MAYBE
The TRS could not be proven terminating. The proof attempt took 1126 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 (5ms), PolynomialLinearRange4iUR (242ms), DependencyGraph (5ms), PolynomialLinearRange8NegiUR (394ms), DependencyGraph (2ms), ReductionPairSAT (305ms), DependencyGraph (2ms), SizeChangePrinciple (11ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, x) | | a#(h, x) | → | a#(f, x) |
| a#(h, x) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, x) | | a(h, x) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a, h
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, x) | | a#(h, x) | → | a#(f, x) |
| a#(h, x) | → | a#(g, a(f, x)) | | a#(h, x) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, x) | | a(h, x) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a, h
Strategy
The following SCCs where found
| a#(f, a(f, x)) → a#(x, x) | a#(h, x) → a#(f, x) |
| a#(h, x) → a#(f, a(g, a(f, x))) |