+(-(

-(+(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Forward Instantiation Transformation

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

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

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

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

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

-(+(x,y),y) ->x

innermost

The following dependency pair can be strictly oriented:

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

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

-(+(x,y),y) ->x

Used ordering: Polynomial ordering with Polynomial interpretation:

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

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,z),y)

-(+(x,y),y) ->x

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes