Certification Problem

Input (TPDB TRS_Standard/SK90/4.47)

The rewrite relation of the following TRS is considered.

f(g(i(a,b,b'),c),d) → if(e,f(.(b,c),d'),f(.(b',c),d')) (1)
f(g(h(a,b),c),d) → if(e,f(.(b,g(h(a,b),c)),d),f(c,d')) (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#(g(h(a,b),c),d) → f#(c,d') (3)
f#(g(i(a,b,b'),c),d) → f#(.(b,c),d') (4)
f#(g(h(a,b),c),d) → f#(.(b,g(h(a,b),c)),d) (5)
f#(g(i(a,b,b'),c),d) → f#(.(b',c),d') (6)

1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.