YES
The TRS could be proven terminating. The proof took 214 ms.
The following DP Processors were used
Problem 1 was processed with processor PolynomialLinearRange4iUR (186ms).
Problem 1: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| f#(g(X)) | → | f#(f(X)) | | f#(g(X)) | → | f#(X) |
Rewrite Rules
| f(g(X)) | → | g(f(f(X))) | | f(h(X)) | → | h(g(X)) |
Original Signature
Termination of terms over the following signature is verified: f, g, h
Strategy
Polynomial Interpretation
- f(x): x
- f#(x): x
- g(x): 2x + 1
- h(x): 2
Improved Usable rules
| f(h(X)) | → | h(g(X)) | | f(g(X)) | → | g(f(f(X))) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| f#(g(X)) | → | f#(f(X)) | | f#(g(X)) | → | f#(X) |