Certification Problem

Input (TPDB TRS_Standard/Mixed_TRS/hydra)

The rewrite relation of the following TRS is considered.

f(cons(nil,y)) y (1)
f(cons(f(cons(nil,y)),z)) copy(n,y,z) (2)
copy(0,y,z) f(z) (3)
copy(s(x),y,z) copy(x,y,cons(f(y),z)) (4)

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.
copy#(0,y,z) f#(z) (5)
copy#(s(x),y,z) copy#(x,y,cons(f(y),z)) (6)
f#(cons(f(cons(nil,y)),z)) copy#(n,y,z) (7)
copy#(s(x),y,z) f#(y) (8)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.