f(0) -> cons(0, n

f(s(0)) -> f(p(s(0)))

f(

p(s(0)) -> 0

activate(n

activate(

R

↳Dependency Pair Analysis

F(s(0)) -> F(p(s(0)))

F(s(0)) -> P(s(0))

ACTIVATE(n_{f}(X)) -> F(X)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**F(s(0)) -> F(p(s(0)))**

f(0) -> cons(0, n_{f}(s(0)))

f(s(0)) -> f(p(s(0)))

f(X) -> n_{f}(X)

p(s(0)) -> 0

activate(n_{f}(X)) -> f(X)

activate(X) ->X

The following dependency pair can be strictly oriented:

F(s(0)) -> F(p(s(0)))

Additionally, the following usable rule w.r.t. to the implicit AFS can be oriented:

p(s(0)) -> 0

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 _{ }^{ }_{ }^{ }POL(F(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(p(x)_{1})= 0 _{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

f(0) -> cons(0, n_{f}(s(0)))

f(s(0)) -> f(p(s(0)))

f(X) -> n_{f}(X)

p(s(0)) -> 0

activate(n_{f}(X)) -> f(X)

activate(X) ->X

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes