*(

*(

R

↳Dependency Pair Analysis

*'(x, *(y,z)) -> *'(*(x,y),z)

*'(x, *(y,z)) -> *'(x,y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Forward Instantiation Transformation

***'( x, *(y, z)) -> *'(x, y)**

*(x, *(y,z)) -> *(*(x,y),z)

*(x,x) ->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:

*'(x, *(y,z)) -> *'(x,y)

*'(x'', *(*(y'',z''),z)) -> *'(x'', *(y'',z''))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Polynomial Ordering

***'( x'', *(*(y'', z''), z)) -> *'(x'', *(y'', z''))**

*(x, *(y,z)) -> *(*(x,y),z)

*(x,x) ->x

innermost

The following dependency pair can be strictly oriented:

*'(x'', *(*(y'',z''),z)) -> *'(x'', *(y'',z''))

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

*(x, *(y,z)) -> *(*(x,y),z)

*(x,x) ->x

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(*'(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(*(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

*(x, *(y,z)) -> *(*(x,y),z)

*(x,x) ->x

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes