Certification Problem

Input (TPDB SRS_Standard/Trafo_06/dup08)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
b#(b(c(c(a(a(x1)))))) b#(x1) (4)
b#(b(c(c(a(a(x1)))))) b#(b(x1)) (5)
b#(b(c(c(a(a(x1)))))) a#(b(b(x1))) (6)
b#(b(c(c(a(a(x1)))))) a#(a(b(b(x1)))) (7)
b#(b(c(c(a(a(x1)))))) a#(a(a(b(b(x1))))) (8)
b#(b(c(c(a(a(x1)))))) a#(a(a(a(b(b(x1)))))) (9)
b#(b(a(a(x1)))) b#(x1) (10)
b#(b(a(a(x1)))) b#(b(x1)) (11)
b#(b(a(a(x1)))) b#(b(b(x1))) (12)
b#(b(a(a(x1)))) b#(b(b(b(x1)))) (13)
b#(b(a(a(x1)))) a#(b(b(b(b(x1))))) (14)
b#(b(a(a(x1)))) a#(a(b(b(b(b(x1)))))) (15)
a#(a(a(a(b(b(x1)))))) b#(b(a(a(b(b(x1)))))) (16)
a#(a(a(a(b(b(x1)))))) b#(a(a(b(b(x1))))) (17)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.