Certification Problem

Input (TPDB TRS_Standard/Zantema_05/jw42)

The rewrite relation of the following TRS is considered.

f(f(a,x),a) f(f(f(a,f(a,a)),x),a) (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#(f(a,x),a) f#(f(f(a,f(a,a)),x),a) (2)
f#(f(a,x),a) f#(f(a,f(a,a)),x) (3)
f#(f(a,x),a) f#(a,f(a,a)) (4)
f#(f(a,x),a) f#(a,a) (5)

1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.