YES
The TRS could be proven terminating. The proof took 17 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (3ms).
| – Problem 2 was processed with processor SubtermCriterion (0ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| +#(-(x, y), z) | → | +#(x, z) | | +#(-(x, y), z) | → | -#(+(x, z), y) |
Rewrite Rules
| +(-(x, y), z) | → | -(+(x, z), y) | | -(+(x, y), y) | → | x |
Original Signature
Termination of terms over the following signature is verified: +, -
Strategy
The following SCCs where found
| +#(-(x, y), z) → +#(x, z) |
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| +#(-(x, y), z) | → | +#(x, z) |
Rewrite Rules
| +(-(x, y), z) | → | -(+(x, z), y) | | -(+(x, y), y) | → | x |
Original Signature
Termination of terms over the following signature is verified: +, -
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| +#(-(x, y), z) | → | +#(x, z) |