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 (21ms).
| – Problem 2 remains open; application of the following processors failed [SubtermCriterion (2ms), DependencyGraph (3ms), PolynomialLinearRange4iUR (360ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (5008ms), DependencyGraph (1ms), ReductionPairSAT (timeout)].
| – Problem 3 was processed with processor SubtermCriterion (1ms).
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(0, 1, g(x, y), z) | → | f#(g(x, y), g(x, y), g(x, y), h(x)) |
Rewrite Rules
| f(0, 1, g(x, y), z) | → | f(g(x, y), g(x, y), g(x, y), h(x)) | | g(0, 1) | → | 0 |
| g(0, 1) | → | 1 | | h(g(x, y)) | → | h(x) |
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, g(x, y), z) | → | h#(x) | | f#(0, 1, g(x, y), z) | → | g#(x, y) |
| h#(g(x, y)) | → | h#(x) | | f#(0, 1, g(x, y), z) | → | f#(g(x, y), g(x, y), g(x, y), h(x)) |
Rewrite Rules
| f(0, 1, g(x, y), z) | → | f(g(x, y), g(x, y), g(x, y), h(x)) | | g(0, 1) | → | 0 |
| g(0, 1) | → | 1 | | h(g(x, y)) | → | h(x) |
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, g(x, y), z) → f#(g(x, y), g(x, y), g(x, y), h(x)) |
Problem 3: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| f(0, 1, g(x, y), z) | → | f(g(x, y), g(x, y), g(x, y), h(x)) | | g(0, 1) | → | 0 |
| g(0, 1) | → | 1 | | h(g(x, y)) | → | h(x) |
Original Signature
Termination of terms over the following signature is verified: f, g, 1, 0, h
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed: