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

↳Argument Filtering and Ordering

**F(g( X), Y) -> 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(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: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }

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

↳AFS

→DP Problem 2

↳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