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

↳Polynomial 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)

Additionally, the following rules can be oriented:

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

g(0) -> 0

f(0) -> s(0)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(g(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(G(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(f(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→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