a(b(a(

R

↳Dependency Pair Analysis

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

The following dependency pair can be strictly oriented:

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

There are no usable rules w.r.t. to the AFS that need to be oriented.

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.

Used Argument Filtering System:

A(x) -> A(_{1}x)_{1}

b(x) -> b(_{1}x)_{1}

a(x) -> a(_{1}x)_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes