Certification Problem

Input (TPDB TRS_Standard/Zantema_05/jw03)

The rewrite relation of the following TRS is considered.

f(x,f(a,a)) f(f(f(a,a),a),x) (1)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Switch to Innermost Termination

The TRS is overlay and locally confluent:

10

Hence, it suffices to show innermost termination in the following.

1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
f#(x,f(a,a)) f#(f(f(a,a),a),x) (2)
f#(x,f(a,a)) f#(f(a,a),a) (3)

1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.