YES

The TRS could be proven terminating. The proof took 256 ms.

The following DP Processors were used


Problem 1 was processed with processor PolynomialOrderingProcessor (96ms).

Problem 1: PolynomialOrderingProcessor

Dependency Pair Problem

Dependency Pairs

f#(x, s(s(y))) → f#(y, x)f#(s(x), y) → f#(x, s(s(x)))

Rewrite Rules

f(s(x), y) → f(x, s(s(x)))f(x, s(s(y))) → f(y, x)

Original Signature

Termination of terms over the following signature is verified: f, s

Strategy

Polynomial Interpretation

There are no usable rules

The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:

f#(x, s(s(y))) → f#(y, x)f#(s(x), y) → f#(x, s(s(x)))