TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60368 ms.
The following DP Processors were used
Problem 1 was processed with processor PolynomialLinearRange4iUR (550ms).
| – Problem 2 remains open; application of the following processors failed [DependencyGraph (1ms), PolynomialLinearRange4iUR (288ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (3898ms), DependencyGraph (0ms), ReductionPairSAT (timeout)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| p#(a(x0), p(a(a(a(x1))), x2)) | → | p#(a(x2), p(a(a(b(x0))), x2)) |
Rewrite Rules
| p(a(x0), p(a(a(a(x1))), x2)) | → | p(a(x2), p(a(a(b(x0))), x2)) |
Original Signature
Termination of terms over the following signature is verified: b, p, a
Problem 1: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| p#(a(x0), p(a(a(a(x1))), x2)) | → | p#(a(x2), p(a(a(b(x0))), x2)) | | p#(a(x0), p(a(a(a(x1))), x2)) | → | p#(a(a(b(x0))), x2) |
Rewrite Rules
| p(a(x0), p(a(a(a(x1))), x2)) | → | p(a(x2), p(a(a(b(x0))), x2)) |
Original Signature
Termination of terms over the following signature is verified: b, p, a
Strategy
Polynomial Interpretation
- a(x): x
- b(x): 2
- p(x,y): 2y + 1
- p#(x,y): 2y
Improved Usable rules
| p(a(x0), p(a(a(a(x1))), x2)) | → | p(a(x2), p(a(a(b(x0))), x2)) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| p#(a(x0), p(a(a(a(x1))), x2)) | → | p#(a(a(b(x0))), x2) |