TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60046 ms.
The following DP Processors were used
Problem 1 was processed with processor PolynomialLinearRange4iUR (782ms).
| – Problem 2 remains open; application of the following processors failed [DependencyGraph (1ms), PolynomialLinearRange4iUR (455ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (12301ms), DependencyGraph (1ms), ReductionPairSAT (timeout)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| p#(p(b(a(x0)), x1), p(x2, x3)) | → | p#(p(b(x2), a(a(b(x1)))), p(x3, x0)) |
Rewrite Rules
| p(p(b(a(x0)), x1), p(x2, x3)) | → | p(p(b(x2), a(a(b(x1)))), p(x3, x0)) |
Original Signature
Termination of terms over the following signature is verified: b, p, a
Problem 1: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| p#(p(b(a(x0)), x1), p(x2, x3)) | → | p#(x3, x0) | | p#(p(b(a(x0)), x1), p(x2, x3)) | → | p#(b(x2), a(a(b(x1)))) |
| p#(p(b(a(x0)), x1), p(x2, x3)) | → | p#(p(b(x2), a(a(b(x1)))), p(x3, x0)) |
Rewrite Rules
| p(p(b(a(x0)), x1), p(x2, x3)) | → | p(p(b(x2), a(a(b(x1)))), p(x3, x0)) |
Original Signature
Termination of terms over the following signature is verified: b, p, a
Strategy
Polynomial Interpretation
- a(x): x
- b(x): x
- p(x,y): y + x + 1
- p#(x,y): y + x
Improved Usable rules
| p(p(b(a(x0)), x1), p(x2, x3)) | → | p(p(b(x2), a(a(b(x1)))), p(x3, x0)) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| p#(p(b(a(x0)), x1), p(x2, x3)) | → | p#(x3, x0) | | p#(p(b(a(x0)), x1), p(x2, x3)) | → | p#(b(x2), a(a(b(x1)))) |