MAYBE
The TRS could not be proven terminating. The proof attempt took 3207 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 (3ms), PolynomialLinearRange4iUR (317ms), DependencyGraph (3ms), PolynomialLinearRange8NegiUR (1890ms), DependencyGraph (2ms), ReductionPairSAT (878ms), DependencyGraph (1ms), SizeChangePrinciple (15ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(h(x), y) | → | f#(y, f(x, h(f(a, a)))) | | f#(h(x), y) | → | f#(x, h(f(a, a))) |
Rewrite Rules
| f(h(x), y) | → | h(f(y, f(x, h(f(a, a))))) |
Original Signature
Termination of terms over the following signature is verified: f, a, h
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(h(x), y) | → | f#(y, f(x, h(f(a, a)))) | | f#(h(x), y) | → | f#(x, h(f(a, a))) |
| f#(h(x), y) | → | f#(a, a) |
Rewrite Rules
| f(h(x), y) | → | h(f(y, f(x, h(f(a, a))))) |
Original Signature
Termination of terms over the following signature is verified: f, a, h
Strategy
The following SCCs where found
| f#(h(x), y) → f#(y, f(x, h(f(a, a)))) | f#(h(x), y) → f#(x, h(f(a, a))) |