MAYBE
The TRS could not be proven terminating. The proof attempt took 397 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (0ms).
| – Problem 2 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (1ms), PolynomialLinearRange4iUR (83ms), DependencyGraph (0ms), PolynomialLinearRange8NegiUR (123ms), DependencyGraph (1ms), ReductionPairSAT (70ms), DependencyGraph (0ms), SizeChangePrinciple (4ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(X, g(X)) | → | f#(1, g(X)) |
Rewrite Rules
| f(X, g(X)) | → | f(1, g(X)) | | g(1) | → | g(0) |
Original Signature
Termination of terms over the following signature is verified: f, g, 1, 0
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(X, g(X)) | → | g#(X) | | g#(1) | → | g#(0) |
| f#(X, g(X)) | → | f#(1, g(X)) |
Rewrite Rules
| f(X, g(X)) | → | f(1, g(X)) | | g(1) | → | g(0) |
Original Signature
Termination of terms over the following signature is verified: f, g, 1, 0
Strategy
The following SCCs where found
| f#(X, g(X)) → f#(1, g(X)) |