YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

a(a(x0))	→	x0
a(b(a(b(x0))))	→	b(a(b(b(a(a(x0))))))

The following set of initial dependency pairs has been identified.

The dependency pairs are split into 1 component.

The 1^st component contains the pairs

a^#(b(a(b(x0))))	→	a^#(a(x0))
a^#(b(a(b(x0))))	→	a^#(x0)

Using the linear polynomial interpretation over (3 x 3)-matrices with strict dimension 1 over the naturals

[b(x₁)]

· x₁ +

[a(x₁)]

· x₁ +

[a^#(x₁)]

· x₁ +

all pairs could be removed.

There are no pairs anymore.