f(0,

f(s(

R

↳Dependency Pair Analysis

F(s(x),y) -> F(f(x,y),y)

F(s(x),y) -> F(x,y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

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

f(0,y) -> 0

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

innermost

The following dependency pairs can be strictly oriented:

F(s(x),y) -> F(x,y)

F(s(x),y) -> F(f(x,y),y)

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

f(0,y) -> 0

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(f(x)_{1}, x_{2})= 0 _{ }^{ }_{ }^{ }POL(F(x)_{1}, x_{2})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

f(0,y) -> 0

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes