YES
The TRS could be proven terminating. The proof took 57 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (5ms).
| – Problem 2 was processed with processor SubtermCriterion (0ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(f(X)) | → | b#(f(X)) | | f#(a(g(X))) | → | b#(X) |
| f#(f(X)) | → | f#(X) | | f#(f(X)) | → | f#(a(b(f(X)))) |
Rewrite Rules
| f(f(X)) | → | f(a(b(f(X)))) | | f(a(g(X))) | → | b(X) |
| b(X) | → | a(X) |
Original Signature
Termination of terms over the following signature is verified: f, g, b, a
Strategy
The following SCCs where found
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| f(f(X)) | → | f(a(b(f(X)))) | | f(a(g(X))) | → | b(X) |
| b(X) | → | a(X) |
Original Signature
Termination of terms over the following signature is verified: f, g, b, a
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed: