Certification Problem

Input (TPDB SRS_Standard/Secret_06_SRS/2-matchbox)

The rewrite relation of the following TRS is considered.

Prove or disprove termination.

Yes.

Using the linear polynomial interpretation over (2 x 2)-matrices with strict dimension 1 over the arctic semiring over the integers

[b(x₁)]

0	0
0	0

· x₁ +

-∞	-∞
-∞	-∞

[c(x₁)]

0	1
0	0

· x₁ +

-∞	-∞
-∞	-∞

[a(x₁)]

0	0
-∞	-∞

· x₁ +

-∞	-∞
-∞	-∞

all of the following rules can be deleted.

c(c(x1))

→

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

(1)

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

Using the

together with the usable rules

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

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

could be deleted.

There are no pairs anymore.