Certification Problem

Input (TPDB SRS_Standard/Secret_06_SRS/secr7)

The rewrite relation of the following TRS is considered.

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

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.
a#(b(c(x1))) b#(x1) (5)
a#(b(c(x1))) c#(b(x1)) (6)
a#(b(c(x1))) a#(c(b(x1))) (7)
a#(b(c(x1))) a#(a(c(b(x1)))) (8)
a#(b(c(x1))) b#(a(a(c(b(x1))))) (9)
a#(b(c(x1))) c#(b(a(a(c(b(x1)))))) (10)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.