TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60000 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (8ms).
| – Problem 2 remains open; application of the following processors failed [SubtermCriterion (2ms), DependencyGraph (2ms), PolynomialLinearRange4iUR (141ms), DependencyGraph (2ms), PolynomialLinearRange8NegiUR (295ms), DependencyGraph (2ms), ReductionPairSAT (507ms), DependencyGraph (2ms), SizeChangePrinciple (5ms), ForwardNarrowing (1ms), BackwardInstantiation (1ms), ForwardInstantiation (1ms), Propagation (0ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(0, 1, x) | → | f#(h(x), h(x), x) |
Rewrite Rules
| f(0, 1, x) | → | f(h(x), h(x), x) | | h(0) | → | 0 |
| h(g(x, y)) | → | y |
Original Signature
Termination of terms over the following signature is verified: f, g, 1, 0, h
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(0, 1, x) | → | h#(x) | | f#(0, 1, x) | → | f#(h(x), h(x), x) |
Rewrite Rules
| f(0, 1, x) | → | f(h(x), h(x), x) | | h(0) | → | 0 |
| h(g(x, y)) | → | y |
Original Signature
Termination of terms over the following signature is verified: f, g, 1, 0, h
Strategy
The following SCCs where found
| f#(0, 1, x) → f#(h(x), h(x), x) |