MAYBE
The TRS could not be proven terminating. The proof attempt took 599 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 (2ms), DependencyGraph (3ms), PolynomialLinearRange4iUR (127ms), DependencyGraph (4ms), PolynomialLinearRange8NegiUR (223ms), DependencyGraph (2ms), ReductionPairSAT (60ms), DependencyGraph (2ms), SizeChangePrinciple (10ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(x, i(x)) | → | f#(x, x) | | f#(x, x) | → | f#(i(x), g(g(x))) |
Rewrite Rules
| f(x, x) | → | f(i(x), g(g(x))) | | f(x, y) | → | x |
| g(x) | → | i(x) | | f(x, i(x)) | → | f(x, x) |
| f(i(x), i(g(x))) | → | a |
Original Signature
Termination of terms over the following signature is verified: f, g, a, i
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(x, i(x)) | → | f#(x, x) | | f#(x, x) | → | f#(i(x), g(g(x))) |
| f#(x, x) | → | g#(g(x)) | | f#(x, x) | → | g#(x) |
Rewrite Rules
| f(x, x) | → | f(i(x), g(g(x))) | | f(x, y) | → | x |
| g(x) | → | i(x) | | f(x, i(x)) | → | f(x, x) |
| f(i(x), i(g(x))) | → | a |
Original Signature
Termination of terms over the following signature is verified: f, g, a, i
Strategy
The following SCCs where found
| f#(x, i(x)) → f#(x, x) | f#(x, x) → f#(i(x), g(g(x))) |