YES
The TRS could be proven terminating. The proof took 318 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (3ms).
| – Problem 2 was processed with processor PolynomialOrderingProcessor (62ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| f#(s(0)) | → | f#(p(s(0))) | | f#(s(0)) | → | p#(s(0)) |
Rewrite Rules
| f(0) | → | cons(0) | | f(s(0)) | → | f(p(s(0))) |
| p(s(X)) | → | X |
Original Signature
Termination of terms over the following signature is verified: f, 0, s, p, cons
Strategy
The following SCCs where found
Problem 2: PolynomialOrderingProcessor
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| f(0) | → | cons(0) | | f(s(0)) | → | f(p(s(0))) |
| p(s(X)) | → | X |
Original Signature
Termination of terms over the following signature is verified: f, 0, s, p, cons
Strategy
Polynomial Interpretation
- 0: -2
- cons(x): -2
- f(x): -2
- f#(x): 4x - 2
- p(x): 2x - 2
- s(x): 4x + 1
Improved Usable rules
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed: