f(s(0), g(

g(s(

R

↳Dependency Pair Analysis

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

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

The following dependency pair can be strictly oriented:

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

There are no usable rules using the Ce-refinement that need to be oriented.

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Remaining

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

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

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

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

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

Duration:

0:00 minutes