Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z018)

The rewrite relation of the following TRS is considered.

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

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.
b#(c(x1)) b#(x1) (4)
a#(b(x1)) a#(x1) (5)
a#(b(x1)) b#(c(a(x1))) (6)
b#(a(x1)) a#(c(b(x1))) (7)
b#(c(x1)) b#(b(x1)) (8)
b#(a(x1)) b#(x1) (9)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.