Certification Problem

Input (TPDB SRS_Standard/Trafo_06/dup15)

The rewrite relation of the following TRS is considered.

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

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.
a#(a(x1)) b#(b(b(b(b(x1))))) (5)
a#(a(x1)) b#(x1) (6)
b#(b(d(d(b(b(x1)))))) c#(c(x1)) (7)
a#(a(d(d(x1)))) b#(b(x1)) (8)
a#(a(d(d(x1)))) b#(x1) (9)
b#(b(d(d(b(b(x1)))))) a#(a(c(c(x1)))) (10)
b#(b(d(d(b(b(x1)))))) c#(x1) (11)
a#(a(x1)) b#(b(x1)) (12)
a#(a(x1)) b#(b(b(b(x1)))) (13)
a#(a(x1)) b#(b(b(b(b(b(x1)))))) (14)
b#(b(d(d(b(b(x1)))))) a#(c(c(x1))) (15)
a#(a(x1)) b#(b(b(x1))) (16)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.