Certification Problem

Input (TPDB TRS_Standard/Secret_06_TRS/gen-14)

The rewrite relation of the following TRS is considered.

b(f(b(x,z)),y) f(f(f(b(z,b(y,z))))) (1)
c(f(f(c(x,a,z))),a,y) b(y,f(b(a,z))) (2)
b(b(c(b(a,a),a,z),f(a)),y) z (3)

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.
b#(f(b(x,z)),y) b#(z,b(y,z)) (4)
b#(f(b(x,z)),y) b#(y,z) (5)
c#(f(f(c(x,a,z))),a,y) b#(y,f(b(a,z))) (6)
c#(f(f(c(x,a,z))),a,y) b#(a,z) (7)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.