Certification Problem

Input (TPDB TRS_Standard/Mixed_TRS/4)

The rewrite relation of the following TRS is considered.

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

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.