Certification Problem

Input (TPDB TRS_Standard/Zantema_05/jw25)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by NaTT @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
f#(f(a,a),x) f#(a,f(a,f(a,a))) (2)
f#(f(a,a),x) f#(a,f(a,a)) (3)
f#(f(a,a),x) f#(x,f(a,f(a,f(a,a)))) (4)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.