a(b(a(

R

↳Dependency Pair Analysis

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Forward Instantiation Transformation

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

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

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Polynomial Ordering

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

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

innermost

The following dependency pair can be strictly oriented:

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

Additionally, the following usable rule for innermost w.r.t. to the implicit AFS can be oriented:

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(b(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(a(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(A(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes