p(s(

fac(0) -> s(0)

fac(s(

R

↳Dependency Pair Analysis

FAC(s(x)) -> FAC(p(s(x)))

FAC(s(x)) -> P(s(x))

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

**FAC(s( x)) -> FAC(p(s(x)))**

p(s(x)) ->x

fac(0) -> s(0)

fac(s(x)) -> times(s(x), fac(p(s(x))))

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

FAC(s(x)) -> FAC(p(s(x)))

FAC(s(x'')) -> FAC(x'')

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Polynomial Ordering

**FAC(s( x'')) -> FAC(x'')**

p(s(x)) ->x

fac(0) -> s(0)

fac(s(x)) -> times(s(x), fac(p(s(x))))

The following dependency pair can be strictly oriented:

FAC(s(x'')) -> FAC(x'')

Additionally, the following rules can be oriented:

p(s(x)) ->x

fac(0) -> s(0)

fac(s(x)) -> times(s(x), fac(p(s(x))))

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(FAC(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(fac(x)_{1})= 1 _{ }^{ }_{ }^{ }POL(times(x)_{1}, x_{2})= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(p(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

p(s(x)) ->x

fac(0) -> s(0)

fac(s(x)) -> times(s(x), fac(p(s(x))))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes