YES
The TRS could be proven terminating. The proof took 124 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (3ms).
| – Problem 2 was processed with processor PolynomialLinearRange4iUR (104ms).
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(0)) | → | 0 |
Original Signature
Termination of terms over the following signature is verified: f, 0, s, p, cons
Strategy
The following SCCs where found
Problem 2: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
Rewrite Rules
| f(0) | → | cons(0) | | f(s(0)) | → | f(p(s(0))) |
| p(s(0)) | → | 0 |
Original Signature
Termination of terms over the following signature is verified: f, 0, s, p, cons
Strategy
Polynomial Interpretation
- 0: 0
- cons(x): 0
- f(x): 0
- f#(x): x + 1
- p(x): 0
- s(x): 1
Improved Usable rules
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed: