YES
The TRS could be proven terminating. The proof took 6771 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (302ms).
| – Problem 2 was processed with processor SubtermCriterion (1ms).
| | – Problem 6 was processed with processor SubtermCriterion (1ms).
| – Problem 3 was processed with processor SubtermCriterion (0ms).
| – Problem 4 was processed with processor PolynomialLinearRange4iUR (3496ms).
| | – Problem 8 was processed with processor PolynomialLinearRange4iUR (2797ms).
| | | – Problem 9 was processed with processor DependencyGraph (1ms).
| | | | – Problem 10 was processed with processor PolynomialLinearRange4iUR (13ms).
| – Problem 5 was processed with processor SubtermCriterion (1ms).
| | – Problem 7 was processed with processor SubtermCriterion (1ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| mark#(__(X1, X2)) | → | __#(mark(X1), mark(X2)) | | and#(active(X1), X2) | → | and#(X1, X2) |
| mark#(isNePal(X)) | → | isNePal#(mark(X)) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| and#(X1, active(X2)) | → | and#(X1, X2) | | mark#(tt) | → | active#(tt) |
| active#(__(__(X, Y), Z)) | → | __#(X, __(Y, Z)) | | active#(__(X, nil)) | → | mark#(X) |
| __#(X1, active(X2)) | → | __#(X1, X2) | | __#(active(X1), X2) | → | __#(X1, X2) |
| mark#(nil) | → | active#(nil) | | mark#(and(X1, X2)) | → | active#(and(mark(X1), X2)) |
| mark#(isNePal(X)) | → | mark#(X) | | mark#(__(X1, X2)) | → | mark#(X2) |
| and#(X1, mark(X2)) | → | and#(X1, X2) | | __#(mark(X1), X2) | → | __#(X1, X2) |
| isNePal#(active(X)) | → | isNePal#(X) | | mark#(and(X1, X2)) | → | and#(mark(X1), X2) |
| active#(__(nil, X)) | → | mark#(X) | | active#(__(__(X, Y), Z)) | → | __#(Y, Z) |
| __#(X1, mark(X2)) | → | __#(X1, X2) | | isNePal#(mark(X)) | → | isNePal#(X) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | and#(mark(X1), X2) | → | and#(X1, X2) |
| active#(and(tt, X)) | → | mark#(X) | | mark#(isNePal(X)) | → | active#(isNePal(mark(X))) |
| mark#(and(X1, X2)) | → | mark#(X1) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(tt) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, active, __, mark, nil, and
Strategy
The following SCCs where found
| mark#(and(X1, X2)) → mark#(X1) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | active#(__(nil, X)) → mark#(X) |
| mark#(and(X1, X2)) → active#(and(mark(X1), X2)) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(isNePal(X)) → active#(isNePal(mark(X))) |
| active#(and(tt, X)) → mark#(X) | mark#(isNePal(X)) → mark#(X) |
| mark#(__(X1, X2)) → mark#(X2) |
| __#(mark(X1), X2) → __#(X1, X2) | __#(active(X1), X2) → __#(X1, X2) |
| __#(X1, mark(X2)) → __#(X1, X2) | __#(X1, active(X2)) → __#(X1, X2) |
| and#(active(X1), X2) → and#(X1, X2) | and#(X1, active(X2)) → and#(X1, X2) |
| and#(mark(X1), X2) → and#(X1, X2) | and#(X1, mark(X2)) → and#(X1, X2) |
| isNePal#(active(X)) → isNePal#(X) | isNePal#(mark(X)) → isNePal#(X) |
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| __#(mark(X1), X2) | → | __#(X1, X2) | | __#(active(X1), X2) | → | __#(X1, X2) |
| __#(X1, mark(X2)) | → | __#(X1, X2) | | __#(X1, active(X2)) | → | __#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, active, __, mark, nil, and
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| __#(active(X1), X2) | → | __#(X1, X2) | | __#(mark(X1), X2) | → | __#(X1, X2) |
Problem 6: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| __#(X1, mark(X2)) | → | __#(X1, X2) | | __#(X1, active(X2)) | → | __#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, __, active, mark, and, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| __#(X1, mark(X2)) | → | __#(X1, X2) | | __#(X1, active(X2)) | → | __#(X1, X2) |
Problem 3: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| isNePal#(active(X)) | → | isNePal#(X) | | isNePal#(mark(X)) | → | isNePal#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, active, __, mark, nil, and
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| isNePal#(active(X)) | → | isNePal#(X) | | isNePal#(mark(X)) | → | isNePal#(X) |
Problem 4: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| mark#(and(X1, X2)) | → | mark#(X1) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(and(X1, X2)) | → | active#(and(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(__(X1, X2)) | → | mark#(X1) | | mark#(isNePal(X)) | → | active#(isNePal(mark(X))) |
| active#(and(tt, X)) | → | mark#(X) | | mark#(isNePal(X)) | → | mark#(X) |
| mark#(__(X1, X2)) | → | mark#(X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, active, __, mark, nil, and
Strategy
Polynomial Interpretation
- __(x,y): y + 2x
- active(x): x
- active#(x): 2x
- and(x,y): y + x
- isNePal(x): 2x + 1
- mark(x): x
- mark#(x): 2x
- nil: 0
- tt: 0
Improved Usable rules
| isNePal(active(X)) | → | isNePal(X) | | active(__(nil, X)) | → | mark(X) |
| active(__(X, nil)) | → | mark(X) | | __(active(X1), X2) | → | __(X1, X2) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(tt) | → | active(tt) |
| __(X1, mark(X2)) | → | __(X1, X2) | | and(active(X1), X2) | → | and(X1, X2) |
| active(and(tt, X)) | → | mark(X) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| and(X1, mark(X2)) | → | and(X1, X2) | | and(mark(X1), X2) | → | and(X1, X2) |
| mark(and(X1, X2)) | → | active(and(mark(X1), X2)) | | __(mark(X1), X2) | → | __(X1, X2) |
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | isNePal(mark(X)) | → | isNePal(X) |
| and(X1, active(X2)) | → | and(X1, X2) | | mark(nil) | → | active(nil) |
| __(X1, active(X2)) | → | __(X1, X2) | | active(isNePal(__(I, __(P, I)))) | → | mark(tt) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| mark#(isNePal(X)) | → | mark#(X) |
Problem 8: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| mark#(and(X1, X2)) | → | mark#(X1) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(and(X1, X2)) | → | active#(and(mark(X1), X2)) | | mark#(__(X1, X2)) | → | mark#(X1) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | active#(and(tt, X)) | → | mark#(X) |
| mark#(isNePal(X)) | → | active#(isNePal(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, __, active, mark, and, nil
Strategy
Polynomial Interpretation
- __(x,y): y + 2x + 1
- active(x): x
- active#(x): x
- and(x,y): y + x
- isNePal(x): x + 1
- mark(x): x
- mark#(x): x + 1
- nil: 0
- tt: 2
Improved Usable rules
| isNePal(active(X)) | → | isNePal(X) | | active(__(nil, X)) | → | mark(X) |
| active(__(X, nil)) | → | mark(X) | | __(active(X1), X2) | → | __(X1, X2) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(tt) | → | active(tt) |
| __(X1, mark(X2)) | → | __(X1, X2) | | and(active(X1), X2) | → | and(X1, X2) |
| active(and(tt, X)) | → | mark(X) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| and(X1, mark(X2)) | → | and(X1, X2) | | and(mark(X1), X2) | → | and(X1, X2) |
| mark(and(X1, X2)) | → | active(and(mark(X1), X2)) | | __(mark(X1), X2) | → | __(X1, X2) |
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | isNePal(mark(X)) | → | isNePal(X) |
| and(X1, active(X2)) | → | and(X1, X2) | | mark(nil) | → | active(nil) |
| __(X1, active(X2)) | → | __(X1, X2) | | active(isNePal(__(I, __(P, I)))) | → | mark(tt) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| mark#(and(X1, X2)) | → | active#(and(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(__(X1, X2)) | → | mark#(X1) | | mark#(isNePal(X)) | → | active#(isNePal(mark(X))) |
| active#(and(tt, X)) | → | mark#(X) | | mark#(__(X1, X2)) | → | mark#(X2) |
Problem 9: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| mark#(and(X1, X2)) | → | mark#(X1) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | active#(__(nil, X)) | → | mark#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, active, __, mark, nil, and
Strategy
The following SCCs where found
| mark#(and(X1, X2)) → mark#(X1) |
Problem 10: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| mark#(and(X1, X2)) | → | mark#(X1) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, active, __, mark, nil, and
Strategy
Polynomial Interpretation
- __(x,y): 0
- active(x): 0
- and(x,y): x + 2
- isNePal(x): 0
- mark(x): 0
- mark#(x): x + 1
- nil: 0
- tt: 0
There are no usable rules
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| mark#(and(X1, X2)) | → | mark#(X1) |
Problem 5: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| and#(active(X1), X2) | → | and#(X1, X2) | | and#(X1, active(X2)) | → | and#(X1, X2) |
| and#(mark(X1), X2) | → | and#(X1, X2) | | and#(X1, mark(X2)) | → | and#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, active, __, mark, nil, and
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| and#(active(X1), X2) | → | and#(X1, X2) | | and#(mark(X1), X2) | → | and#(X1, X2) |
Problem 7: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| and#(X1, active(X2)) | → | and#(X1, X2) | | and#(X1, mark(X2)) | → | and#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(and(tt, X)) | → | mark(X) |
| active(isNePal(__(I, __(P, I)))) | → | mark(tt) | | mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) |
| mark(nil) | → | active(nil) | | mark(and(X1, X2)) | → | active(and(mark(X1), X2)) |
| mark(tt) | → | active(tt) | | mark(isNePal(X)) | → | active(isNePal(mark(X))) |
| __(mark(X1), X2) | → | __(X1, X2) | | __(X1, mark(X2)) | → | __(X1, X2) |
| __(active(X1), X2) | → | __(X1, X2) | | __(X1, active(X2)) | → | __(X1, X2) |
| and(mark(X1), X2) | → | and(X1, X2) | | and(X1, mark(X2)) | → | and(X1, X2) |
| and(active(X1), X2) | → | and(X1, X2) | | and(X1, active(X2)) | → | and(X1, X2) |
| isNePal(mark(X)) | → | isNePal(X) | | isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: tt, isNePal, __, active, mark, and, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| and#(X1, active(X2)) | → | and#(X1, X2) | | and#(X1, mark(X2)) | → | and#(X1, X2) |