Certification Problem

Input (TPDB TRS_Standard/Mixed_TRS/2)

The rewrite relation of the following TRS is considered.

f(a,f(f(a,a),x)) f(f(a,a),f(a,f(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#(a,f(f(a,a),x)) f#(f(a,a),f(a,f(a,x))) (2)
f#(a,f(f(a,a),x)) f#(a,f(a,x)) (3)
f#(a,f(f(a,a),x)) f#(a,x) (4)

1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.