Certification Problem

Input (TPDB TRS_Standard/Secret_06_TRS/gen-18)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
b#(b(y,z),c(a,a,a)) c#(z,y,z) (4)
b#(b(y,z),c(a,a,a)) f#(c(z,y,z)) (5)
c#(y,x,f(z)) b#(z,x) (6)
c#(y,x,f(z)) f#(b(z,x)) (7)
c#(y,x,f(z)) b#(f(b(z,x)),z) (8)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.