g(s(

g(0) -> 0

f(0) -> s(0)

f(s(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

g(0) -> 0

f(0) -> s(0)

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

The following dependency pairs can be strictly oriented:

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

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

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

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

{G, s} > F

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

g(0) -> 0

f(0) -> s(0)

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes