f(g(

g(s(

g(0) -> 0

R

↳Dependency Pair Analysis

F(g(x), s(0),y) -> F(y,y, g(x))

G(s(x)) -> G(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳Remaining

**G(s( x)) -> G(x)**

f(g(x), s(0),y) -> f(y,y, g(x))

g(s(x)) -> s(g(x))

g(0) -> 0

The following dependency pair can be strictly oriented:

G(s(x)) -> G(x)

The following rules can be oriented:

f(g(x), s(0),y) -> f(y,y, g(x))

g(s(x)) -> s(g(x))

g(0) -> 0

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

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

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

f(x,_{1}x,_{2}x) -> f_{3}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Remaining

f(g(x), s(0),y) -> f(y,y, g(x))

g(s(x)) -> s(g(x))

g(0) -> 0

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

**F(g( x), s(0), y) -> F(y, y, g(x))**

f(g(x), s(0),y) -> f(y,y, g(x))

g(s(x)) -> s(g(x))

g(0) -> 0

Duration:

0:00 minutes