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

↳AFS

**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 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:

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

↳AFS

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

↳Argument Filtering and Ordering

**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

The following dependency pair can be strictly oriented:

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

The following usable rules for innermost can be oriented:

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

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

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

{f, 0}

resulting in one new DP problem.

Used Argument Filtering System:

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

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

f(x) -> f_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳Dependency Graph

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.

Duration:

0:00 minutes