YES (VAR X Y) (RULES f(s(X),Y) -> h(s(f(h(Y),X))) ) The TRS is an overlay system and all critical pairs are trivial, thus termination of innermost rewriting is equivalent to termination of rewriting. Proving termination of innermost rewriting for mfp95: -> Dependency pairs: nF_f(s(X),Y) -> nF_f(h(Y),X) -> Proof of termination for mfp95_1: Termination proved: No cycles in dependency graph. SETTINGS: Base ordering: Polynomial ordering Proof mode: SCCs in DG + base ordering Upper bound for coeffs: 1 Rationals below 1 for all non-replacing args: No Polynomial interpretation: Linear Coeffs in polynomials: No rationals Delta: automatic Termination was proved succesfully.