YES
The TRS could be proven terminating. The proof took 19 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (2ms).
| – Problem 2 was processed with processor SubtermCriterion (1ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(g(x)) | → | f#(x) | | f#(g(x)) | → | f#(a(g(g(f(x))), g(f(x)))) |
Rewrite Rules
| f(g(x)) | → | f(a(g(g(f(x))), g(f(x)))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The following SCCs where found
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| f(g(x)) | → | f(a(g(g(f(x))), g(f(x)))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed: