MAYBE
The TRS could not be proven terminating. The proof attempt took 261 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 (2ms), PolynomialLinearRange4iUR (75ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (34ms), DependencyGraph (2ms), ReductionPairSAT (16ms), DependencyGraph (1ms), SizeChangePrinciple (4ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
Rewrite Rules
| 2nd(cons1(X, cons(Y, Z))) | → | Y | | 2nd(cons(X, X1)) | → | 2nd(cons1(X, X1)) |
| from(X) | → | cons(X, from(s(X))) |
Original Signature
Termination of terms over the following signature is verified: 2nd, cons1, s, from, cons
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| 2nd#(cons(X, X1)) | → | 2nd#(cons1(X, X1)) | | from#(X) | → | from#(s(X)) |
Rewrite Rules
| 2nd(cons1(X, cons(Y, Z))) | → | Y | | 2nd(cons(X, X1)) | → | 2nd(cons1(X, X1)) |
| from(X) | → | cons(X, from(s(X))) |
Original Signature
Termination of terms over the following signature is verified: 2nd, cons1, s, from, cons
Strategy
The following SCCs where found