MAYBE
The TRS could not be proven terminating. The proof attempt took 803 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (0ms).
| – Problem 2 was processed with processor SubtermCriterion (0ms).
| – Problem 3 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (2ms), PolynomialLinearRange4iUR (93ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (159ms), DependencyGraph (1ms), ReductionPairSAT (446ms), DependencyGraph (1ms), SizeChangePrinciple (7ms)].
The following open problems remain:
Open Dependency Pair Problem 3
Dependency Pairs
| f#(g(x), x, y) | → | f#(y, y, g(y)) |
Rewrite Rules
| f(g(x), x, y) | → | f(y, y, g(y)) | | g(g(x)) | → | g(x) |
Original Signature
Termination of terms over the following signature is verified: f, g
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(g(x), x, y) | → | f#(y, y, g(y)) | | g#(g(x)) | → | g#(x) |
| f#(g(x), x, y) | → | g#(y) |
Rewrite Rules
| f(g(x), x, y) | → | f(y, y, g(y)) | | g(g(x)) | → | g(x) |
Original Signature
Termination of terms over the following signature is verified: f, g
Strategy
The following SCCs where found
| f#(g(x), x, y) → f#(y, y, g(y)) |
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| f(g(x), x, y) | → | f(y, y, g(y)) | | g(g(x)) | → | g(x) |
Original Signature
Termination of terms over the following signature is verified: f, g
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed: