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

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))