p(

p(

p(

R

↳Dependency Pair Analysis

P(m,n, s(r)) -> P(m,r,n)

P(m, s(n), 0) -> P(0,n,m)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**P( m, s(n), 0) -> P(0, n, m)**

p(m,n, s(r)) -> p(m,r,n)

p(m, s(n), 0) -> p(0,n,m)

p(m, 0, 0) ->m

The following dependency pairs can be strictly oriented:

P(m, s(n), 0) -> P(0,n,m)

P(m,n, s(r)) -> P(m,r,n)

The following rules can be oriented:

p(m,n, s(r)) -> p(m,r,n)

p(m, s(n), 0) -> p(0,n,m)

p(m, 0, 0) ->m

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(P(x)_{1}, x_{2}, x_{3})= x _{1}+ x_{2}+ x_{3}_{ }^{ }_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(p(x)_{1}, x_{2}, x_{3})= x _{1}+ x_{2}+ x_{3}_{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

P(x,_{1}x,_{2}x) -> P(_{3}x,_{1}x,_{2}x)_{3}

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

p(x,_{1}x,_{2}x) -> p(_{3}x,_{1}x,_{2}x)_{3}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

p(m,n, s(r)) -> p(m,r,n)

p(m, s(n), 0) -> p(0,n,m)

p(m, 0, 0) ->m

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes