f(f(

f(s(

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

R

↳Dependency Pair Analysis

F(s(x)) -> F(x)

G(s(0)) -> G(f(s(0)))

G(s(0)) -> F(s(0))

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳Remaining

**F(s( x)) -> F(x)**

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

f(s(x)) -> f(x)

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

innermost

The following dependency pair can be strictly oriented:

F(s(x)) -> F(x)

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

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

F(x) -> F(_{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(f(x)) -> f(x)

f(s(x)) -> f(x)

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

innermost

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:

**G(s(0)) -> G(f(s(0)))**

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

f(s(x)) -> f(x)

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

innermost

Duration:

0:00 minutes