Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z060)

The rewrite relation of the following TRS is considered.

b(b(a(b(b(b(x1)))))) a(b(b(b(b(b(a(x1))))))) (1)

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(a(b(b(b(x1)))))) b#(b(b(b(b(a(x1)))))) (2)
b#(b(a(b(b(b(x1)))))) b#(b(b(b(a(x1))))) (3)
b#(b(a(b(b(b(x1)))))) b#(b(b(a(x1)))) (4)
b#(b(a(b(b(b(x1)))))) b#(b(a(x1))) (5)
b#(b(a(b(b(b(x1)))))) b#(a(x1)) (6)

1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[b(x1)] = x1 +
1
[a(x1)] = x1 +
0
[b#(x1)] = x1 +
0
together with the usable rule
b(b(a(b(b(b(x1)))))) a(b(b(b(b(b(a(x1))))))) (1)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
b#(b(a(b(b(b(x1)))))) b#(b(b(b(a(x1))))) (3)
b#(b(a(b(b(b(x1)))))) b#(b(b(a(x1)))) (4)
b#(b(a(b(b(b(x1)))))) b#(b(a(x1))) (5)
b#(b(a(b(b(b(x1)))))) b#(a(x1)) (6)
and no rules could be deleted.

1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.