a(b(a(b(

R

↳Dependency Pair Analysis

A(b(a(b(x)))) -> A(b(a(a(b(x)))))

A(b(a(b(x)))) -> A(a(b(x)))

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

**A(b(a(b( x)))) -> A(a(b(x)))**

a(b(a(b(x)))) -> b(a(b(a(a(b(x))))))

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

As a result of transforming the rule

one new Dependency Pair is created:

A(b(a(b(x)))) -> A(b(a(a(b(x)))))

A(b(a(b(a(b(x'')))))) -> A(b(a(b(a(b(a(a(b(x'')))))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Narrowing Transformation

**A(b(a(b(a(b( x'')))))) -> A(b(a(b(a(b(a(a(b(x'')))))))))**

a(b(a(b(x)))) -> b(a(b(a(a(b(x))))))

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

As a result of transforming the rule

one new Dependency Pair is created:

A(b(a(b(x)))) -> A(a(b(x)))

A(b(a(b(a(b(x'')))))) -> A(b(a(b(a(a(b(x'')))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Nar

...

→DP Problem 3

↳Remaining Obligation(s)

The following remains to be proven:

**A(b(a(b(a(b( x'')))))) -> A(b(a(b(a(a(b(x'')))))))**

a(b(a(b(x)))) -> b(a(b(a(a(b(x))))))

Duration:

0:00 minutes