))
mark^#(if(if(f(_x61), false, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))	mark^#(if(if(mark(active(_x81)), _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(if(_x101, _x102, _x103)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x101), mark(_x102), _x103)))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), active(_x23)))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))	mark^#(if(if(f(_x61), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x81, f(_x91), active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(f(mark(_x91))), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(true, if(_x41, true, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(true), _x43)), X3))
mark^#(if(if(mark(_x71), true, active(mark(active(_x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, if(_x121, _x122, _x123), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(if(mark(_x121), mark(_x122), _x123)), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(c), true, active(mark(_x53))), f(f(c)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(true, if(false, _x62, _x63), X3))	→	active^#(if(active(true), active(if(active(false), _x62, _x63)), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(true, if(false, _x42, _x43), _x23))	→	active^#(if(true, active(if(active(false), mark(_x42), _x43)), _x23))	mark^#(if(if(_x31, _x32, _x33), f(false), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(false))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(c, f(if(_x61, true, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(true), _x63))), _x33))
mark^#(if(if(true, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x51, _x32, _x53), f(_x41), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(mark(if(mark(_x31), c, f(true))), mark(X2), X3))
mark^#(if(if(_x31, if(if(_x111, _x112, _x113), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))
mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))
mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(f(c), X2, X3))	→	active^#(if(active(f(active(c))), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(true, if(false, _x42, mark(_x53)), _x23))	→	active^#(if(active(true), if(active(false), mark(_x42), _x53), _x23))	mark^#(if(if(_x31, if(_x81, if(_x121, _x122, _x123), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(if(mark(_x121), mark(_x122), _x123)), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x112, active(_x113)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(mark(_x63))), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(true, false, X3))	→	active^#(if(active(true), active(false), X3))
mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))	mark^#(if(if(active(_x71), _x32, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(false))))), X3))	mark^#(if(if(_x31, _x62, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(if(_x31, if(_x81, _x82, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))	mark^#(if(c, X2, mark(mark(_x23))))	→	active^#(if(c, mark(X2), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), active(true), _x83), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(true, _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(true), mark(_x42), _x43)), X3))	mark^#(if(if(_x31, true, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(if(_x71, _x72, _x73), if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23))	→	active^#(if(active(if(_x41, active(true), _x43)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(_x31, true, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), X3))
mark^#(if(true, if(false, _x42, mark(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x63)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x23))
mark^#(if(if(_x31, f(_x81), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(false, false, _x63), X3))	→	active^#(if(active(true), active(if(false, active(false), _x63)), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(f(mark(_x91))), c, f(true))), c, f(true))), X3))
mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))	mark^#(if(if(c, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(active(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(if(mark(true), true, active(mark(_x43))), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(true, if(false, _x42, _x43), _x33))	→	active^#(if(true, if(active(false), mark(_x42), _x43), _x33))	mark^#(if(if(_x71, _x32, active(active(_x73))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(c), c, f(true))), c, f(true))), X3))	mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(_x41, _x42, active(_x63)), X3))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x63)), X3))	mark^#(if(if(_x31, false, _x53), c, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(c), X3))
mark^#(if(if(mark(_x71), true, active(mark(true))), f(f(_x71)), X3))	→	active^#(if(active(true), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(c, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, active(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(f(true))), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(c, f(if(_x61, if(_x91, _x92, _x93), _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(if(mark(_x91), mark(_x92), _x93)), _x63))), _x33))
mark^#(if(if(c, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(true, false, _x33), X2, _x23))	→	active^#(if(if(active(true), active(false), _x33), mark(X2), _x23))	mark^#(if(if(false, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(c, false, mark(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))	mark^#(if(if(_x31, if(_x101, true, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(false, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, false, mark(_x23)))	→	active^#(if(c, false, _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x71, _x72, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, _x72, _x73)), active(f(mark(_x41))), _x23))
mark^#(if(true, if(false, false, active(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), active(false), _x63)), X3))	mark^#(if(if(if(_x71, _x72, _x73), false, _x53), X2, X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), false, _x53)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(if(_x41, _x42, _x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x41), mark(_x42), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(true), true, active(_x31)), f(f(true)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(false, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(f(_x31), X2, active(_x23)))	→	active^#(if(active(f(mark(_x31))), mark(X2), _x23))
mark^#(if(if(_x81, c, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(c), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, true, _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, true, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(true), _x43), _x23))	mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(if(_x31, c, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, false, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(false), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, f(_x81), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x81), true, active(mark(_x31))), f(f(_x81)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(if(c, false, _x53), X2, X3))	→	active^#(if(active(if(active(c), false, _x53)), mark(X2), X3))
mark^#(if(if(mark(_x71), f(_x101), active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(f(mark(_x101))), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x61, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))	mark^#(if(if(_x31, _x32, mark(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(true, if(false, _x42, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x43)), _x23))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x81), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(_x81)), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(c))))), X3))
mark^#(if(if(mark(_x41), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(true, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(true, if(_x41, false, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(false), _x43)), X3))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(if(_x91, _x92, _x93)), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(if(mark(_x91), mark(_x92), _x93)))), _x23))	mark^#(if(if(c, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(mark(c), true, active(mark(_x31))), f(f(c)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(c, if(_x41, _x42, _x43), mark(_x33)))	→	active^#(if(c, active(if(mark(_x41), mark(_x42), _x43)), _x33))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(f(mark(_x71)))), X3))	mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))
mark^#(if(if(_x51, _x32, active(active(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(true, if(false, c, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(c), _x43), _x23))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(true, if(false, false, _x43), active(_x23)))	→	active^#(if(active(true), active(if(active(false), active(false), _x43)), _x23))
mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(f(_x91), _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(f(mark(_x91))), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x51, _x52, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, _x52, _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x52, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))
mark^#(if(if(true, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x61, if(_x71, _x72, _x73), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x71), mark(_x72), _x73)), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(active(_x53))))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x53))	mark^#(if(if(_x31, _x32, active(_x53)), f(c), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), _x23))
mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))	mark^#(if(if(mark(_x71), if(_x101, _x102, _x103), active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(if(mark(_x101), mark(_x102), _x103)), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(active(_x23))))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x23))	mark^#(if(if(mark(false), true, active(mark(_x31))), f(f(false)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(true, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), _x23))	mark^#(if(c, c, mark(_x33)))	→	active^#(if(c, active(c), _x33))
mark^#(if(if(_x31, if(false, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(false, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(_x31, false, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(active(f(mark(_x71)))), _x23))	mark^#(if(c, f(if(_x61, f(_x91), _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(f(mark(_x91))), _x63))), _x33))
mark^#(if(if(f(_x71), _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(if(_x71, _x72, _x73)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))
mark^#(if(if(_x31, _x32, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), _x23))	→	active^#(if(mark(_x31), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(true, if(_x41, _x62, _x63), X3))	→	active^#(if(active(true), active(if(mark(_x41), _x62, _x63)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(if(_x31, f(_x101), active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x101))), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(c))))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(if(_x121, _x122, _x123), _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x121), mark(_x122), _x123)), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, mark(_x32), _x63), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(mark(true), true, active(mark(_x31))), f(f(true)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(_x41, _x42, _x43), _x23))	→	active^#(if(active(true), if(mark(_x41), mark(_x42), _x43), _x23))
mark^#(if(if(active(_x51), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(active(_x53)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), mark(_x82), _x83), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, c, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(mark(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(_x71), true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x31))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(_x31, if(c, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(c), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), X3))
mark^#(if(if(_x31, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(true, if(false, _x42, _x63), X3))	→	active^#(if(active(true), active(if(false, mark(_x42), _x63)), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x81), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(_x81)), _x23))
mark^#(if(c, f(if(f(_x81), _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(f(mark(_x81))), mark(_x62), _x63))), _x33))	mark^#(if(if(_x31, _x32, _x33), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(true, if(false, _x52, _x53), _x23))	→	active^#(if(active(true), if(active(false), _x52, _x53), _x23))
mark^#(if(if(_x31, _x32, active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, _x53), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(if(_x31, if(_x101, _x82, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x63)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x63))
mark^#(if(if(_x31, if(_x81, true, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(true, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(_x31, if(_x81, mark(_x112), _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))
mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))	mark^#(if(if(mark(_x71), _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(true, if(false, _x42, _x43), mark(_x33)))	→	active^#(if(active(true), if(active(false), mark(_x42), _x43), _x33))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), if(mark(if(mark(_x71), c, f(true))), c, f(true)), _x23))	mark^#(if(if(c, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(if(c, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(f(_x71), _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(f(mark(_x71))), mark(_x42), _x43)), X3))	mark^#(if(true, if(false, _x42, active(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x63)), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(true, c, f(true))))), X3))	mark^#(if(f(false), X2, X3))	→	active^#(if(active(f(active(false))), mark(X2), X3))
mark^#(if(f(_x31), X2, _x23))	→	active^#(if(f(mark(_x31)), mark(X2), _x23))	mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(active(true), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, mark(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(if(_x31, f(_x71), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))
mark^#(if(if(mark(true), true, active(_x43)), f(f(true)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(true, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x82, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), _x82, _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x21))), f(f(_x71)), _x23))	→	active^#(if(_x21, active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), true, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(_x61, c, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(c), _x63))), _x33))
mark^#(if(if(_x31, if(c, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x23)))	→	active^#(if(c, f(active(if(mark(_x61), mark(_x62), _x63))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), mark(_x23)))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, false, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))	mark^#(if(if(mark(true), true, active(active(_x43))), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, f(if(false, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(false), mark(_x62), _x63))), _x33))	mark^#(if(c, f(if(_x71, _x62, _x73)), active(_x33)))	→	active^#(if(active(c), f(active(if(_x71, mark(_x62), _x73))), _x33))
mark^#(if(if(mark(c), true, active(mark(_x43))), f(f(c)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(if(true, false, active(_x53)), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x53)), mark(X2), X3))
mark^#(if(if(true, false, _x33), true, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(true), X3))	mark^#(if(if(true, false, _x33), f(_x41), X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(f(mark(_x41))), X3))
mark^#(if(f(_x31), false, X3))	→	active^#(if(active(f(mark(_x31))), active(false), X3))	mark^#(if(if(mark(f(_x91)), true, active(mark(_x31))), f(f(f(_x91))), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(active(if(mark(mark(_x71)), mark(c), f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x23))
mark^#(if(if(false, false, _x53), X2, X3))	→	active^#(if(active(if(active(false), false, _x53)), mark(X2), X3))	mark^#(if(if(mark(true), true, active(_x31)), f(f(true)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23))	→	active^#(if(if(_x41, active(true), _x43), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(_x81), true, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(mark(if(active(true), c, f(true))))), _x23))	mark^#(if(if(_x61, _x32, active(_x63)), f(_x41), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(if(f(_x71), if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x41, true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x61, f(_x71), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(f(mark(_x71))), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(f(_x71), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x101)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x101))))), _x23))
mark^#(if(if(mark(true), true, active(_x43)), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(_x31, if(false, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(mark(_x63))))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x63))
mark^#(if(if(_x31, if(f(_x111), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(false, false, _x63), X3))	→	active^#(if(active(true), active(if(active(false), false, _x63)), X3))
mark^#(if(if(_x31, c, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x53)))	→	active^#(if(if(_x81, mark(_x32), _x83), active(f(mark(_x41))), _x53))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(mark(_x23))))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x23))	mark^#(if(if(_x31, c, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(true), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), _x23))	mark^#(if(if(_x31, _x32, active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(if(_x71, _x72, _x73)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(_x81)))), X3))
mark^#(if(f(if(_x61, _x62, _x63)), X2, X3))	→	active^#(if(active(f(active(if(mark(_x61), mark(_x62), _x63)))), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, c, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(c), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(f(_x51), X2, X3))	→	active^#(if(active(f(_x51)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(true, if(_x41, _x42, _x43), active(_x23)))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x43)), _x23))	mark^#(if(if(true, false, _x33), false, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(false), X3))
mark^#(if(if(_x31, _x52, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(false, _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(_x61), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, f(_x121), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(f(mark(_x121))), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(false))), f(f(_x71)), X3))	→	active^#(if(active(false), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(mark(_x71), true, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(true), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(_x81)))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(false), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), X3))
mark^#(if(if(_x61, true, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(f(mark(_x91))))))), X3))	mark^#(if(if(_x31, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))
mark^#(if(if(_x31, f(_x71), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), active(f(mark(_x41))), X3))	mark^#(if(c, f(if(_x61, _x62, active(_x73))), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x73))), _x33))
mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(if(_x31, if(_x81, c, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(_x81, c, f(true))), c, f(true))), X3))
mark^#(if(if(_x51, _x32, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, f(_x121), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(f(mark(_x121))), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(if(c, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(c), mark(_x62), _x63))), _x33))	mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(false))))), X3))	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, X2, mark(active(_x23))))	→	active^#(if(c, mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(false), c, f(true))), c, f(true))), X3))
mark^#(if(true, X2, mark(_x23)))	→	active^#(if(active(true), mark(X2), _x23))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(true, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(f(true), X2, X3))	→	active^#(if(active(f(active(true))), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(c, false, mark(mark(_x23))))	→	active^#(if(c, active(false), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), X3))	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(if(_x31, if(f(_x121), _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x121))), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(true), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x81), _x32, active(mark(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3)) 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 Terms	Irrelevant Terms
active^#(if(mark(_x31), active(f(mark(if(active(c), c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(_x81, c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(active(false), c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
active^#(if(active(false), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
active^#(if(mark(_x31), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
active^#(if(active(true), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
active^#(if(mark(_x31), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
active^#(if(mark(_x31), active(f(if(mark(_x71), c, f(true)))), X3))
active^#(if(mark(_x31), f(mark(if(mark(_x71), c, f(true)))), _x23))
active^#(if(mark(_x31), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
active^#(if(active(c), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(f(mark(_x41))), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(_x21, active(f(mark(if(mark(_x71), c, f(true))))), _x23))
active^#(if(active(if(mark(_x41), mark(_x42), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))

Thus, the rule mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3)) is replaced by the following rules:

mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x31))), f(f(if(_x91, _x92, _x93))), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(mark(_x81), true, active(mark(_x31))), f(f(_x81)), X3)) → active^#(if(mark(_x31), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(c))), f(f(_x71)), X3)) → active^#(if(active(c), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), mark(_x23))) → active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(f(_x91)), true, active(mark(_x31))), f(f(f(_x91))), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(true))), f(f(_x71)), X3)) → active^#(if(active(true), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(if(_x41, _x42, _x43)))), f(f(_x71)), X3)) → active^#(if(active(if(mark(_x41), mark(_x42), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(false))), f(f(_x71)), X3)) → active^#(if(active(false), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(true), true, active(mark(_x31))), f(f(true)), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(mark(false), true, active(mark(_x31))), f(f(false)), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(f(_x41)))), f(f(_x71)), X3)) → active^#(if(active(f(mark(_x41))), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(c), true, active(mark(_x31))), f(f(c)), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), _x23)) → active^#(if(mark(_x31), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), active(_x23))) → active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x21))), f(f(_x71)), _x23)) → active^#(if(_x21, active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), active(f(if(mark(_x71), c, f(true)))), X3))

Problem 31: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(active(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(_x31, if(true, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x71, _x32, active(mark(_x73))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(c, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(mark(f(_x41)))), f(f(_x71)), X3))	→	active^#(if(active(f(mark(_x41))), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
mark^#(if(if(mark(_x71), true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x81), _x82, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, _x82, _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(true, false, _x33), c, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(c), X3))	mark^#(if(true, if(if(_x71, _x72, _x73), _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x42), _x43)), X3))
mark^#(if(true, if(false, if(_x71, _x72, _x73), _x43), _x23))	→	active^#(if(active(true), if(active(false), active(if(mark(_x71), mark(_x72), _x73)), _x43), _x23))	mark^#(if(true, if(c, _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(c), mark(_x42), _x43)), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), mark(if(active(f(mark(_x71))), c, f(true))), X3))	mark^#(if(if(_x31, true, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(true, if(_x41, _x42, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x43)), _x23))	mark^#(if(true, if(_x61, _x42, _x63), X3))	→	active^#(if(active(true), active(if(_x61, mark(_x42), _x63)), X3))
mark^#(if(if(_x31, false, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(if(_x111, _x112, _x113), true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(f(_x71), false, _x53), X2, X3))	→	active^#(if(active(if(active(f(mark(_x71))), false, _x53)), mark(X2), X3))	mark^#(if(if(false, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(f(_x31), f(_x41), X3))	→	active^#(if(active(f(mark(_x31))), active(f(mark(_x41))), X3))	mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))
mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(f(mark(_x71)))), X3))
mark^#(if(if(_x31, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(if(mark(_x61), mark(_x62), _x63)), _x33))	mark^#(if(if(mark(true), _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(mark(_x32)), active(f(mark(_x41))), _x23))
mark^#(if(if(false, false, _x33), X2, X3))	→	active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(mark(_x53))))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x53))
mark^#(if(if(false, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))
mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))	mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x101, _x82, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(f(_x71), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(false, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, false, _x43), _x23))	→	active^#(if(true, active(if(active(false), active(false), _x43)), _x23))	mark^#(if(if(_x81, false, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(false), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(if(_x61, _x72, _x73)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), _x72, _x73))), _x33))	mark^#(if(if(_x31, _x32, active(active(_x63))), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(if(_x61, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x112, mark(_x113)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(_x41, c, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(c), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(if(_x91, _x92, _x93), _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(if(mark(_x91), mark(_x92), _x93)), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(false, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(if(f(_x61), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))	mark^#(if(c, true, mark(_x33)))	→	active^#(if(c, active(true), _x33))
mark^#(if(true, if(false, _x42, _x53), _x23))	→	active^#(if(active(true), if(false, mark(_x42), _x53), _x23))	mark^#(if(f(_x31), true, X3))	→	active^#(if(active(f(mark(_x31))), active(true), X3))
mark^#(if(if(_x31, false, _x53), X2, _x23))	→	active^#(if(if(mark(_x31), false, _x53), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(f(_x71), if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(true), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(true))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))
mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))	mark^#(if(true, if(false, false, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(false), _x43), _x23))
mark^#(if(if(true, false, _x33), _x22, _x23))	→	active^#(if(active(if(active(true), active(false), _x33)), _x22, _x23))	mark^#(if(true, if(false, f(_x81), _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(f(mark(_x81))), _x43)), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(if(mark(_x41), c, f(true))), X3))	mark^#(if(if(_x81, true, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(true), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(true, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(active(f(mark(_x71))), c, f(true))), X3))
mark^#(if(if(mark(mark(_x41)), _x32, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), mark(if(mark(_x41), c, f(true))), _x23))	mark^#(if(c, f(_x41), mark(_x33)))	→	active^#(if(c, active(f(mark(_x41))), _x33))
mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), f(mark(_x41)), _x23))	mark^#(if(true, f(_x41), X3))	→	active^#(if(active(true), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x61), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x61)), X3))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(if(true, if(false, _x42, active(_x53)), _x23))	→	active^#(if(active(true), if(active(false), mark(_x42), _x53), _x23))	mark^#(if(if(_x31, false, _x53), false, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(false), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))
mark^#(if(if(c, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x61), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(_x61)), X3))	mark^#(if(if(_x31, false, _x53), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(f(_x91)), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(f(mark(_x91))))), _x23))	mark^#(if(if(mark(_x81), true, active(mark(_x43))), f(f(_x81)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(if(f(_x71), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(mark(false), true, active(mark(_x53))), f(f(false)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(true), c, f(true))))), _x23))
mark^#(if(if(mark(true), true, active(f(true))), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(if(mark(active(true)), mark(c), f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, false, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))	mark^#(if(if(_x31, true, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), active(f(mark(_x41))), X3))
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(c, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x53))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(if(mark(mark(if(mark(_x71), c, f(true)))), mark(c), f(true))), X3))	mark^#(if(if(_x81, if(_x91, _x92, _x93), active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(if(mark(_x91), mark(_x92), _x93)), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x43))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(_x41, true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(if(_x31, _x62, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x61, if(_x81, true, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))
mark^#(if(if(_x51, _x32, _x53), X2, X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23))	→	active^#(if(if(_x51, active(true), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(true, true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(true, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, if(_x81, _x82, _x83), _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x43)), X3))	mark^#(if(if(_x31, false, _x53), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(c, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(_x81)))), X3))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(_x81, _x32, active(_x83)), f(if(_x91, _x92, _x93)), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(if(mark(_x91), mark(_x92), _x93)))), _x23))	mark^#(if(if(_x31, true, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(if(true, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(true), mark(_x62), _x63))), _x33))	mark^#(if(true, if(_x41, _x42, mark(_x63)), X3))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x63)), X3))
mark^#(if(if(_x31, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(true, if(false, false, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(active(false), active(false), _x43)), _x23))
mark^#(if(if(mark(_x71), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(f(_x91)), true, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(true), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(true))), X3))	mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(true, if(_x41, f(_x81), _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(f(mark(_x81))), _x43)), X3))	mark^#(if(if(mark(_x71), true, active(mark(mark(_x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(f(_x91)), true, active(mark(_x53))), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))
mark^#(if(true, if(false, true, _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(true), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(true), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(f(f(_x61)), X2, X3))	→	active^#(if(active(f(active(f(mark(_x61))))), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(c))), f(f(_x71)), X3))	→	active^#(if(active(c), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x51), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(f(mark(_x71)))), X3))
mark^#(if(if(_x31, _x32, active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(mark(_x53))))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x53))
mark^#(if(if(_x31, true, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))	mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, false, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(true, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(false, _x32, active(_x41)), f(f(_x71)), X3))	→	active^#(if(mark(_x41), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, false, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(false), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x53)), mark(X2), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(false), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(false))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x91), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x91)), _x23))
mark^#(if(if(_x31, if(_x81, active(_x112), _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, _x32, active(_x41)), f(f(_x71)), X3))	→	active^#(if(mark(mark(_x32)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x61, if(_x81, _x102, _x103), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(mark(_x53)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, if(f(_x111), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))
mark^#(if(if(_x31, false, _x53), _x22, _x23))	→	active^#(if(active(if(mark(_x31), false, _x53)), _x22, _x23))	mark^#(if(if(_x61, false, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(false), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(mark(_x81), true, active(mark(_x53))), f(f(_x81)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(true, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, _x53), true, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(true), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(c), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(c))), _x23))	mark^#(if(f(_x31), _x22, _x23))	→	active^#(if(active(f(mark(_x31))), _x22, _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(false, c, _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(c), _x43)), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(_x53)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), f(mark(_x41)), _x53))	mark^#(if(if(_x31, if(c, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))	mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(mark(_x81)), _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))
mark^#(if(if(true, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, true, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(f(mark(_x91))))))), X3))	mark^#(if(if(_x41, true, active(active(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, true, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x111, _x112, _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x111, _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(false), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), _x23))
mark^#(if(if(_x31, _x32, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))	mark^#(if(true, if(_x41, _x42, _x43), _x23))	→	active^#(if(true, active(if(mark(_x41), mark(_x42), _x43)), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(false))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x53)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), f(mark(_x41)), _x53))
mark^#(if(if(_x61, false, _x63), X2, X3))	→	active^#(if(active(if(_x61, false, _x63)), mark(X2), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(true, if(false, f(_x71), _x43), _x23))	→	active^#(if(active(true), if(active(false), active(f(mark(_x71))), _x43), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), _x102, _x103), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(false), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(false))), _x23))	mark^#(if(if(_x31, false, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))
mark^#(if(true, X2, _x23))	→	active^#(if(true, mark(X2), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))	mark^#(if(if(mark(false), true, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23))	→	active^#(if(active(if(_x51, active(true), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, f(if(_x61, false, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(false), _x63))), _x33))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), mark(_x82), _x83), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(false, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(true, active(false), _x53)), mark(X2), X3))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(true, if(false, false, mark(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), active(false), _x63)), X3))
mark^#(if(if(_x31, _x32, _x33), f(c), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(c))), X3))	mark^#(if(f(_x31), X2, mark(_x23)))	→	active^#(if(active(f(mark(_x31))), mark(X2), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(if(active(true), c, f(true)))), X3))
mark^#(if(true, X2, active(_x23)))	→	active^#(if(active(true), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(mark(_x71), false, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(false), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(active(f(mark(_x71)))), _x23))	mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(_x61, c, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(c), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, if(_x101, _x102, _x103), active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x101), mark(_x102), _x103)), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(true, _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(mark(_x32)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, if(c, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(mark(if(active(true), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(true), true, active(mark(_x53))), f(f(true)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(c, false, _x33), X2, X3))	→	active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(if(true, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(active(_x53))))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x53))
mark^#(if(if(if(_x61, _x62, _x63), false, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(if(_x31, if(false, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, false, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))
mark^#(if(if(_x31, if(true, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x81), _x32, active(active(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, _x22, _x23))	→	active^#(if(active(true), _x22, _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(f(mark(_x91))))))), X3))
mark^#(if(if(f(_x71), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(false, true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(mark(false), true, active(mark(_x43))), f(f(false)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(mark(c), true, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(_x31, c, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))	mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(c))))), X3))	mark^#(if(if(false, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(_x53)))	→	active^#(if(if(_x71, mark(_x32), _x73), active(f(mark(_x41))), _x53))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(true), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(true))), _x23))	mark^#(if(if(_x81, _x32, active(_x83)), f(c), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(c))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(active(f(mark(_x71))), c, f(true))), X3))	mark^#(if(c, f(if(if(_x81, _x82, _x83), _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(if(mark(_x81), mark(_x82), _x83)), mark(_x62), _x63))), _x33))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(f(_x91)), true, active(mark(_x43))), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(true, if(false, _x42, _x43), active(_x23)))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x43)), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(if(_x31, if(if(_x111, _x112, _x113), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(active(_x41), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(true, if(_x41, if(_x81, _x82, _x83), _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(if(mark(_x81), mark(_x82), _x83)), _x43)), X3))
mark^#(if(if(_x31, f(_x81), active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(_x41))), X3))	mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(if(mark(false), _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(_x61), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x63)))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x63))
mark^#(if(if(_x31, if(_x81, _x82, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, false, _x23))	→	active^#(if(active(c), false, _x23))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, f(if(_x61, _x62, mark(_x73))), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x73))), _x33))
mark^#(if(if(mark(_x71), c, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(c), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, c, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), active(f(mark(_x41))), X3))
mark^#(if(true, if(false, _x42, _x43), active(_x33)))	→	active^#(if(active(true), if(active(false), mark(_x42), _x43), _x33))	mark^#(if(true, true, X3))	→	active^#(if(active(true), active(true), X3))
mark^#(if(if(false, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), mark(if(mark(_x41), c, f(true))), _x23))
mark^#(if(if(_x31, if(_x81, c, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(mark(if(active(true), c, f(true)))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(true))))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(true), c, f(true))))), _x23))	mark^#(if(if(_x51, false, _x53), X2, X3))	→	active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, _x62, active(_x63)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), f(active(f(mark(_x71)))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(f(true))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(if(mark(_x71), c, f(true)), c, f(true))), X3))	mark^#(if(if(_x31, false, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(active(_x63))))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x63))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(f(_x111), true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(f(_x31), if(_x41, _x42, _x43), X3))	→	active^#(if(active(f(mark(_x31))), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, false, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))	mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))	mark^#(if(if(_x31, if(_x81, c, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(c), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(f(_x91)), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(f(mark(_x91))))), _x23))	mark^#(if(c, false, mark(active(_x23))))	→	active^#(if(c, active(false), _x23))
mark^#(if(if(f(_x61), false, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))	mark^#(if(if(mark(active(_x81)), _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(if(_x101, _x102, _x103)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x101), mark(_x102), _x103)))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), active(_x23)))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))	mark^#(if(if(f(_x61), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x81, f(_x91), active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(f(mark(_x91))), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(true, if(_x41, true, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(true), _x43)), X3))
mark^#(if(if(mark(_x71), true, active(mark(active(_x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, if(_x121, _x122, _x123), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(if(mark(_x121), mark(_x122), _x123)), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(c), true, active(mark(_x53))), f(f(c)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(true, if(false, _x62, _x63), X3))	→	active^#(if(active(true), active(if(active(false), _x62, _x63)), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(true, if(false, _x42, _x43), _x23))	→	active^#(if(true, active(if(active(false), mark(_x42), _x43)), _x23))	mark^#(if(if(_x31, _x32, _x33), f(false), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(false))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(c, f(if(_x61, true, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(true), _x63))), _x33))
mark^#(if(if(true, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x51, _x32, _x53), f(_x41), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(mark(if(mark(_x31), c, f(true))), mark(X2), X3))
mark^#(if(if(_x31, if(if(_x111, _x112, _x113), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))
mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))
mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(f(c), X2, X3))	→	active^#(if(active(f(active(c))), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(true, if(false, _x42, mark(_x53)), _x23))	→	active^#(if(active(true), if(active(false), mark(_x42), _x53), _x23))	mark^#(if(if(_x31, if(_x81, if(_x121, _x122, _x123), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(if(mark(_x121), mark(_x122), _x123)), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x112, active(_x113)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(mark(_x63))), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(true, false, X3))	→	active^#(if(active(true), active(false), X3))
mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))	mark^#(if(if(active(_x71), _x32, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(false))))), X3))	mark^#(if(if(_x31, _x62, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(if(_x31, if(_x81, _x82, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))	mark^#(if(c, X2, mark(mark(_x23))))	→	active^#(if(c, mark(X2), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), active(true), _x83), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(true, _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(true), mark(_x42), _x43)), X3))	mark^#(if(if(_x31, true, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(if(_x71, _x72, _x73), if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23))	→	active^#(if(active(if(_x41, active(true), _x43)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(_x31, true, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), X3))
mark^#(if(true, if(false, _x42, mark(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x63)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x23))
mark^#(if(if(_x31, f(_x81), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(false, false, _x63), X3))	→	active^#(if(active(true), active(if(false, active(false), _x63)), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(f(mark(_x91))), c, f(true))), c, f(true))), X3))
mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))	mark^#(if(if(c, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(active(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(if(mark(true), true, active(mark(_x43))), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(true, if(false, _x42, _x43), _x33))	→	active^#(if(true, if(active(false), mark(_x42), _x43), _x33))	mark^#(if(if(_x71, _x32, active(active(_x73))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(c), c, f(true))), c, f(true))), X3))	mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(_x41, _x42, active(_x63)), X3))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x63)), X3))	mark^#(if(if(_x31, false, _x53), c, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(c), X3))
mark^#(if(if(mark(_x71), true, active(mark(true))), f(f(_x71)), X3))	→	active^#(if(active(true), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(c, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, active(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(f(true))), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(c, f(if(_x61, if(_x91, _x92, _x93), _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(if(mark(_x91), mark(_x92), _x93)), _x63))), _x33))
mark^#(if(if(c, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(true, false, _x33), X2, _x23))	→	active^#(if(if(active(true), active(false), _x33), mark(X2), _x23))	mark^#(if(if(false, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(c, false, mark(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))	mark^#(if(if(_x31, if(_x101, true, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(false, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, false, mark(_x23)))	→	active^#(if(c, false, _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x71, _x72, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, _x72, _x73)), active(f(mark(_x41))), _x23))
mark^#(if(true, if(false, false, active(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), active(false), _x63)), X3))	mark^#(if(if(if(_x71, _x72, _x73), false, _x53), X2, X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), false, _x53)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(if(_x41, _x42, _x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x41), mark(_x42), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(true), true, active(_x31)), f(f(true)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(false, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(f(_x31), X2, active(_x23)))	→	active^#(if(active(f(mark(_x31))), mark(X2), _x23))
mark^#(if(if(_x81, c, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(c), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, true, _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, true, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(true), _x43), _x23))	mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(if(_x31, c, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, false, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(false), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, f(_x81), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x81), true, active(mark(_x31))), f(f(_x81)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(if(c, false, _x53), X2, X3))	→	active^#(if(active(if(active(c), false, _x53)), mark(X2), X3))
mark^#(if(if(mark(_x71), f(_x101), active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(f(mark(_x101))), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x61, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))	mark^#(if(if(_x31, _x32, mark(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(true, if(false, _x42, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x43)), _x23))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x81), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(_x81)), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(c))))), X3))
mark^#(if(if(mark(_x41), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(true, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(true, if(_x41, false, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(false), _x43)), X3))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(if(_x91, _x92, _x93)), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(if(mark(_x91), mark(_x92), _x93)))), _x23))	mark^#(if(if(c, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(mark(c), true, active(mark(_x31))), f(f(c)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(c, if(_x41, _x42, _x43), mark(_x33)))	→	active^#(if(c, active(if(mark(_x41), mark(_x42), _x43)), _x33))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(f(mark(_x71)))), X3))	mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))
mark^#(if(if(_x51, _x32, active(active(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(true, if(false, c, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(c), _x43), _x23))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(true, if(false, false, _x43), active(_x23)))	→	active^#(if(active(true), active(if(active(false), active(false), _x43)), _x23))
mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(f(_x91), _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(f(mark(_x91))), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x51, _x52, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, _x52, _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x52, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))
mark^#(if(if(true, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x61, if(_x71, _x72, _x73), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x71), mark(_x72), _x73)), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(active(_x53))))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x53))	mark^#(if(if(_x31, _x32, active(_x53)), f(c), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), _x23))
mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))	mark^#(if(if(mark(_x71), if(_x101, _x102, _x103), active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(if(mark(_x101), mark(_x102), _x103)), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(active(_x23))))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x23))	mark^#(if(if(mark(false), true, active(mark(_x31))), f(f(false)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(true, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), _x23))	mark^#(if(c, c, mark(_x33)))	→	active^#(if(c, active(c), _x33))
mark^#(if(if(_x31, if(false, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(false, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(_x31, false, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(active(f(mark(_x71)))), _x23))	mark^#(if(c, f(if(_x61, f(_x91), _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(f(mark(_x91))), _x63))), _x33))
mark^#(if(if(f(_x71), _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(if(_x71, _x72, _x73)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))
mark^#(if(if(_x31, _x32, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), _x23))	→	active^#(if(mark(_x31), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(true, if(_x41, _x62, _x63), X3))	→	active^#(if(active(true), active(if(mark(_x41), _x62, _x63)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(if(_x31, f(_x101), active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x101))), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(c))))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(if(_x121, _x122, _x123), _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x121), mark(_x122), _x123)), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, mark(_x32), _x63), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(mark(true), true, active(mark(_x31))), f(f(true)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(_x41, _x42, _x43), _x23))	→	active^#(if(active(true), if(mark(_x41), mark(_x42), _x43), _x23))
mark^#(if(if(active(_x51), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(active(_x53)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), mark(_x82), _x83), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, c, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(mark(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(_x71), true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x31))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(_x31, if(c, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(c), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), X3))
mark^#(if(if(_x31, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(true, if(false, _x42, _x63), X3))	→	active^#(if(active(true), active(if(false, mark(_x42), _x63)), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x81), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(_x81)), _x23))
mark^#(if(c, f(if(f(_x81), _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(f(mark(_x81))), mark(_x62), _x63))), _x33))	mark^#(if(if(_x31, _x32, _x33), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(true, if(false, _x52, _x53), _x23))	→	active^#(if(active(true), if(active(false), _x52, _x53), _x23))
mark^#(if(if(_x31, _x32, active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, _x53), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(if(_x31, if(_x101, _x82, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x63)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x63))
mark^#(if(if(_x31, if(_x81, true, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(true, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(_x31, if(_x81, mark(_x112), _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))
mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))	mark^#(if(if(mark(_x71), _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(true, if(false, _x42, _x43), mark(_x33)))	→	active^#(if(active(true), if(active(false), mark(_x42), _x43), _x33))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), if(mark(if(mark(_x71), c, f(true))), c, f(true)), _x23))	mark^#(if(if(c, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(if(c, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(f(_x71), _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(f(mark(_x71))), mark(_x42), _x43)), X3))	mark^#(if(true, if(false, _x42, active(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x63)), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(true, c, f(true))))), X3))	mark^#(if(f(false), X2, X3))	→	active^#(if(active(f(active(false))), mark(X2), X3))
mark^#(if(f(_x31), X2, _x23))	→	active^#(if(f(mark(_x31)), mark(X2), _x23))	mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(active(true), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, mark(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(if(_x31, f(_x71), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))
mark^#(if(if(mark(true), true, active(_x43)), f(f(true)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(true, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x82, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), _x82, _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x21))), f(f(_x71)), _x23))	→	active^#(if(_x21, active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), true, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(_x61, c, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(c), _x63))), _x33))
mark^#(if(if(_x31, if(c, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x23)))	→	active^#(if(c, f(active(if(mark(_x61), mark(_x62), _x63))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), mark(_x23)))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, false, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))	mark^#(if(if(mark(true), true, active(active(_x43))), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, f(if(false, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(false), mark(_x62), _x63))), _x33))	mark^#(if(c, f(if(_x71, _x62, _x73)), active(_x33)))	→	active^#(if(active(c), f(active(if(_x71, mark(_x62), _x73))), _x33))
mark^#(if(if(mark(c), true, active(mark(_x43))), f(f(c)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(if(true, false, active(_x53)), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x53)), mark(X2), X3))
mark^#(if(if(true, false, _x33), true, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(true), X3))	mark^#(if(if(true, false, _x33), f(_x41), X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(f(mark(_x41))), X3))
mark^#(if(f(_x31), false, X3))	→	active^#(if(active(f(mark(_x31))), active(false), X3))	mark^#(if(if(mark(f(_x91)), true, active(mark(_x31))), f(f(f(_x91))), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(active(if(mark(mark(_x71)), mark(c), f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x23))
mark^#(if(if(false, false, _x53), X2, X3))	→	active^#(if(active(if(active(false), false, _x53)), mark(X2), X3))	mark^#(if(if(mark(true), true, active(_x31)), f(f(true)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23))	→	active^#(if(if(_x41, active(true), _x43), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(_x81), true, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(mark(if(active(true), c, f(true))))), _x23))	mark^#(if(if(_x61, _x32, active(_x63)), f(_x41), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(if(f(_x71), if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x41, true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x61, f(_x71), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(f(mark(_x71))), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(f(_x71), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x101)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x101))))), _x23))
mark^#(if(if(mark(true), true, active(_x43)), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(_x31, if(false, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(mark(_x63))))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x63))
mark^#(if(if(_x31, if(f(_x111), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(false, false, _x63), X3))	→	active^#(if(active(true), active(if(active(false), false, _x63)), X3))
mark^#(if(if(_x31, c, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x53)))	→	active^#(if(if(_x81, mark(_x32), _x83), active(f(mark(_x41))), _x53))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(mark(_x23))))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x23))	mark^#(if(if(_x31, c, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(true), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), _x23))	mark^#(if(if(_x31, _x32, active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(if(_x71, _x72, _x73)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(_x81)))), X3))
mark^#(if(f(if(_x61, _x62, _x63)), X2, X3))	→	active^#(if(active(f(active(if(mark(_x61), mark(_x62), _x63)))), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, c, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(c), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(f(_x51), X2, X3))	→	active^#(if(active(f(_x51)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(true, if(_x41, _x42, _x43), active(_x23)))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x43)), _x23))	mark^#(if(if(true, false, _x33), false, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(false), X3))
mark^#(if(if(_x31, _x52, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(false, _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(_x61), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, f(_x121), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(f(mark(_x121))), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(false))), f(f(_x71)), X3))	→	active^#(if(active(false), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(mark(_x71), true, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(true), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(_x81)))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(false), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), X3))
mark^#(if(if(_x61, true, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(f(mark(_x91))))))), X3))	mark^#(if(if(_x31, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))
mark^#(if(if(_x31, f(_x71), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), active(f(mark(_x41))), X3))	mark^#(if(c, f(if(_x61, _x62, active(_x73))), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x73))), _x33))
mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(if(_x31, if(_x81, c, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(_x81, c, f(true))), c, f(true))), X3))
mark^#(if(if(_x51, _x32, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, f(_x121), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(f(mark(_x121))), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(if(c, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(c), mark(_x62), _x63))), _x33))	mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(false))))), X3))	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, X2, mark(active(_x23))))	→	active^#(if(c, mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(false), c, f(true))), c, f(true))), X3))
mark^#(if(true, X2, mark(_x23)))	→	active^#(if(active(true), mark(X2), _x23))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(true, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(f(true), X2, X3))	→	active^#(if(active(f(active(true))), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(c, false, mark(mark(_x23))))	→	active^#(if(c, active(false), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), X3))	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(if(_x31, if(f(_x121), _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x121))), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(true), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x81), _x32, active(mark(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3)) 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 Terms	Irrelevant Terms
active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))
active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(_x81, c, f(true))))), X3))
active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(false), c, f(true))))), X3))
active^#(if(active(if(_x51, true, _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(if(_x41, active(true), _x43)), f(mark(if(mark(_x71), c, f(true)))), _x23))
active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(if(_x41, active(true), _x43)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(c), c, f(true))))), X3))
active^#(if(active(if(_x41, active(true), _x43)), active(f(if(mark(_x71), c, f(true)))), X3))
active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
active^#(if(if(_x41, active(true), _x43), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
active^#(if(active(if(_x41, active(true), _x43)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))

Thus, the rule mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3)) is replaced by the following rules:

mark^#(if(if(mark(false), true, active(mark(_x43))), f(f(false)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), mark(_x23))) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), active(_x23))) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23)) → active^#(if(active(if(_x41, active(true), _x43)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23)) → active^#(if(if(_x41, active(true), _x43), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x43))), f(f(if(_x91, _x92, _x93))), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x81), true, active(mark(_x43))), f(f(_x81)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(f(_x91)), true, active(mark(_x43))), f(f(f(_x91))), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(if(mark(c), true, active(mark(_x43))), f(f(c)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(mark(true), true, active(mark(_x43))), f(f(true)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3)) → active^#(if(active(if(_x51, true, _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(active(_x53)))), f(f(_x71)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(mark(_x53)))), f(f(_x71)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))

Problem 32: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(active(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(_x31, if(true, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(true, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x71, _x32, active(mark(_x73))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(c, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), true, active(mark(f(_x41)))), f(f(_x71)), X3))	→	active^#(if(active(f(mark(_x41))), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))	mark^#(if(if(mark(_x71), true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x81), _x82, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, _x82, _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(true, false, _x33), c, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(c), X3))
mark^#(if(true, if(if(_x71, _x72, _x73), _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x42), _x43)), X3))	mark^#(if(true, if(false, if(_x71, _x72, _x73), _x43), _x23))	→	active^#(if(active(true), if(active(false), active(if(mark(_x71), mark(_x72), _x73)), _x43), _x23))
mark^#(if(true, if(c, _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(c), mark(_x42), _x43)), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), mark(if(active(f(mark(_x71))), c, f(true))), X3))
mark^#(if(if(_x31, true, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(true, if(_x41, _x42, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x43)), _x23))
mark^#(if(true, if(_x61, _x42, _x63), X3))	→	active^#(if(active(true), active(if(_x61, mark(_x42), _x63)), X3))	mark^#(if(if(_x31, false, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(if(_x111, _x112, _x113), true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(f(_x71), false, _x53), X2, X3))	→	active^#(if(active(if(active(f(mark(_x71))), false, _x53)), mark(X2), X3))
mark^#(if(if(false, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(f(_x31), f(_x41), X3))	→	active^#(if(active(f(mark(_x31))), active(f(mark(_x41))), X3))
mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))	mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(f(mark(_x71)))), X3))	mark^#(if(if(_x31, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))	mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(if(mark(_x61), mark(_x62), _x63)), _x33))
mark^#(if(if(mark(true), _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(mark(_x32)), active(f(mark(_x41))), _x23))	mark^#(if(if(false, false, _x33), X2, X3))	→	active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(mark(_x53))))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x53))	mark^#(if(if(false, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))	mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))
mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x101, _x82, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(f(_x71), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(false, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(false, false, _x43), _x23))	→	active^#(if(true, active(if(active(false), active(false), _x43)), _x23))
mark^#(if(if(_x81, false, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(false), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(c, f(if(_x61, _x72, _x73)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), _x72, _x73))), _x33))
mark^#(if(if(_x31, _x32, active(active(_x63))), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))	mark^#(if(if(_x61, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, if(_x81, _x112, mark(_x113)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(_x41, c, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(c), _x43)), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(if(_x91, _x92, _x93), _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(if(mark(_x91), mark(_x92), _x93)), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(false, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(true, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))
mark^#(if(if(f(_x61), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))
mark^#(if(c, true, mark(_x33)))	→	active^#(if(c, active(true), _x33))	mark^#(if(true, if(false, _x42, _x53), _x23))	→	active^#(if(active(true), if(false, mark(_x42), _x53), _x23))
mark^#(if(f(_x31), true, X3))	→	active^#(if(active(f(mark(_x31))), active(true), X3))	mark^#(if(if(_x31, false, _x53), X2, _x23))	→	active^#(if(if(mark(_x31), false, _x53), mark(X2), _x23))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(f(_x71), if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(true), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(true))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))	mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))
mark^#(if(true, if(false, false, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(false), _x43), _x23))	mark^#(if(if(true, false, _x33), _x22, _x23))	→	active^#(if(active(if(active(true), active(false), _x33)), _x22, _x23))
mark^#(if(true, if(false, f(_x81), _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(f(mark(_x81))), _x43)), X3))	mark^#(if(if(_x31, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(if(mark(_x41), c, f(true))), X3))
mark^#(if(if(_x81, true, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(true), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(true, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))
mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))	mark^#(if(if(_x31, _x32, _x33), f(_x41), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(active(f(mark(_x71))), c, f(true))), X3))	mark^#(if(if(mark(mark(_x41)), _x32, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), mark(if(mark(_x41), c, f(true))), _x23))
mark^#(if(c, f(_x41), mark(_x33)))	→	active^#(if(c, active(f(mark(_x41))), _x33))	mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), f(mark(_x41)), _x23))
mark^#(if(true, f(_x41), X3))	→	active^#(if(active(true), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x61), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x61)), X3))
mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))	mark^#(if(true, if(false, _x42, active(_x53)), _x23))	→	active^#(if(active(true), if(active(false), mark(_x42), _x53), _x23))
mark^#(if(if(_x31, false, _x53), false, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(false), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))	mark^#(if(if(c, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), f(_x61), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(_x61)), X3))
mark^#(if(if(_x31, false, _x53), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(f(_x91)), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(f(mark(_x91))))), _x23))
mark^#(if(if(mark(_x81), true, active(mark(_x43))), f(f(_x81)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))
mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))	mark^#(if(if(f(_x71), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(mark(false), true, active(mark(_x53))), f(f(false)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(true), c, f(true))))), _x23))	mark^#(if(if(mark(true), true, active(f(true))), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(if(mark(active(true)), mark(c), f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, false, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))
mark^#(if(if(_x31, true, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), active(f(mark(_x41))), X3))	mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(c, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x53))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(if(mark(mark(if(mark(_x71), c, f(true)))), mark(c), f(true))), X3))
mark^#(if(if(_x81, if(_x91, _x92, _x93), active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(if(mark(_x91), mark(_x92), _x93)), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x43))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(_x41, true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(if(_x31, _x62, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x61, if(_x81, true, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(if(_x51, _x32, _x53), X2, X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23))	→	active^#(if(if(_x51, active(true), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(true, true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(true, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(false, if(_x81, _x82, _x83), _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x43)), X3))
mark^#(if(if(_x31, false, _x53), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(c, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(_x81)))), X3))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(_x81, _x32, active(_x83)), f(if(_x91, _x92, _x93)), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(if(mark(_x91), mark(_x92), _x93)))), _x23))
mark^#(if(if(_x31, true, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(c, f(if(true, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(true), mark(_x62), _x63))), _x33))
mark^#(if(true, if(_x41, _x42, mark(_x63)), X3))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x63)), X3))	mark^#(if(if(_x31, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))
mark^#(if(true, if(false, false, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(active(false), active(false), _x43)), _x23))	mark^#(if(if(mark(_x71), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(f(_x91)), true, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), f(true), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(true))), X3))
mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(true, if(_x41, f(_x81), _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(f(mark(_x81))), _x43)), X3))
mark^#(if(if(mark(_x71), true, active(mark(mark(_x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(f(_x91)), true, active(mark(_x53))), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))	mark^#(if(true, if(false, true, _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(true), _x43)), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(true), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(f(f(_x61)), X2, X3))	→	active^#(if(active(f(active(f(mark(_x61))))), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(c))), f(f(_x71)), X3))	→	active^#(if(active(c), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x51), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(f(mark(_x71)))), X3))	mark^#(if(if(_x31, _x32, active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(mark(_x53))))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x53))	mark^#(if(if(_x31, true, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))
mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, false, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(true, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(false, _x32, active(_x41)), f(f(_x71)), X3))	→	active^#(if(mark(_x41), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, false, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(false), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(true, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x53)), mark(X2), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(false), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(false))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x91), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x91)), _x23))	mark^#(if(if(_x31, if(_x81, active(_x112), _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(true, _x32, active(_x41)), f(f(_x71)), X3))	→	active^#(if(mark(mark(_x32)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x61, if(_x81, _x102, _x103), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(mark(_x53)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(f(_x111), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))	mark^#(if(if(_x31, false, _x53), _x22, _x23))	→	active^#(if(active(if(mark(_x31), false, _x53)), _x22, _x23))
mark^#(if(if(_x61, false, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(false), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(mark(_x81), true, active(mark(_x53))), f(f(_x81)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(true, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, _x53), true, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(true), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(c), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(c))), _x23))
mark^#(if(f(_x31), _x22, _x23))	→	active^#(if(active(f(mark(_x31))), _x22, _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, c, _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(c), _x43)), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(_x53)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), f(mark(_x41)), _x53))
mark^#(if(if(_x31, if(c, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))
mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(mark(_x81)), _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))	mark^#(if(if(true, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, true, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(f(mark(_x91))))))), X3))
mark^#(if(if(_x41, true, active(active(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, true, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x111, _x112, _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x111, _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(false), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), _x23))	mark^#(if(if(_x31, _x32, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))
mark^#(if(true, if(_x41, _x42, _x43), _x23))	→	active^#(if(true, active(if(mark(_x41), mark(_x42), _x43)), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(false))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x53)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), f(mark(_x41)), _x53))	mark^#(if(if(_x61, false, _x63), X2, X3))	→	active^#(if(active(if(_x61, false, _x63)), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))
mark^#(if(X1, X2, X3))	→	mark^#(X2)	mark^#(if(true, if(false, f(_x71), _x43), _x23))	→	active^#(if(active(true), if(active(false), active(f(mark(_x71))), _x43), _x23))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), _x102, _x103), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(false), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(false))), _x23))
mark^#(if(if(_x31, false, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))	mark^#(if(true, X2, _x23))	→	active^#(if(true, mark(X2), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))
mark^#(if(if(mark(false), true, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23))	→	active^#(if(active(if(_x51, active(true), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, f(if(_x61, false, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(false), _x63))), _x33))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), mark(_x82), _x83), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(false, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(true, active(false), _x53)), mark(X2), X3))	mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))
mark^#(if(true, if(false, false, mark(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), active(false), _x63)), X3))	mark^#(if(if(_x31, _x32, _x33), f(c), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(c))), X3))
mark^#(if(f(_x31), X2, mark(_x23)))	→	active^#(if(active(f(mark(_x31))), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(if(active(true), c, f(true)))), X3))	mark^#(if(true, X2, active(_x23)))	→	active^#(if(active(true), mark(X2), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(mark(_x71), false, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(false), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(active(f(mark(_x71)))), _x23))
mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	mark^#(if(if(_x61, c, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(c), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(_x31, if(_x101, _x102, _x103), active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x101), mark(_x102), _x103)), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(true, _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(mark(_x32)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(if(_x31, if(c, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(mark(if(active(true), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(true), true, active(mark(_x53))), f(f(true)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(c, false, _x33), X2, X3))	→	active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(if(true, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(active(_x53))))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x53))	mark^#(if(if(if(_x61, _x62, _x63), false, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))
mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(if(_x31, if(false, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, false, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))	mark^#(if(if(_x31, if(true, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x81), _x32, active(active(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(true, _x22, _x23))	→	active^#(if(active(true), _x22, _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(f(mark(_x91))))))), X3))	mark^#(if(if(f(_x71), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(false, true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(mark(false), true, active(mark(_x43))), f(f(false)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(mark(c), true, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, c, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))
mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(c))))), X3))
mark^#(if(if(false, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(_x53)))	→	active^#(if(if(_x71, mark(_x32), _x73), active(f(mark(_x41))), _x53))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(true), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(true))), _x23))
mark^#(if(if(_x81, _x32, active(_x83)), f(c), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(c))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(active(f(mark(_x71))), c, f(true))), X3))
mark^#(if(c, f(if(if(_x81, _x82, _x83), _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(if(mark(_x81), mark(_x82), _x83)), mark(_x62), _x63))), _x33))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(f(_x91)), true, active(mark(_x43))), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(true, if(false, _x42, _x43), active(_x23)))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x43)), _x23))
mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(if(_x31, if(if(_x111, _x112, _x113), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(active(_x41), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(true, if(_x41, if(_x81, _x82, _x83), _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(if(mark(_x81), mark(_x82), _x83)), _x43)), X3))	mark^#(if(if(_x31, f(_x81), active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(_x41))), X3))
mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))	mark^#(if(if(mark(false), _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(_x61), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x63)))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x63))	mark^#(if(if(_x31, if(_x81, _x82, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, false, _x23))	→	active^#(if(active(c), false, _x23))	mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))
mark^#(if(c, f(if(_x61, _x62, mark(_x73))), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x73))), _x33))	mark^#(if(if(mark(_x71), c, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(c), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, c, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), active(f(mark(_x41))), X3))	mark^#(if(true, if(false, _x42, _x43), active(_x33)))	→	active^#(if(active(true), if(active(false), mark(_x42), _x43), _x33))
mark^#(if(true, true, X3))	→	active^#(if(active(true), active(true), X3))	mark^#(if(if(false, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), mark(if(mark(_x41), c, f(true))), _x23))	mark^#(if(if(_x31, if(_x81, c, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
active^#(f(X))	→	mark^#(if(X, c, f(true)))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(mark(if(active(true), c, f(true)))), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(true))))), X3))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(true), c, f(true))))), _x23))
mark^#(if(if(_x51, false, _x53), X2, X3))	→	active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(if(_x31, _x62, active(_x63)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), f(active(f(mark(_x71)))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(f(true))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(if(mark(_x71), c, f(true)), c, f(true))), X3))
mark^#(if(if(_x31, false, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(active(_x63))))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x63))
mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(f(_x111), true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(f(_x31), if(_x41, _x42, _x43), X3))	→	active^#(if(active(f(mark(_x31))), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(f(X))	→	mark^#(X)	mark^#(if(if(_x31, false, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))
mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))	mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))
mark^#(if(if(_x31, if(_x81, c, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(c), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(f(_x91)), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(f(mark(_x91))))), _x23))
mark^#(if(c, false, mark(active(_x23))))	→	active^#(if(c, active(false), _x23))	mark^#(if(if(f(_x61), false, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))
mark^#(if(if(mark(active(_x81)), _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(if(_x101, _x102, _x103)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x101), mark(_x102), _x103)))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), active(_x23)))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))
mark^#(if(if(f(_x61), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(_x81, f(_x91), active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(f(mark(_x91))), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(true, if(_x41, true, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(true), _x43)), X3))	mark^#(if(if(mark(_x71), true, active(mark(active(_x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, if(_x121, _x122, _x123), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(if(mark(_x121), mark(_x122), _x123)), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(mark(c), true, active(mark(_x53))), f(f(c)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(true, if(false, _x62, _x63), X3))	→	active^#(if(active(true), active(if(active(false), _x62, _x63)), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(true, if(false, _x42, _x43), _x23))	→	active^#(if(true, active(if(active(false), mark(_x42), _x43)), _x23))
mark^#(if(if(_x31, _x32, _x33), f(false), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(false))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(c, f(if(_x61, true, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(true), _x63))), _x33))	mark^#(if(if(true, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x51, _x32, _x53), f(_x41), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(f(_x31), X2, X3))	→	active^#(if(mark(if(mark(_x31), c, f(true))), mark(X2), X3))	mark^#(if(if(_x31, if(if(_x111, _x112, _x113), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))	mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))	mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(f(c), X2, X3))	→	active^#(if(active(f(active(c))), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(true, if(false, _x42, mark(_x53)), _x23))	→	active^#(if(active(true), if(active(false), mark(_x42), _x53), _x23))
mark^#(if(if(_x31, if(_x81, if(_x121, _x122, _x123), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(if(mark(_x121), mark(_x122), _x123)), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x112, active(_x113)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(mark(_x63))), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))	mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))
mark^#(if(true, false, X3))	→	active^#(if(active(true), active(false), X3))	mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))
mark^#(if(if(active(_x71), _x32, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(false))))), X3))
mark^#(if(if(_x31, _x62, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(X1, X2, X3))	→	mark^#(X1)
mark^#(if(if(_x31, if(_x81, _x82, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))
mark^#(if(c, X2, mark(mark(_x23))))	→	active^#(if(c, mark(X2), _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), active(true), _x83), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(true, _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(true), mark(_x42), _x43)), X3))
mark^#(if(if(_x31, true, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(if(_x71, _x72, _x73), if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23))	→	active^#(if(active(if(_x41, active(true), _x43)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(if(_x31, true, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), X3))	mark^#(if(true, if(false, _x42, mark(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x63)), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x23))	mark^#(if(if(_x31, f(_x81), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(true, if(false, false, _x63), X3))	→	active^#(if(active(true), active(if(false, active(false), _x63)), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(f(mark(_x91))), c, f(true))), c, f(true))), X3))	mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))
mark^#(if(if(c, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), true, active(active(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(if(mark(true), true, active(mark(_x43))), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(true, if(false, _x42, _x43), _x33))	→	active^#(if(true, if(active(false), mark(_x42), _x43), _x33))
mark^#(if(if(_x71, _x32, active(active(_x73))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(c), c, f(true))), c, f(true))), X3))
mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(true, if(_x41, _x42, active(_x63)), X3))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x63)), X3))
mark^#(if(if(_x31, false, _x53), c, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(c), X3))	mark^#(if(if(mark(_x71), true, active(mark(true))), f(f(_x71)), X3))	→	active^#(if(active(true), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(c, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, active(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), true, active(f(true))), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(c, f(if(_x61, if(_x91, _x92, _x93), _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(if(mark(_x91), mark(_x92), _x93)), _x63))), _x33))	mark^#(if(if(c, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(true, false, _x33), X2, _x23))	→	active^#(if(if(active(true), active(false), _x33), mark(X2), _x23))
mark^#(if(if(false, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(c, false, mark(_x23)))	→	active^#(if(active(c), active(false), _x23))
mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))
mark^#(if(if(_x31, if(_x101, true, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(false, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, false, mark(_x23)))	→	active^#(if(c, false, _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(if(_x71, _x72, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, _x72, _x73)), active(f(mark(_x41))), _x23))	mark^#(if(true, if(false, false, active(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), active(false), _x63)), X3))
mark^#(if(if(if(_x71, _x72, _x73), false, _x53), X2, X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), false, _x53)), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(if(_x41, _x42, _x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x41), mark(_x42), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(true), true, active(_x31)), f(f(true)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(false, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
active^#(if(true, X, Y))	→	mark^#(X)	mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))
mark^#(if(f(_x31), X2, active(_x23)))	→	active^#(if(active(f(mark(_x31))), mark(X2), _x23))	mark^#(if(if(_x81, c, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(c), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, true, _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(false, true, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(true), _x43), _x23))
mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(if(_x31, c, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, false, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(false), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, f(_x81), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x81), true, active(mark(_x31))), f(f(_x81)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))
mark^#(if(if(c, false, _x53), X2, X3))	→	active^#(if(active(if(active(c), false, _x53)), mark(X2), X3))	mark^#(if(if(mark(_x71), f(_x101), active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(f(mark(_x101))), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x61, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))
mark^#(if(if(_x31, _x32, mark(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(true, if(false, _x42, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x43)), _x23))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x81), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(_x81)), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(c))))), X3))	mark^#(if(if(mark(_x41), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(true, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(_x41, false, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(false), _x43)), X3))	mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(if(_x91, _x92, _x93)), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(if(mark(_x91), mark(_x92), _x93)))), _x23))
mark^#(if(if(c, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(mark(c), true, active(mark(_x31))), f(f(c)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(c, if(_x41, _x42, _x43), mark(_x33)))	→	active^#(if(c, active(if(mark(_x41), mark(_x42), _x43)), _x33))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(f(mark(_x71)))), X3))
mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))	mark^#(if(if(_x51, _x32, active(active(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(true, if(false, c, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(c), _x43), _x23))	mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))
mark^#(if(true, if(false, false, _x43), active(_x23)))	→	active^#(if(active(true), active(if(active(false), active(false), _x43)), _x23))	mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(f(_x91), _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(f(mark(_x91))), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x51, _x52, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, _x52, _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, _x52, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))	mark^#(if(if(true, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, if(_x71, _x72, _x73), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x71), mark(_x72), _x73)), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(active(_x53))))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x53))
mark^#(if(if(_x31, _x32, active(_x53)), f(c), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), _x23))	mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))
mark^#(if(if(mark(_x71), if(_x101, _x102, _x103), active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(if(mark(_x101), mark(_x102), _x103)), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(c, f(if(_x61, _x62, _x63)), active(active(_x23))))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x23))
mark^#(if(if(mark(false), true, active(mark(_x31))), f(f(false)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(true, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), _x23))
mark^#(if(c, c, mark(_x33)))	→	active^#(if(c, active(c), _x33))	mark^#(if(if(_x31, if(false, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(false, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(if(_x31, false, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(active(f(mark(_x71)))), _x23))
mark^#(if(c, f(if(_x61, f(_x91), _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(f(mark(_x91))), _x63))), _x33))	mark^#(if(if(f(_x71), _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(if(_x71, _x72, _x73)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))	mark^#(if(if(_x31, _x32, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), _x23))	→	active^#(if(mark(_x31), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(true, if(_x41, _x62, _x63), X3))	→	active^#(if(active(true), active(if(mark(_x41), _x62, _x63)), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, f(_x101), active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x101))), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(c))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(if(_x121, _x122, _x123), _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x121), mark(_x122), _x123)), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, mark(_x32), _x63), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(mark(true), true, active(mark(_x31))), f(f(true)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(_x41, _x42, _x43), _x23))	→	active^#(if(active(true), if(mark(_x41), mark(_x42), _x43), _x23))	mark^#(if(if(active(_x51), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(active(_x53)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), mark(_x82), _x83), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, c, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(mark(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(mark(_x71), true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x31))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(_x31, if(c, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(c), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), X3))	mark^#(if(if(_x31, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))
mark^#(if(true, if(false, _x42, _x63), X3))	→	active^#(if(active(true), active(if(false, mark(_x42), _x63)), X3))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(_x81), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(_x81)), _x23))	mark^#(if(c, f(if(f(_x81), _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(f(mark(_x81))), mark(_x62), _x63))), _x33))
mark^#(if(if(_x31, _x32, _x33), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))
mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(true, if(false, _x52, _x53), _x23))	→	active^#(if(active(true), if(active(false), _x52, _x53), _x23))	mark^#(if(if(_x31, _x32, active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, _x53), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))	mark^#(if(if(_x31, if(_x101, _x82, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x63)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x63))	mark^#(if(if(_x31, if(_x81, true, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(true, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(if(_x31, if(_x81, mark(_x112), _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))	mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))
mark^#(if(if(mark(_x71), _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(true, if(false, _x42, _x43), mark(_x33)))	→	active^#(if(active(true), if(active(false), mark(_x42), _x43), _x33))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), if(mark(if(mark(_x71), c, f(true))), c, f(true)), _x23))
mark^#(if(if(c, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	active^#(if(false, X, Y))	→	mark^#(Y)
mark^#(if(if(c, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(true, if(f(_x71), _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(f(mark(_x71))), mark(_x42), _x43)), X3))
mark^#(if(true, if(false, _x42, active(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x63)), X3))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(true, c, f(true))))), X3))
mark^#(if(f(false), X2, X3))	→	active^#(if(active(f(active(false))), mark(X2), X3))	mark^#(if(f(_x31), X2, _x23))	→	active^#(if(f(mark(_x31)), mark(X2), _x23))
mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(active(true), false, _x53)), mark(X2), X3))	mark^#(if(if(_x31, false, mark(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))
mark^#(if(if(_x31, f(_x71), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))	mark^#(if(if(mark(true), true, active(_x43)), f(f(true)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(true, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x82, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), _x82, _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x21))), f(f(_x71)), _x23))	→	active^#(if(_x21, active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, if(_x81, true, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), true, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(if(_x61, c, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(c), _x63))), _x33))	mark^#(if(if(_x31, if(c, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x23)))	→	active^#(if(c, f(active(if(mark(_x61), mark(_x62), _x63))), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), mark(_x23)))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, false, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))
mark^#(if(if(mark(true), true, active(active(_x43))), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))
mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))	mark^#(if(c, f(if(false, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(false), mark(_x62), _x63))), _x33))
mark^#(if(c, f(if(_x71, _x62, _x73)), active(_x33)))	→	active^#(if(active(c), f(active(if(_x71, mark(_x62), _x73))), _x33))	mark^#(if(if(mark(c), true, active(mark(_x43))), f(f(c)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))
mark^#(if(if(true, false, active(_x53)), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x53)), mark(X2), X3))	mark^#(if(if(true, false, _x33), true, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(true), X3))
mark^#(if(if(true, false, _x33), f(_x41), X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(f(mark(_x41))), X3))	mark^#(if(f(_x31), false, X3))	→	active^#(if(active(f(mark(_x31))), active(false), X3))
mark^#(if(if(mark(f(_x91)), true, active(mark(_x31))), f(f(f(_x91))), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(active(if(mark(mark(_x71)), mark(c), f(true))), c, f(true))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x23))	mark^#(if(if(false, false, _x53), X2, X3))	→	active^#(if(active(if(active(false), false, _x53)), mark(X2), X3))
mark^#(if(if(mark(true), true, active(_x31)), f(f(true)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23))	→	active^#(if(if(_x41, active(true), _x43), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x81), true, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(mark(if(active(true), c, f(true))))), _x23))
mark^#(if(if(_x61, _x32, active(_x63)), f(_x41), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(_x41))), X3))	mark^#(if(if(f(_x71), if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x41, true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x61, f(_x71), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(f(mark(_x71))), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(f(_x71), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x101)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x101))))), _x23))	mark^#(if(if(mark(true), true, active(_x43)), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, if(false, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(mark(_x63))))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x63))	mark^#(if(if(_x31, if(f(_x111), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, false, _x63), X3))	→	active^#(if(active(true), active(if(active(false), false, _x63)), X3))	mark^#(if(if(_x31, c, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x53)))	→	active^#(if(if(_x81, mark(_x32), _x83), active(f(mark(_x41))), _x53))	mark^#(if(c, f(if(_x61, _x62, _x63)), active(mark(_x23))))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x23))
mark^#(if(if(_x31, c, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(true), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), _x23))
mark^#(if(if(_x31, _x32, active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, _x32, _x33), f(if(_x71, _x72, _x73)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(_x81)))), X3))	mark^#(if(f(if(_x61, _x62, _x63)), X2, X3))	→	active^#(if(active(f(active(if(mark(_x61), mark(_x62), _x63)))), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, c, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(c), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(f(_x51), X2, X3))	→	active^#(if(active(f(_x51)), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(true, if(_x41, _x42, _x43), active(_x23)))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x43)), _x23))
mark^#(if(if(true, false, _x33), false, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(false), X3))	mark^#(if(if(_x31, _x52, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(false, _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(_x61), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, f(_x121), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(f(mark(_x121))), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(false))), f(f(_x71)), X3))	→	active^#(if(active(false), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(mark(_x71), true, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(true), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(_x81)))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(false), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), X3))	mark^#(if(if(_x61, true, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(f(mark(_x91))))))), X3))
mark^#(if(if(_x31, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(if(_x31, f(_x71), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), active(f(mark(_x41))), X3))
mark^#(if(c, f(if(_x61, _x62, active(_x73))), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x73))), _x33))	mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), _x23))	mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(if(_x31, if(_x81, c, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(_x81, c, f(true))), c, f(true))), X3))	mark^#(if(if(_x51, _x32, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, f(_x121), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(f(mark(_x121))), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(c, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(c), mark(_x62), _x63))), _x33))
mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(false))))), X3))
mark^#(f(X))	→	active^#(f(mark(X)))	mark^#(if(c, X2, mark(active(_x23))))	→	active^#(if(c, mark(X2), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(false), c, f(true))), c, f(true))), X3))	mark^#(if(true, X2, mark(_x23)))	→	active^#(if(active(true), mark(X2), _x23))
mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(if(true, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(f(true), X2, X3))	→	active^#(if(active(f(active(true))), mark(X2), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(c, false, mark(mark(_x23))))	→	active^#(if(c, active(false), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), X3))
mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(if(_x31, if(f(_x121), _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x121))), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(true), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x81), _x32, active(mark(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

The right-hand side of the rule mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3)) 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 Terms	Irrelevant Terms
active^#(if(if(_x51, active(true), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(if(_x51, active(true), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))
active^#(if(active(if(_x51, active(true), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(if(_x51, active(true), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
active^#(if(active(if(_x51, active(true), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))

Thus, the rule mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3)) is replaced by the following rules:

mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(_x71), true, active(mark(active(_x43)))), f(f(_x71)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(true), true, active(mark(_x53))), f(f(true)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(mark(c), true, active(mark(_x53))), f(f(c)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x53))), f(f(if(_x91, _x92, _x93))), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(mark(_x81), true, active(mark(_x53))), f(f(_x81)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), mark(_x23))) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), active(_x23))) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(mark(_x43)))), f(f(_x71)), X3)) → active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(f(_x91)), true, active(mark(_x53))), f(f(f(_x91))), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3)) → active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23)) → active^#(if(if(_x51, active(true), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23)) → active^#(if(active(if(_x51, active(true), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(if(mark(false), true, active(mark(_x53))), f(f(false)), X3)) → active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))

Problem 33: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(active(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(_x31, if(true, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x71, _x32, active(mark(_x73))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(c, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(mark(f(_x41)))), f(f(_x71)), X3))	→	active^#(if(active(f(mark(_x41))), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(_x81, _x82, _x83)), active(_x23)))	→	active^#(if(active(c), active(f(active(if(mark(_x81), mark(_x82), _x83)))), _x23))
mark^#(if(if(mark(_x71), true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x81), _x82, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, _x82, _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(true, false, _x33), c, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(c), X3))	mark^#(if(true, if(if(_x71, _x72, _x73), _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x42), _x43)), X3))
mark^#(if(true, if(false, if(_x71, _x72, _x73), _x43), _x23))	→	active^#(if(active(true), if(active(false), active(if(mark(_x71), mark(_x72), _x73)), _x43), _x23))	mark^#(if(true, if(c, _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(c), mark(_x42), _x43)), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), mark(if(active(f(mark(_x71))), c, f(true))), X3))	mark^#(if(if(_x31, true, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(true, if(_x41, _x42, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x43)), _x23))	mark^#(if(true, if(_x61, _x42, _x63), X3))	→	active^#(if(active(true), active(if(_x61, mark(_x42), _x63)), X3))
mark^#(if(if(_x31, false, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(if(_x111, _x112, _x113), true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(f(_x71), false, _x53), X2, X3))	→	active^#(if(active(if(active(f(mark(_x71))), false, _x53)), mark(X2), X3))	mark^#(if(if(false, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(f(_x31), f(_x41), X3))	→	active^#(if(active(f(mark(_x31))), active(f(mark(_x41))), X3))	mark^#(if(true, c, X3))	→	active^#(if(active(true), active(c), X3))
mark^#(if(c, true, X3))	→	active^#(if(active(c), active(true), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(f(mark(_x71)))), X3))
mark^#(if(if(_x31, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(X1, true, X3))	→	active^#(if(mark(X1), active(true), X3))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(if(mark(_x61), mark(_x62), _x63)), _x33))	mark^#(if(if(mark(true), _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(mark(_x32)), active(f(mark(_x41))), _x23))
mark^#(if(if(false, false, _x33), X2, X3))	→	active^#(if(active(if(active(false), active(false), _x33)), mark(X2), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(mark(_x53))))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x53))
mark^#(if(if(false, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))
mark^#(if(X1, c, _x23))	→	active^#(if(mark(X1), c, _x23))	mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x101, _x82, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(f(_x71), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(false, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, false, _x43), _x23))	→	active^#(if(true, active(if(active(false), active(false), _x43)), _x23))	mark^#(if(if(_x81, false, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(false), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(if(_x61, _x72, _x73)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), _x72, _x73))), _x33))	mark^#(if(if(_x31, _x32, active(active(_x63))), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(if(_x61, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x112, mark(_x113)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(_x41, c, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(c), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(if(_x91, _x92, _x93), _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(if(mark(_x91), mark(_x92), _x93)), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(false, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, _x32, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))	mark^#(if(if(f(_x61), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(c, f(_x71), active(_x33)))	→	active^#(if(c, active(f(_x71)), _x33))	mark^#(if(c, true, mark(_x33)))	→	active^#(if(c, active(true), _x33))
mark^#(if(true, if(false, _x42, _x53), _x23))	→	active^#(if(active(true), if(false, mark(_x42), _x53), _x23))	mark^#(if(f(_x31), true, X3))	→	active^#(if(active(f(mark(_x31))), active(true), X3))
mark^#(if(if(_x31, false, _x53), X2, _x23))	→	active^#(if(if(mark(_x31), false, _x53), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(f(_x71), if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(true), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(true))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))
mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), mark(X2), X3))	mark^#(if(true, if(false, false, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(false), _x43), _x23))
mark^#(if(if(true, false, _x33), _x22, _x23))	→	active^#(if(active(if(active(true), active(false), _x33)), _x22, _x23))	mark^#(if(true, if(false, f(_x81), _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(f(mark(_x81))), _x43)), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(if(mark(_x41), c, f(true))), X3))	mark^#(if(if(_x81, true, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(true), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(true, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(c, c, _x23))	→	active^#(if(c, active(c), _x23))	mark^#(if(X1, false, X3))	→	active^#(if(mark(X1), active(false), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x41), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(active(f(mark(_x71))), c, f(true))), X3))
mark^#(if(if(mark(mark(_x41)), _x32, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), mark(if(mark(_x41), c, f(true))), _x23))	mark^#(if(c, f(_x41), mark(_x33)))	→	active^#(if(c, active(f(mark(_x41))), _x33))
mark^#(if(if(_x31, _x32, _x33), f(_x41), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), f(mark(_x41)), _x23))	mark^#(if(true, f(_x41), X3))	→	active^#(if(active(true), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x61), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x61)), X3))	mark^#(if(X1, _x22, _x23))	→	active^#(if(mark(X1), _x22, _x23))
mark^#(if(true, if(false, _x42, active(_x53)), _x23))	→	active^#(if(active(true), if(active(false), mark(_x42), _x53), _x23))	mark^#(if(if(_x31, false, _x53), false, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(false), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, f(_x71), active(active(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, if(_x41, _x42, _x43), X3))	→	active^#(if(active(c), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, f(true), active(_x33)))	→	active^#(if(active(c), f(active(true)), _x33))
mark^#(if(if(c, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(_x61), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(_x61)), X3))	mark^#(if(if(_x31, false, _x53), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(f(_x91)), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(f(mark(_x91))))), _x23))	mark^#(if(if(mark(_x81), true, active(mark(_x43))), f(f(_x81)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x33), mark(X2), _x23))	mark^#(if(c, true, active(_x23)))	→	active^#(if(active(c), active(true), _x23))
mark^#(if(if(f(_x71), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(mark(false), true, active(mark(_x53))), f(f(false)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(true), c, f(true))))), _x23))
mark^#(if(if(mark(true), true, active(f(true))), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(if(mark(active(true)), mark(c), f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, false, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(c), X3))	mark^#(if(if(_x31, true, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), active(f(mark(_x41))), X3))
mark^#(if(c, c, X3))	→	active^#(if(active(c), active(c), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(c, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x53))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(if(mark(mark(if(mark(_x71), c, f(true)))), mark(c), f(true))), X3))	mark^#(if(if(_x81, if(_x91, _x92, _x93), active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(if(mark(_x91), mark(_x92), _x93)), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x43))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(_x41, true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(false, c, active(_x23)))	→	active^#(if(active(false), active(c), _x23))	mark^#(if(if(_x31, _x62, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x61, if(_x81, true, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), mark(X2), _x23))
mark^#(if(if(_x51, _x32, _x53), X2, X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), mark(X2), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23))	→	active^#(if(if(_x51, active(true), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(true, true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(true, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, if(_x81, _x82, _x83), _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(if(mark(_x81), mark(_x82), _x83)), _x43)), X3))	mark^#(if(if(_x31, false, _x53), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(c, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(_x81)))), X3))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(if(_x81, _x32, active(_x83)), f(if(_x91, _x92, _x93)), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(if(mark(_x91), mark(_x92), _x93)))), _x23))	mark^#(if(if(_x31, true, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(if(true, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(true), mark(_x62), _x63))), _x33))	mark^#(if(true, if(_x41, _x42, mark(_x63)), X3))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x63)), X3))
mark^#(if(if(_x31, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))	mark^#(if(true, if(false, false, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(active(false), active(false), _x43)), _x23))
mark^#(if(if(mark(_x71), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(f(_x91)), true, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(true), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(true))), X3))	mark^#(if(c, mark(active(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(true, if(_x41, f(_x81), _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(f(mark(_x81))), _x43)), X3))	mark^#(if(if(mark(_x71), true, active(mark(mark(_x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(f(_x91)), true, active(mark(_x53))), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(c, f(c), active(_x23)))	→	active^#(if(active(c), active(f(active(c))), _x23))
mark^#(if(true, if(false, true, _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(true), _x43)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(true), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(f(f(_x61)), X2, X3))	→	active^#(if(active(f(active(f(mark(_x61))))), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(c))), f(f(_x71)), X3))	→	active^#(if(active(c), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x51), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(f(mark(_x71)))), X3))
mark^#(if(if(_x31, _x32, active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(mark(_x53))))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x53))
mark^#(if(if(_x31, true, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(true), _x33)), mark(X2), X3))	mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, false, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(true, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(false, _x32, active(_x41)), f(f(_x71)), X3))	→	active^#(if(mark(_x41), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, false, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(false), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x53)), mark(X2), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(false), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(false))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x91), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(_x91)), _x23))
mark^#(if(if(_x31, if(_x81, active(_x112), _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(true, _x32, active(_x41)), f(f(_x71)), X3))	→	active^#(if(mark(mark(_x32)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x61, if(_x81, _x102, _x103), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(mark(_x53)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, if(f(_x111), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(c, X2, active(active(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(c, f(false), active(_x33)))	→	active^#(if(active(c), f(active(false)), _x33))
mark^#(if(if(_x31, false, _x53), _x22, _x23))	→	active^#(if(active(if(mark(_x31), false, _x53)), _x22, _x23))	mark^#(if(if(_x61, false, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(false), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(mark(_x81), true, active(mark(_x53))), f(f(_x81)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, mark(mark(_x22)), mark(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(true, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, _x53), true, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(true), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(c), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(c))), _x23))	mark^#(if(f(_x31), _x22, _x23))	→	active^#(if(active(f(mark(_x31))), _x22, _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(false, c, _x43), X3))	→	active^#(if(active(true), active(if(active(false), active(c), _x43)), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(_x53)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), f(mark(_x41)), _x53))	mark^#(if(if(_x31, if(c, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))	mark^#(if(if(_x31, if(_x71, _x72, _x73), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x71), mark(_x72), _x73)), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(mark(_x81)), _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(true), X3))
mark^#(if(if(true, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, true, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(f(mark(_x91))))))), X3))	mark^#(if(if(_x41, true, active(active(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, true, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x111, _x112, _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x111, _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(false), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), _x23))
mark^#(if(if(_x31, _x32, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(false), X3))	mark^#(if(true, if(_x41, _x42, _x43), _x23))	→	active^#(if(true, active(if(mark(_x41), mark(_x42), _x43)), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(false))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x53)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), f(mark(_x41)), _x53))
mark^#(if(if(_x61, false, _x63), X2, X3))	→	active^#(if(active(if(_x61, false, _x63)), mark(X2), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(c, false, active(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(X1, X2, X3))	→	mark^#(X2)
mark^#(if(true, if(false, f(_x71), _x43), _x23))	→	active^#(if(active(true), if(active(false), active(f(mark(_x71))), _x43), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), _x102, _x103), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(false), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(false))), _x23))	mark^#(if(if(_x31, false, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), _x22, _x23))
mark^#(if(true, X2, _x23))	→	active^#(if(true, mark(X2), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(active(f(mark(_x71))))), _x23))
mark^#(if(_x21, c, _x23))	→	active^#(if(_x21, active(c), _x23))	mark^#(if(if(mark(false), true, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), _x23))	→	active^#(if(active(if(_x51, active(true), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, f(if(_x61, false, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(false), _x63))), _x33))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), mark(_x82), _x83), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(false, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(true, active(false), _x53)), mark(X2), X3))
mark^#(if(_x21, X2, _x23))	→	active^#(if(_x21, mark(X2), _x23))	mark^#(if(true, if(false, false, mark(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), active(false), _x63)), X3))
mark^#(if(if(_x31, _x32, _x33), f(c), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(c))), X3))	mark^#(if(f(_x31), X2, mark(_x23)))	→	active^#(if(active(f(mark(_x31))), mark(X2), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(if(active(true), c, f(true)))), X3))
mark^#(if(true, X2, active(_x23)))	→	active^#(if(active(true), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(mark(_x71), false, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(false), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(c, f(_x51), active(mark(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(active(f(mark(_x71)))), _x23))	mark^#(if(c, f(active(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(_x61, c, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(c), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(c, c, active(_x23)))	→	active^#(if(active(c), active(c), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, mark(_x22), _x23))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, if(_x101, _x102, _x103), active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x101), mark(_x102), _x103)), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(true, _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(mark(_x32)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, if(c, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(mark(if(active(true), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(true), true, active(mark(_x53))), f(f(true)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(c, false, _x33), X2, X3))	→	active^#(if(active(if(active(c), active(false), _x33)), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, _x32, mark(active(_x33))))	→	active^#(if(c, _x32, _x33))
mark^#(if(if(true, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(active(_x53))))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x53))
mark^#(if(if(if(_x61, _x62, _x63), false, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), active(false), _x33)), mark(X2), X3))	mark^#(if(c, if(_x51, _x52, _x53), _x23))	→	active^#(if(c, active(if(mark(_x51), mark(_x52), _x53)), _x23))
mark^#(if(if(_x31, if(false, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, false, _x33), false, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(false), X3))
mark^#(if(if(_x31, if(true, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x81), _x32, active(active(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, _x22, _x23))	→	active^#(if(active(true), _x22, _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(f(mark(_x91))))))), X3))
mark^#(if(if(f(_x71), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(false, true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(mark(false), true, active(mark(_x43))), f(f(false)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(mark(c), true, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(_x31, c, _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), mark(X2), X3))	mark^#(if(c, mark(_x22), mark(mark(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(c))))), X3))	mark^#(if(if(false, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x41), active(_x53)))	→	active^#(if(if(_x71, mark(_x32), _x73), active(f(mark(_x41))), _x53))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(true), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(true))), _x23))	mark^#(if(if(_x81, _x32, active(_x83)), f(c), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(c))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(active(f(mark(_x71))), c, f(true))), X3))	mark^#(if(c, f(if(if(_x81, _x82, _x83), _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(if(mark(_x81), mark(_x82), _x83)), mark(_x62), _x63))), _x33))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(f(_x91)), true, active(mark(_x43))), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(true, if(false, _x42, _x43), active(_x23)))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x43)), _x23))	mark^#(if(X1, c, active(_x23)))	→	active^#(if(mark(X1), active(c), _x23))
mark^#(if(if(_x31, if(if(_x111, _x112, _x113), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(active(_x41), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, _x32, mark(mark(_x33))))	→	active^#(if(c, _x32, _x33))	mark^#(if(true, if(_x41, if(_x81, _x82, _x83), _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(if(mark(_x81), mark(_x82), _x83)), _x43)), X3))
mark^#(if(if(_x31, f(_x81), active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(_x41))), X3))	mark^#(if(c, f(_x51), active(active(_x23))))	→	active^#(if(active(c), f(mark(_x51)), _x23))
mark^#(if(if(mark(false), _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(_x61), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x63)))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x63))
mark^#(if(if(_x31, if(_x81, _x82, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, false, _x23))	→	active^#(if(active(c), false, _x23))
mark^#(if(c, f(_x51), active(active(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(c, f(if(_x61, _x62, mark(_x73))), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x73))), _x33))
mark^#(if(if(mark(_x71), c, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(c), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, c, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x33)), active(f(mark(_x41))), X3))
mark^#(if(true, if(false, _x42, _x43), active(_x33)))	→	active^#(if(active(true), if(active(false), mark(_x42), _x43), _x33))	mark^#(if(true, true, X3))	→	active^#(if(active(true), active(true), X3))
mark^#(if(if(false, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), mark(if(mark(_x41), c, f(true))), _x23))
mark^#(if(if(_x31, if(_x81, c, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	active^#(f(X))	→	mark^#(if(X, c, f(true)))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(mark(if(active(true), c, f(true)))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(true))))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(true), c, f(true))))), _x23))	mark^#(if(if(_x51, false, _x53), X2, X3))	→	active^#(if(active(if(_x51, active(false), _x53)), mark(X2), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(_x31, _x62, active(_x63)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(c, _x22, active(_x23)))	→	active^#(if(c, _x22, _x23))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), f(active(f(mark(_x71)))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(f(true))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(if(mark(_x71), c, f(true)), c, f(true))), X3))	mark^#(if(if(_x31, false, _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(active(_x63))))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x63))	mark^#(if(c, X2, mark(_x23)))	→	active^#(if(active(c), mark(X2), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(f(_x111), true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(f(_x31), if(_x41, _x42, _x43), X3))	→	active^#(if(active(f(mark(_x31))), active(if(mark(_x41), mark(_x42), _x43)), X3))	mark^#(f(X))	→	mark^#(X)
mark^#(if(if(_x31, false, _x33), X2, _x23))	→	active^#(if(if(mark(_x31), active(false), _x33), mark(X2), _x23))	mark^#(if(c, X2, active(_x33)))	→	active^#(if(c, mark(X2), _x33))
mark^#(if(c, f(_x51), active(_x33)))	→	active^#(if(c, active(f(mark(_x51))), _x33))	mark^#(if(if(_x31, if(_x81, c, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(c), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(f(_x91)), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(active(f(mark(_x91))))), _x23))	mark^#(if(c, false, mark(active(_x23))))	→	active^#(if(c, active(false), _x23))
mark^#(if(if(f(_x61), false, _x33), X2, X3))	→	active^#(if(active(if(active(f(mark(_x61))), active(false), _x33)), mark(X2), X3))	mark^#(if(if(mark(active(_x81)), _x32, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(if(_x101, _x102, _x103)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x101), mark(_x102), _x103)))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), active(_x23)))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(c, active(_x32), mark(_x33)))	→	active^#(if(c, _x32, _x33))	mark^#(if(if(f(_x61), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(f(mark(_x61))), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x81, f(_x91), active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(f(mark(_x91))), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(true, if(_x41, true, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(true), _x43)), X3))
mark^#(if(if(mark(_x71), true, active(mark(active(_x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, if(_x121, _x122, _x123), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(if(mark(_x121), mark(_x122), _x123)), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(c), true, active(mark(_x53))), f(f(c)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(true, if(false, _x62, _x63), X3))	→	active^#(if(active(true), active(if(active(false), _x62, _x63)), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(true, if(false, _x42, _x43), _x23))	→	active^#(if(true, active(if(active(false), mark(_x42), _x43)), _x23))	mark^#(if(if(_x31, _x32, _x33), f(false), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(false))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(c, f(if(_x61, true, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(true), _x63))), _x33))
mark^#(if(if(true, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x51, _x32, _x53), f(_x41), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(f(_x31), X2, X3))	→	active^#(if(mark(if(mark(_x31), c, f(true))), mark(X2), X3))
mark^#(if(if(_x31, if(if(_x111, _x112, _x113), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x111), mark(_x112), _x113)), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(true), active(_x23)))	→	active^#(if(active(c), active(f(active(true))), _x23))
mark^#(if(c, f(_x51), active(mark(_x33))))	→	active^#(if(active(c), active(f(mark(_x51))), _x33))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), _x23))
mark^#(if(if(if(_x71, _x72, _x73), _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(f(c), X2, X3))	→	active^#(if(active(f(active(c))), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(true, if(false, _x42, mark(_x53)), _x23))	→	active^#(if(active(true), if(active(false), mark(_x42), _x53), _x23))	mark^#(if(if(_x31, if(_x81, if(_x121, _x122, _x123), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(if(mark(_x121), mark(_x122), _x123)), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x112, active(_x113)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(mark(_x63))), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(X1, f(_x41), X3))	→	active^#(if(mark(X1), active(f(mark(_x41))), X3))	mark^#(if(true, false, X3))	→	active^#(if(active(true), active(false), X3))
mark^#(if(c, f(false), active(_x23)))	→	active^#(if(active(c), active(f(active(false))), _x23))	mark^#(if(if(active(_x71), _x32, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(active(false))))), X3))	mark^#(if(if(_x31, _x62, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), _x62, _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(X1, X2, X3))	→	mark^#(X1)	mark^#(if(if(_x31, if(_x81, _x82, active(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(f(_x31), c, X3))	→	active^#(if(active(f(mark(_x31))), active(c), X3))	mark^#(if(c, X2, mark(mark(_x23))))	→	active^#(if(c, mark(X2), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(c, f(mark(_x51)), _x23))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), active(true), _x83), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(true, _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(true), mark(_x42), _x43)), X3))	mark^#(if(if(_x31, true, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(if(_x71, _x72, _x73), if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(c), active(_x33)))	→	active^#(if(active(c), f(active(c)), _x33))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23))	→	active^#(if(active(if(_x41, active(true), _x43)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(_x31, true, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(true), _x53)), active(f(mark(_x41))), X3))
mark^#(if(true, if(false, _x42, mark(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x63)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x23))
mark^#(if(if(_x31, f(_x81), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(false, false, _x63), X3))	→	active^#(if(active(true), active(if(false, active(false), _x63)), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(f(mark(_x91))), c, f(true))), c, f(true))), X3))
mark^#(if(c, c, _x23))	→	active^#(if(active(c), c, _x23))	mark^#(if(if(c, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(active(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(c, f(active(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))	mark^#(if(if(mark(true), true, active(mark(_x43))), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(true, if(false, _x42, _x43), _x33))	→	active^#(if(true, if(active(false), mark(_x42), _x43), _x33))	mark^#(if(if(_x71, _x32, active(active(_x73))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(c), c, f(true))), c, f(true))), X3))	mark^#(if(false, c, mark(_x23)))	→	active^#(if(active(false), active(c), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(_x41, _x42, active(_x63)), X3))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x63)), X3))	mark^#(if(if(_x31, false, _x53), c, X3))	→	active^#(if(active(if(mark(_x31), false, _x53)), active(c), X3))
mark^#(if(if(mark(_x71), true, active(mark(true))), f(f(_x71)), X3))	→	active^#(if(active(true), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(c, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, false, active(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(c, f(_x41), X3))	→	active^#(if(active(c), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(f(true))), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(c, f(if(_x61, if(_x91, _x92, _x93), _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(if(mark(_x91), mark(_x92), _x93)), _x63))), _x33))
mark^#(if(if(c, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(true, false, _x33), X2, _x23))	→	active^#(if(if(active(true), active(false), _x33), mark(X2), _x23))	mark^#(if(if(false, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), _x23))
mark^#(if(c, false, mark(_x23)))	→	active^#(if(active(c), active(false), _x23))	mark^#(if(c, f(f(_x81)), active(_x23)))	→	active^#(if(active(c), active(f(active(f(mark(_x81))))), _x23))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(mark(_x51), c, f(true))), _x23))	mark^#(if(if(_x31, if(_x101, true, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, active(true), _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(X1, X2, mark(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(false, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(if(_x61, _x62, _x63), _x32, _x33), X2, X3))	→	active^#(if(active(if(active(if(mark(_x61), mark(_x62), _x63)), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), mark(_x23)))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, false, mark(_x23)))	→	active^#(if(c, false, _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x71, _x72, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, _x72, _x73)), active(f(mark(_x41))), _x23))
mark^#(if(true, if(false, false, active(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), active(false), _x63)), X3))	mark^#(if(if(if(_x71, _x72, _x73), false, _x53), X2, X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), false, _x53)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(if(_x41, _x42, _x43)))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x41), mark(_x42), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(true), true, active(_x31)), f(f(true)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(f(_x91))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(c, f(_x41), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(if(_x71, _x72, _x73), if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(if(mark(_x71), mark(_x72), _x73)), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(false, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	active^#(if(true, X, Y))	→	mark^#(X)
mark^#(if(c, f(_x71), active(mark(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(f(_x31), X2, active(_x23)))	→	active^#(if(active(f(mark(_x31))), mark(X2), _x23))
mark^#(if(if(_x81, c, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, active(c), _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, true, _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(true, if(false, true, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(true), _x43), _x23))	mark^#(if(c, f(mark(_x61)), active(_x23)))	→	active^#(if(active(c), active(f(_x61)), _x23))
mark^#(if(if(_x31, c, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, false, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(false), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, f(_x81), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x81))), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x81), true, active(mark(_x31))), f(f(_x81)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(c, _x32, active(_x33)))	→	active^#(if(active(c), _x32, _x33))	mark^#(if(if(c, false, _x53), X2, X3))	→	active^#(if(active(if(active(c), false, _x53)), mark(X2), X3))
mark^#(if(if(mark(_x71), f(_x101), active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(f(mark(_x101))), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x61, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x81), mark(_x82), _x83)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(_x51), active(_x23)))	→	active^#(if(active(c), mark(if(_x51, c, f(true))), _x23))	mark^#(if(if(_x31, _x32, mark(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(true, if(false, _x42, _x43), mark(_x23)))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x43)), _x23))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(_x81), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(_x81)), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(c))))), X3))
mark^#(if(if(mark(_x41), true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, _x32, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(c, X2, active(mark(_x33))))	→	active^#(if(active(c), mark(X2), _x33))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(true, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(true), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(true, if(_x41, false, _x43), X3))	→	active^#(if(active(true), active(if(mark(_x41), active(false), _x43)), X3))
mark^#(if(c, f(_x51), _x23))	→	active^#(if(c, active(f(mark(_x51))), _x23))	mark^#(if(if(_x61, true, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(if(mark(_x91), mark(_x92), _x93)))))), X3))
mark^#(if(if(mark(_x71), _x32, active(_x73)), f(if(_x91, _x92, _x93)), active(_x23)))	→	active^#(if(active(if(_x71, mark(_x32), _x73)), active(f(active(if(mark(_x91), mark(_x92), _x93)))), _x23))	mark^#(if(if(c, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(c), mark(_x32), _x33)), mark(X2), X3))
mark^#(if(if(mark(c), true, active(mark(_x31))), f(f(c)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(c, if(_x41, _x42, _x43), mark(_x33)))	→	active^#(if(c, active(if(mark(_x41), mark(_x42), _x43)), _x33))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(f(mark(_x71)))), X3))	mark^#(if(false, c, _x23))	→	active^#(if(false, active(c), _x23))
mark^#(if(if(_x51, _x32, active(active(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(true, if(false, c, _x43), _x23))	→	active^#(if(active(true), if(active(false), active(c), _x43), _x23))
mark^#(if(c, true, _x23))	→	active^#(if(c, active(true), _x23))	mark^#(if(true, if(false, false, _x43), active(_x23)))	→	active^#(if(active(true), active(if(active(false), active(false), _x43)), _x23))
mark^#(if(X1, c, mark(_x23)))	→	active^#(if(mark(X1), active(c), _x23))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(_x63)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(f(_x91), _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(active(f(mark(_x91))), mark(_x32), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x51, _x52, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, _x52, _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, _x82, mark(_x103)), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x52, _x53), X2, X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), mark(X2), X3))
mark^#(if(if(true, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(true), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x61, if(_x71, _x72, _x73), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(if(mark(_x71), mark(_x72), _x73)), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(active(_x53))))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x53))	mark^#(if(if(_x31, _x32, active(_x53)), f(c), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), _x23))
mark^#(if(c, f(_x71), active(_x23)))	→	active^#(if(c, f(_x71), _x23))	mark^#(if(if(mark(_x71), if(_x101, _x102, _x103), active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(if(mark(_x101), mark(_x102), _x103)), _x73)), active(f(mark(_x41))), _x23))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(active(_x23))))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x23))	mark^#(if(if(mark(false), true, active(mark(_x31))), f(f(false)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(true, false, _x33), X2, mark(_x23)))	→	active^#(if(active(if(active(true), active(false), _x33)), mark(X2), _x23))	mark^#(if(c, c, mark(_x33)))	→	active^#(if(c, active(c), _x33))
mark^#(if(if(_x31, if(false, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(false, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(false), mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(_x31, false, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(active(if(_x61, active(true), _x63)), f(active(f(mark(_x71)))), _x23))	mark^#(if(c, f(if(_x61, f(_x91), _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(f(mark(_x91))), _x63))), _x33))
mark^#(if(if(f(_x71), _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(active(f(mark(_x71))), mark(_x32), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(if(_x71, _x72, _x73)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))
mark^#(if(if(_x31, _x32, _x33), _x22, _x23))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), _x22, _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), _x23))	→	active^#(if(mark(_x31), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(true, if(_x41, _x62, _x63), X3))	→	active^#(if(active(true), active(if(mark(_x41), _x62, _x63)), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(if(mark(_x71), c, f(true)))), X3))
mark^#(if(if(_x31, f(_x101), active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x101))), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(c)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(c))))), X3))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(if(_x121, _x122, _x123), _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(if(mark(_x121), mark(_x122), _x123)), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x71)), _x23))	→	active^#(if(if(_x61, mark(_x32), _x63), active(f(active(f(mark(_x71))))), _x23))	mark^#(if(if(mark(true), true, active(mark(_x31))), f(f(true)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(_x41, _x42, _x43), _x23))	→	active^#(if(active(true), if(mark(_x41), mark(_x42), _x43), _x23))
mark^#(if(if(active(_x51), _x32, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(active(_x53)))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), if(mark(_x81), mark(_x82), _x83), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, c, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(_x31, _x32, active(mark(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x83)), active(f(mark(_x41))), _x23))
mark^#(if(if(mark(_x71), true, active(_x31)), f(f(_x71)), X3))	→	active^#(if(mark(active(true)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x31))), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
mark^#(if(if(_x31, if(c, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(c), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(c))), X3))
mark^#(if(if(_x31, false, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x53)), mark(X2), X3))	mark^#(if(true, if(false, _x42, _x63), X3))	→	active^#(if(active(true), active(if(false, mark(_x42), _x63)), X3))
mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x81), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(_x81)), _x23))
mark^#(if(c, f(if(f(_x81), _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(f(mark(_x81))), mark(_x62), _x63))), _x33))	mark^#(if(if(_x31, _x32, _x33), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, f(_x71), active(mark(_x33))))	→	active^#(if(active(c), active(f(_x71)), _x33))	mark^#(if(if(_x31, _x32, mark(_x53)), X2, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(if(_x91, _x92, _x93))), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(true, if(false, _x52, _x53), _x23))	→	active^#(if(active(true), if(active(false), _x52, _x53), _x23))
mark^#(if(if(_x31, _x32, active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, false, _x53), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), false, _x53)), mark(X2), _x23))
mark^#(if(if(_x31, if(_x101, _x82, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(_x101, mark(_x82), _x103)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x63)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), f(mark(_x41)), _x63))
mark^#(if(if(_x31, if(_x81, true, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(_x81, c, f(true))))), X3))	mark^#(if(if(true, false, _x33), if(_x41, _x42, _x43), X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(_x31, if(_x81, mark(_x112), _x113), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x112, _x113)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(false, c, _x23))	→	active^#(if(active(false), c, _x23))
mark^#(if(c, _x22, _x23))	→	active^#(if(active(c), _x22, _x23))	mark^#(if(if(mark(_x71), _x32, active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, active(_x22), _x23))	→	active^#(if(c, _x22, _x23))	mark^#(if(true, if(false, _x42, _x43), mark(_x33)))	→	active^#(if(active(true), if(active(false), mark(_x42), _x43), _x33))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), if(mark(if(mark(_x71), c, f(true))), c, f(true)), _x23))	mark^#(if(if(c, if(_x81, true, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(false, X, Y))	→	mark^#(Y)	mark^#(if(if(c, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(c), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(true, if(f(_x71), _x42, _x43), X3))	→	active^#(if(active(true), active(if(active(f(mark(_x71))), mark(_x42), _x43)), X3))	mark^#(if(true, if(false, _x42, active(_x63)), X3))	→	active^#(if(active(true), active(if(active(false), mark(_x42), _x63)), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(true, c, f(true))))), X3))	mark^#(if(f(false), X2, X3))	→	active^#(if(active(f(active(false))), mark(X2), X3))
mark^#(if(f(_x31), X2, _x23))	→	active^#(if(f(mark(_x31)), mark(X2), _x23))	mark^#(if(if(true, false, _x53), X2, X3))	→	active^#(if(active(if(active(true), false, _x53)), mark(X2), X3))
mark^#(if(if(_x31, false, mark(_x63)), X2, X3))	→	active^#(if(active(if(mark(_x31), false, _x63)), mark(X2), X3))	mark^#(if(if(_x31, f(_x71), _x33), X2, X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), mark(X2), X3))
mark^#(if(if(mark(true), true, active(_x43)), f(f(true)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(true, _x32, _x33), f(_x41), X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), active(f(mark(_x41))), X3))
mark^#(if(if(_x31, _x82, active(_x83)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), _x82, _x83)), active(f(mark(_x41))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x21))), f(f(_x71)), _x23))	→	active^#(if(_x21, active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), true, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(_x61, c, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), active(c), _x63))), _x33))
mark^#(if(if(_x31, if(c, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(c), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, f(if(_x61, _x62, _x63)), active(_x23)))	→	active^#(if(c, f(active(if(mark(_x61), mark(_x62), _x63))), _x23))
mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), mark(_x23)))	→	active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x31, false, _x33), true, X3))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), active(true), X3))	mark^#(if(if(mark(true), true, active(active(_x43))), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, _x33), c, X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(c), X3))	mark^#(if(c, false, _x23))	→	active^#(if(c, active(false), _x23))
mark^#(if(c, f(if(false, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(false), mark(_x62), _x63))), _x33))	mark^#(if(c, f(if(_x71, _x62, _x73)), active(_x33)))	→	active^#(if(active(c), f(active(if(_x71, mark(_x62), _x73))), _x33))
mark^#(if(if(mark(c), true, active(mark(_x43))), f(f(c)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(c), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, true, _x83), active(_x53)), f(f(c)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(true), _x83)), _x53)), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(c, f(_x71), active(active(_x23))))	→	active^#(if(active(c), f(_x71), _x23))	mark^#(if(if(true, false, active(_x53)), X2, X3))	→	active^#(if(active(if(active(true), active(false), _x53)), mark(X2), X3))
mark^#(if(if(true, false, _x33), true, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(true), X3))	mark^#(if(if(true, false, _x33), f(_x41), X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(f(mark(_x41))), X3))
mark^#(if(f(_x31), false, X3))	→	active^#(if(active(f(mark(_x31))), active(false), X3))	mark^#(if(if(mark(f(_x91)), true, active(mark(_x31))), f(f(f(_x91))), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(c, _x22, mark(_x23)))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(active(if(mark(mark(_x71)), mark(c), f(true))), c, f(true))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), _x23))	→	active^#(if(if(mark(_x31), mark(_x32), _x53), active(f(mark(_x41))), _x23))
mark^#(if(if(false, false, _x53), X2, X3))	→	active^#(if(active(if(active(false), false, _x53)), mark(X2), X3))	mark^#(if(if(mark(true), true, active(_x31)), f(f(true)), X3))	→	active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), _x23))	→	active^#(if(if(_x41, active(true), _x43), active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(_x81), true, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(mark(true), true, active(_x63)), f(f(true)), _x23))	→	active^#(if(if(_x61, active(true), _x63), active(f(mark(if(active(true), c, f(true))))), _x23))	mark^#(if(if(_x61, _x32, active(_x63)), f(_x41), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(mark(_x41))), X3))
mark^#(if(if(f(_x71), if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x41, true, active(_x43)), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(c, if(_x51, _x52, _x53), active(_x23)))	→	active^#(if(active(c), active(if(mark(_x51), mark(_x52), _x53)), _x23))	mark^#(if(if(mark(_x71), true, active(_x63)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x61, f(_x71), active(_x63)), f(f(_x71)), X3))	→	active^#(if(active(if(_x61, active(f(mark(_x71))), _x63)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(f(_x71), if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(active(f(mark(_x71))), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3))	→	active^#(if(mark(_x31), active(f(if(mark(_x71), c, f(true)))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x101)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(f(mark(_x101))))), _x23))
mark^#(if(if(mark(true), true, active(_x43)), f(f(true)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(mark(if(active(true), c, f(true))))), X3))	mark^#(if(if(_x31, if(false, _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(false), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), active(f(mark(if(active(false), c, f(true))))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(mark(_x63))))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(_x41))), _x63))
mark^#(if(if(_x31, if(f(_x111), _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x111))), mark(_x82), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(true, if(false, false, _x63), X3))	→	active^#(if(active(true), active(if(active(false), false, _x63)), X3))
mark^#(if(if(_x31, c, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x81, _x32, active(_x83)), f(_x41), active(_x53)))	→	active^#(if(if(_x81, mark(_x32), _x83), active(f(mark(_x41))), _x53))
mark^#(if(c, f(if(_x61, _x62, _x63)), active(mark(_x23))))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x63))), _x23))	mark^#(if(if(_x31, c, active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(c), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, _x32, active(_x53)), f(true), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(true))), _x23))	mark^#(if(if(_x31, _x32, active(mark(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x63)), active(f(active(f(mark(_x71))))), X3))
mark^#(if(if(_x31, _x32, _x33), f(if(_x71, _x72, _x73)), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x33)), active(f(active(if(mark(_x71), mark(_x72), _x73)))), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(_x81)))), X3))
mark^#(if(f(if(_x61, _x62, _x63)), X2, X3))	→	active^#(if(active(f(active(if(mark(_x61), mark(_x62), _x63)))), mark(X2), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, true, _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(_x31, if(_x81, c, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(c), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))	mark^#(if(f(_x51), X2, X3))	→	active^#(if(active(f(_x51)), mark(X2), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, active(true), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x102, _x103), active(_x53)), f(f(_x71)), _x23))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x53)), f(mark(if(mark(_x71), c, f(true)))), _x23))
mark^#(if(true, if(_x41, _x42, _x43), active(_x23)))	→	active^#(if(active(true), active(if(mark(_x41), mark(_x42), _x43)), _x23))	mark^#(if(if(true, false, _x33), false, X3))	→	active^#(if(active(if(active(true), active(false), _x33)), active(false), X3))
mark^#(if(if(_x31, _x52, _x53), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), _x52, _x53)), active(f(mark(_x41))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x43))), f(f(_x71)), X3))	→	active^#(if(active(if(_x41, active(true), _x43)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
mark^#(if(if(false, _x32, active(_x61)), f(_x41), active(_x23)))	→	active^#(if(mark(_x61), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, if(_x81, f(_x121), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(f(mark(_x121))), _x83)), _x53)), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(false, X2, X3))	→	active^#(if(active(false), mark(X2), X3))	mark^#(if(if(_x61, _x32, active(_x63)), f(f(true)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(false))), f(f(_x71)), X3))	→	active^#(if(active(false), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(c, mark(_x22), mark(active(_x23))))	→	active^#(if(c, _x22, _x23))
mark^#(if(if(mark(_x71), true, active(_x73)), f(_x41), active(_x23)))	→	active^#(if(active(if(_x71, active(true), _x73)), active(f(mark(_x41))), _x23))	mark^#(if(if(_x31, _x32, active(_x53)), f(f(_x71)), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(_x61, true, active(_x63)), f(f(_x81)), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(_x81)))), X3))	mark^#(if(if(_x31, _x32, active(_x53)), f(false), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), active(f(active(false))), X3))
mark^#(if(if(_x61, true, active(_x63)), f(f(f(_x91))), X3))	→	active^#(if(active(if(_x61, active(true), _x63)), active(f(active(f(active(f(mark(_x91))))))), X3))	mark^#(if(if(_x31, false, _x33), X2, active(_x23)))	→	active^#(if(active(if(mark(_x31), active(false), _x33)), mark(X2), _x23))
mark^#(if(if(_x31, f(_x71), _x33), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), active(f(mark(_x71))), _x33)), active(f(mark(_x41))), X3))	mark^#(if(c, f(if(_x61, _x62, active(_x73))), active(_x33)))	→	active^#(if(active(c), f(active(if(mark(_x61), mark(_x62), _x73))), _x33))
mark^#(if(c, f(f(_x61)), active(_x33)))	→	active^#(if(active(c), f(active(f(mark(_x61)))), _x33))	mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), active(_x23)))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), _x23))
mark^#(if(c, c, mark(_x23)))	→	active^#(if(active(c), active(c), _x23))	mark^#(if(if(_x31, if(_x81, c, f(true)), active(_x53)), f(f(_x81)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(_x81, c, f(true))), c, f(true))), X3))
mark^#(if(if(_x51, _x32, active(mark(_x53))), f(f(_x71)), X3))	→	active^#(if(active(if(_x51, mark(_x32), _x53)), active(f(active(f(mark(_x71))))), X3))	mark^#(if(if(_x31, if(_x81, f(_x121), _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), active(f(mark(_x121))), _x83)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(c, f(if(c, _x62, _x63)), active(_x33)))	→	active^#(if(active(c), f(active(if(active(c), mark(_x62), _x63))), _x33))	mark^#(if(c, f(mark(_x41)), active(_x33)))	→	active^#(if(active(c), f(_x41), _x33))
mark^#(if(if(_x61, _x32, active(_x63)), f(f(false)), X3))	→	active^#(if(active(if(_x61, mark(_x32), _x63)), active(f(active(f(active(false))))), X3))	mark^#(f(X))	→	active^#(f(mark(X)))
mark^#(if(c, X2, mark(active(_x23))))	→	active^#(if(c, mark(X2), _x23))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(false)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(false), c, f(true))), c, f(true))), X3))
mark^#(if(true, X2, mark(_x23)))	→	active^#(if(active(true), mark(X2), _x23))	mark^#(if(X1, if(_x41, _x42, _x43), X3))	→	active^#(if(mark(X1), active(if(mark(_x41), mark(_x42), _x43)), X3))
mark^#(if(if(true, _x32, _x33), X2, X3))	→	active^#(if(active(if(active(true), mark(_x32), _x33)), mark(X2), X3))	mark^#(if(f(true), X2, X3))	→	active^#(if(active(f(active(true))), mark(X2), X3))
mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(c, false, mark(mark(_x23))))	→	active^#(if(c, active(false), _x23))
mark^#(if(if(_x31, _x32, active(_x53)), f(_x41), X3))	→	active^#(if(active(if(mark(_x31), mark(_x32), _x53)), mark(if(mark(_x41), c, f(true))), X3))	mark^#(if(X1, X2, active(_x23)))	→	active^#(if(mark(X1), mark(X2), _x23))
mark^#(if(if(_x31, if(f(_x121), _x102, _x103), active(_x53)), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(active(f(mark(_x121))), _x102, _x103)), _x53)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(_x31, if(_x81, _x82, _x83), active(_x53)), f(f(true)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), mark(_x82), _x83)), _x53)), mark(if(mark(if(active(true), c, f(true))), c, f(true))), X3))
mark^#(if(if(_x31, if(_x81, _x102, _x103), active(active(_x63))), f(f(_x71)), X3))	→	active^#(if(active(if(mark(_x31), active(if(mark(_x81), _x102, _x103)), _x63)), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x81), _x32, active(mark(_x83))), f(_x41), active(_x23)))	→	active^#(if(active(if(_x81, mark(_x32), _x83)), active(f(mark(_x41))), _x23))

Rewrite Rules

active(f(X))	→	mark(if(X, c, f(true)))	active(if(true, X, Y))	→	mark(X)
active(if(false, X, Y))	→	mark(Y)	mark(f(X))	→	active(f(mark(X)))
mark(if(X1, X2, X3))	→	active(if(mark(X1), mark(X2), X3))	mark(c)	→	active(c)
mark(true)	→	active(true)	mark(false)	→	active(false)
f(mark(X))	→	f(X)	f(active(X))	→	f(X)
if(mark(X1), X2, X3)	→	if(X1, X2, X3)	if(X1, mark(X2), X3)	→	if(X1, X2, X3)
if(X1, X2, mark(X3))	→	if(X1, X2, X3)	if(active(X1), X2, X3)	→	if(X1, X2, X3)
if(X1, active(X2), X3)	→	if(X1, X2, X3)	if(X1, X2, active(X3))	→	if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, c, if, true, active, false, mark

Strategy

Relevant Terms	Irrelevant Terms
active^#(if(mark(_x31), active(f(mark(if(active(c), c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(_x81, c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(active(false), c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))
active^#(if(active(false), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(mark(_x31), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))
active^#(if(active(true), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
active^#(if(mark(_x31), active(f(if(mark(_x71), c, f(true)))), X3))
active^#(if(mark(_x31), f(mark(if(mark(_x71), c, f(true)))), _x23))
active^#(if(mark(_x31), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))
active^#(if(active(c), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(active(f(mark(_x41))), active(f(mark(if(mark(_x71), c, f(true))))), X3))
active^#(if(_x21, active(f(mark(if(mark(_x71), c, f(true))))), _x23))
active^#(if(active(if(mark(_x41), mark(_x42), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))

Thus, the rule mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), X3)) is replaced by the following rules:

mark^#(if(if(mark(if(_x91, _x92, _x93)), true, active(mark(_x31))), f(f(if(_x91, _x92, _x93))), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(if(mark(_x91), mark(_x92), _x93)), c, f(true))))), X3))	mark^#(if(if(mark(_x81), true, active(mark(_x31))), f(f(_x81)), X3)) → active^#(if(mark(_x31), active(f(mark(if(_x81, c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(c))), f(f(_x71)), X3)) → active^#(if(active(c), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), mark(if(mark(if(mark(_x71), c, f(true))), c, f(true))), X3))
mark^#(if(if(mark(f(_x91)), true, active(mark(_x31))), f(f(f(_x91))), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(f(mark(_x91))), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), mark(_x23))) → active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(true))), f(f(_x71)), X3)) → active^#(if(active(true), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(_x71), true, active(mark(if(_x41, _x42, _x43)))), f(f(_x71)), X3)) → active^#(if(active(if(mark(_x41), mark(_x42), _x43)), active(f(mark(if(mark(_x71), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(false))), f(f(_x71)), X3)) → active^#(if(active(false), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(true), true, active(mark(_x31))), f(f(true)), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(true), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), active(f(active(if(mark(mark(_x71)), mark(c), f(true))))), X3))	mark^#(if(if(mark(false), true, active(mark(_x31))), f(f(false)), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(false), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(f(_x41)))), f(f(_x71)), X3)) → active^#(if(active(f(mark(_x41))), active(f(mark(if(mark(_x71), c, f(true))))), X3))	mark^#(if(if(mark(c), true, active(mark(_x31))), f(f(c)), X3)) → active^#(if(mark(_x31), active(f(mark(if(active(c), c, f(true))))), X3))
mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), _x23)) → active^#(if(mark(_x31), f(mark(if(mark(_x71), c, f(true)))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), active(_x23))) → active^#(if(mark(_x31), active(f(mark(if(mark(_x71), c, f(true))))), _x23))
mark^#(if(if(mark(_x71), true, active(mark(_x21))), f(f(_x71)), _x23)) → active^#(if(_x21, active(f(mark(if(mark(_x71), c, f(true))))), _x23))	mark^#(if(if(mark(_x71), true, active(mark(_x31))), f(f(_x71)), X3)) → active^#(if(mark(_x31), active(f(if(mark(_x71), c, f(true)))), X3))