Certification Problem

Input (TPDB TRS_Standard/Rubio_04/mfp90b)

The rewrite relation of the following TRS is considered.

a	→	g(c)	(1)
g(a)	→	b	(2)
f(g(X),b)	→	f(a,X)	(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.

f^#(g(X),b)	→	a^#	(4)
a^#	→	g^#(c)	(5)
f^#(g(X),b)	→	f^#(a,X)	(6)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair
f^#(g(X),b) → f^#(a,X) (6)

1.1.1 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation

[a] = 20654

[b] = 3

[c] = 1

[f(x₁, x₂)] = 0

[f^#(x₁, x₂)] = x₁ + x₂ + 0

[g^#(x₁)] = 0

[a^#] = 0

[g(x₁)] = x₁ + 20653

together with the usable rules

a → g(c) (1)

g(a) → b (2)

(w.r.t. the implicit argument filter of the reduction pair), the pair
f^#(g(X),b) → f^#(a,X) (6)
could be deleted.
1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.