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

↳Argument Filtering and 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'')

There are no usable rules w.r.t. to the AFS that need to be oriented.

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

FAC(x) -> FAC(_{1}x)_{1}

s(x) -> s(_{1}x)_{1}

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳AFS

...

→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