f(g(

f(g(

R

↳Dependency Pair Analysis

F(g(x)) -> F(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Forward Instantiation Transformation

**F(g( x)) -> F(x)**

f(g(x)) -> g(g(f(x)))

f(g(x)) -> g(g(g(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:

F(g(x)) -> F(x)

F(g(g(x''))) -> F(g(x''))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Forward Instantiation Transformation

**F(g(g( x''))) -> F(g(x''))**

f(g(x)) -> g(g(f(x)))

f(g(x)) -> g(g(g(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:

F(g(g(x''))) -> F(g(x''))

F(g(g(g(x'''')))) -> F(g(g(x'''')))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳FwdInst

...

→DP Problem 3

↳Polynomial Ordering

**F(g(g(g( x'''')))) -> F(g(g(x'''')))**

f(g(x)) -> g(g(f(x)))

f(g(x)) -> g(g(g(x)))

innermost

The following dependency pair can be strictly oriented:

F(g(g(g(x'''')))) -> F(g(g(x'''')))

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳FwdInst

...

→DP Problem 4

↳Dependency Graph

f(g(x)) -> g(g(f(x)))

f(g(x)) -> g(g(g(x)))

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes