f(g(

R

↳Dependency Pair Analysis

F(g(X),Y) -> F(X, f(g(X),Y))

F(g(X),Y) -> F(g(X),Y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Rewriting Transformation

**F(g( X), Y) -> F(g(X), Y)**

f(g(X),Y) -> f(X, f(g(X),Y))

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

F(g(X),Y) -> F(X, f(g(X),Y))

F(g(X),Y) -> F(X, f(X, f(g(X),Y)))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Rw

→DP Problem 2

↳Rewriting Transformation

**F(g( X), Y) -> F(X, f(X, f(g(X), Y)))**

f(g(X),Y) -> f(X, f(g(X),Y))

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

F(g(X),Y) -> F(X, f(X, f(g(X),Y)))

F(g(X),Y) -> F(X, f(X, f(X, f(g(X),Y))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Rw

→DP Problem 2

↳Rw

...

→DP Problem 3

↳Argument Filtering and Ordering

**F(g( X), Y) -> F(X, f(X, f(X, f(g(X), Y))))**

f(g(X),Y) -> f(X, f(g(X),Y))

innermost

The following dependency pair can be strictly oriented:

F(g(X),Y) -> F(X, f(X, f(X, f(g(X),Y))))

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

f(g(X),Y) -> f(X, f(g(X),Y))

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

F(x,_{1}x) -> F(_{2}x,_{1}x)_{2}

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

f(x,_{1}x) ->_{2}x_{2}

R

↳DPs

→DP Problem 1

↳Rw

→DP Problem 2

↳Rw

...

→DP Problem 4

↳Remaining Obligation(s)

The following remains to be proven:

**F(g( X), Y) -> F(g(X), Y)**

f(g(X),Y) -> f(X, f(g(X),Y))

innermost

Duration:

0:00 minutes