Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z105)

The rewrite relation of the following TRS is considered.

a(a(x1)) b(b(b(x1))) (1)
a(x1) d(c(d(x1))) (2)
b(b(x1)) c(c(c(x1))) (3)
c(c(x1)) d(d(d(x1))) (4)
c(d(d(x1))) a(x1) (5)

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.
c#(d(d(x1))) a#(x1) (6)
a#(a(x1)) b#(b(b(x1))) (7)
a#(a(x1)) b#(b(x1)) (8)
b#(b(x1)) c#(x1) (9)
b#(b(x1)) c#(c(c(x1))) (10)
a#(x1) c#(d(x1)) (11)
a#(a(x1)) b#(x1) (12)
b#(b(x1)) c#(c(x1)) (13)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.