MAYBE
The TRS could not be proven terminating. The proof attempt took 373 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 (7ms), PolynomialLinearRange4iUR (75ms), DependencyGraph (3ms), PolynomialLinearRange8NegiUR (102ms), DependencyGraph (5ms), ReductionPairSAT (36ms), DependencyGraph (2ms), SizeChangePrinciple (4ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| h#(X) | → | g#(X) | | g#(a) | → | f#(b) |
| f#(X) | → | h#(a) |
Rewrite Rules
| h(X) | → | g(X) | | g(a) | → | f(b) |
| f(X) | → | h(a) | | a | → | b |
Original Signature
Termination of terms over the following signature is verified: f, g, b, a, h
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| h#(X) | → | g#(X) | | g#(a) | → | f#(b) |
| f#(X) | → | a# | | f#(X) | → | h#(a) |
Rewrite Rules
| h(X) | → | g(X) | | g(a) | → | f(b) |
| f(X) | → | h(a) | | a | → | b |
Original Signature
Termination of terms over the following signature is verified: f, g, b, a, h
Strategy
The following SCCs where found
| h#(X) → g#(X) | g#(a) → f#(b) |
| f#(X) → h#(a) |