MAYBE
The TRS could not be proven terminating. The proof attempt took 271 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (5ms).
| – Problem 2 remains open; application of the following processors failed [SubtermCriterion (0ms), DependencyGraph (3ms), PolynomialLinearRange4iUR (0ms), DependencyGraph (2ms), PolynomialOrderingProcessor (0ms), DependencyGraph (2ms), PolynomialLinearRange4 (97ms), DependencyGraph (1ms), ReductionPairSAT (35ms), DependencyGraph (2ms), SizeChangePrinciple (56ms), BackwardsNarrowing (1ms), BackwardInstantiation (timeout), BackwardInstantiation (0ms), ForwardInstantiation (1ms), BackwardInstantiation (2ms), ForwardInstantiation (1ms), Propagation (0ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(X, X) | → | h#(a) | | g#(a, X) | → | f#(b, X) |
| h#(X) | → | g#(X, X) |
Rewrite Rules
| h(X) | → | g(X, X) | | g(a, X) | → | f(b, X) |
| f(X, 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
| f#(X, X) | → | h#(a) | | g#(a, X) | → | f#(b, X) |
| f#(X, X) | → | a# | | h#(X) | → | g#(X, X) |
Rewrite Rules
| h(X) | → | g(X, X) | | g(a, X) | → | f(b, X) |
| f(X, X) | → | h(a) | | a | → | b |
Original Signature
Termination of terms over the following signature is verified: f, g, b, a, h
Strategy
Context-sensitive strategy:
μ(T) = μ(b) = μ(a) = μ(a#) = ∅
μ(f) = μ(g) = μ(f#) = μ(h#) = μ(g#) = μ(h) = {1}
The following SCCs where found
| f#(X, X) → h#(a) | g#(a, X) → f#(b, X) |
| h#(X) → g#(X, X) |