Certification Problem

Input (TPDB SRS_Standard/Waldmann_06_SRS/uni-5)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
b#(b(x1)) c#(c(c(c(x1)))) (4)
b#(b(x1)) c#(c(c(x1))) (5)
b#(b(x1)) c#(c(x1)) (6)
b#(b(x1)) c#(x1) (7)
c#(c(x1)) a#(c(b(x1))) (8)
c#(c(x1)) c#(b(x1)) (9)
c#(c(x1)) b#(x1) (10)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.