Certification Problem

Input (TPDB TRS_Standard/Mixed_TRS/1)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
f#(a,f(a,x)) f#(a,f(x,f(f(a,a),a))) (2)
f#(a,f(a,x)) f#(x,f(f(a,a),a)) (3)
f#(a,f(a,x)) f#(f(a,a),a) (4)
f#(a,f(a,x)) f#(a,a) (5)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.