f(0) -> 1

f(s(

f(s(

g(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

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

f(0) -> 1

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

f(s(x)) -> +(f(x), s(f(x)))

g(x) -> +(x, s(x))

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 implicit AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(s(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

f(0) -> 1

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

f(s(x)) -> +(f(x), s(f(x)))

g(x) -> +(x, s(x))

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes