Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z048)

The rewrite relation of the following TRS is considered.

b(a(b(a(c(b(a(x1)))))))

→

a(b(a(c(b(b(a(b(a(c(x1))))))))))

(1)

Prove or disprove termination.

Yes.

Since only unary symbols occur, one can reverse all terms and obtains the TRS

a(b(c(a(b(a(b(x1)))))))

→

c(a(b(a(b(b(c(a(b(a(x1))))))))))

(2)

The following set of initial dependency pairs has been identified.

The dependency pairs are split into 1 component.

The 1^st component contains the pair

a^#(b(c(a(b(a(b(x1)))))))	→	a^#(x1)	(3)
a^#(b(c(a(b(a(b(x1)))))))	→	a^#(b(a(x1)))	(5)

Using the matrix interpretations of dimension 2 with strict dimension 1 over the naturals

[c(x₁)]

0	1
0	0

· x₁ +

[b(x₁)]

1	0
0	1

· x₁ +

[a(x₁)]

1	1
1	0

· x₁ +

[a^#(x₁)]

1	0
0	0

· x₁ +

together with the usable rule

a(b(c(a(b(a(b(x1)))))))

→

c(a(b(a(b(b(c(a(b(a(x1))))))))))

(2)

(w.r.t. the implicit argument filter of the reduction pair), the pairs

a^#(b(c(a(b(a(b(x1)))))))	→	a^#(x1)	(3)
a^#(b(c(a(b(a(b(x1)))))))	→	a^#(b(a(x1)))	(5)

could be deleted.

The dependency pairs are split into 0 components.