TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60001 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (7ms).
| – Problem 2 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (3ms), PolynomialLinearRange4iUR (100ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (162ms), DependencyGraph (1ms), ReductionPairSAT (302ms), DependencyGraph (1ms), SizeChangePrinciple (5ms), ForwardNarrowing (0ms), BackwardInstantiation (0ms), ForwardInstantiation (0ms), Propagation (1ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(0, 1, X) | → | f#(g(X, X), X, X) |
Rewrite Rules
| f(0, 1, X) | → | f(g(X, X), X, X) | | g(X, Y) | → | X |
| g(X, Y) | → | Y |
Original Signature
Termination of terms over the following signature is verified: f, g, 1, 0
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(0, 1, X) | → | g#(X, X) | | f#(0, 1, X) | → | f#(g(X, X), X, X) |
Rewrite Rules
| f(0, 1, X) | → | f(g(X, X), X, X) | | g(X, Y) | → | X |
| g(X, Y) | → | Y |
Original Signature
Termination of terms over the following signature is verified: f, g, 1, 0
Strategy
The following SCCs where found
| f#(0, 1, X) → f#(g(X, X), X, X) |