YES
The TRS could be proven terminating. The proof took 20 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (5ms).
| – Problem 2 was processed with processor SubtermCriterion (1ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| and#(tt, X) | → | activate#(X) | | __#(__(X, Y), Z) | → | __#(X, __(Y, Z)) |
| __#(__(X, Y), Z) | → | __#(Y, Z) |
Rewrite Rules
| __(__(X, Y), Z) | → | __(X, __(Y, Z)) | | __(X, nil) | → | X |
| __(nil, X) | → | X | | and(tt, X) | → | activate(X) |
| isNePal(__(I, __(P, I))) | → | tt | | activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: activate, tt, isNePal, __, nil, and
Strategy
The following SCCs where found
| __#(__(X, Y), Z) → __#(X, __(Y, Z)) | __#(__(X, Y), Z) → __#(Y, Z) |
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| __#(__(X, Y), Z) | → | __#(X, __(Y, Z)) | | __#(__(X, Y), Z) | → | __#(Y, Z) |
Rewrite Rules
| __(__(X, Y), Z) | → | __(X, __(Y, Z)) | | __(X, nil) | → | X |
| __(nil, X) | → | X | | and(tt, X) | → | activate(X) |
| isNePal(__(I, __(P, I))) | → | tt | | activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: activate, tt, isNePal, __, nil, and
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| __#(__(X, Y), Z) | → | __#(X, __(Y, Z)) | | __#(__(X, Y), Z) | → | __#(Y, Z) |