Certification Problem

Input (TPDB TRS_Standard/Zantema_05/z08)

The rewrite relation of the following TRS is considered.

f(a,f(b,f(a,x))) f(a,f(b,f(b,f(a,x)))) (1)
f(b,f(b,f(b,x))) f(b,f(b,x)) (2)

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

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.