a(f, a(f, a(g, a(g,

R

↳Dependency Pair Analysis

A(f, a(f, a(g, a(g,x)))) -> A(g, a(g, a(g, a(f, a(f, a(f,x))))))

A(f, a(f, a(g, a(g,x)))) -> A(g, a(g, a(f, a(f, a(f,x)))))

A(f, a(f, a(g, a(g,x)))) -> A(g, a(f, a(f, a(f,x))))

A(f, a(f, a(g, a(g,x)))) -> A(f, a(f, a(f,x)))

A(f, a(f, a(g, a(g,x)))) -> A(f, a(f,x))

A(f, a(f, a(g, a(g,x)))) -> A(f,x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

**A(f, a(f, a(g, a(g, x)))) -> A(f, x)**

a(f, a(f, a(g, a(g,x)))) -> a(g, a(g, a(g, a(f, a(f, a(f,x))))))

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

two new Dependency Pairs are created:

A(f, a(f, a(g, a(g,x)))) -> A(f, a(f, a(f,x)))

A(f, a(f, a(g, a(g, a(g, a(g,x'')))))) -> A(f, a(g, a(g, a(g, a(f, a(f, a(f,x'')))))))

A(f, a(f, a(g, a(g, a(f, a(g, a(g,x''))))))) -> A(f, a(f, a(g, a(g, a(g, a(f, a(f, a(f,x''))))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

**A(f, a(f, a(g, a(g, a(f, a(g, a(g, x''))))))) -> A(f, a(f, a(g, a(g, a(g, a(f, a(f, a(f, x''))))))))**

a(f, a(f, a(g, a(g,x)))) -> a(g, a(g, a(g, a(f, a(f, a(f,x))))))

Duration:

0:00 minutes