YES
The TRS could be proven terminating. The proof took 307 ms.
The following DP Processors were used
Problem 1 was processed with processor PolynomialLinearRange4iUR (188ms).
Problem 1: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| f#(s(s(x))) | → | f#(x) | | f#(s(s(x))) | → | f#(f(x)) |
Rewrite Rules
| f(x) | → | s(x) | | f(s(s(x))) | → | s(f(f(x))) |
Original Signature
Termination of terms over the following signature is verified: f, s
Strategy
Polynomial Interpretation
- f(x): x + 1
- f#(x): x
- s(x): x + 1
Improved Usable rules
| f(s(s(x))) | → | s(f(f(x))) | | f(x) | → | s(x) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| f#(s(s(x))) | → | f#(x) | | f#(s(s(x))) | → | f#(f(x)) |