MAYBE
The TRS could not be proven terminating. The proof attempt took 520 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 (75ms), DependencyGraph (2ms), PolynomialLinearRange8NegiUR (71ms), DependencyGraph (2ms), ReductionPairSAT (224ms), DependencyGraph (1ms), SizeChangePrinciple (7ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(k(a), k(b), X) | → | f#(X, X, X) |
Rewrite Rules
| g(X) | → | u(h(X), h(X), X) | | u(d, c(Y), X) | → | k(Y) |
| h(d) | → | c(a) | | h(d) | → | c(b) |
| f(k(a), k(b), X) | → | f(X, X, X) |
Original Signature
Termination of terms over the following signature is verified: f, g, d, u, b, c, a, k, h
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| g#(X) | → | u#(h(X), h(X), X) | | g#(X) | → | h#(X) |
| f#(k(a), k(b), X) | → | f#(X, X, X) |
Rewrite Rules
| g(X) | → | u(h(X), h(X), X) | | u(d, c(Y), X) | → | k(Y) |
| h(d) | → | c(a) | | h(d) | → | c(b) |
| f(k(a), k(b), X) | → | f(X, X, X) |
Original Signature
Termination of terms over the following signature is verified: f, g, u, d, b, c, a, k, h
Strategy
The following SCCs where found
| f#(k(a), k(b), X) → f#(X, X, X) |