g(

g(

f(0, 1,

f(

R

↳Dependency Pair Analysis

F(0, 1,x) -> F(s(x),x,x)

F(x,y, s(z)) -> F(0, 1,z)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**F( x, y, s(z)) -> F(0, 1, z)**

g(x,y) ->x

g(x,y) ->y

f(0, 1,x) -> f(s(x),x,x)

f(x,y, s(z)) -> s(f(0, 1,z))

The following dependency pair can be strictly oriented:

F(x,y, s(z)) -> F(0, 1,z)

The following rules can be oriented:

g(x,y) ->x

g(x,y) ->y

f(0, 1,x) -> f(s(x),x,x)

f(x,y, s(z)) -> s(f(0, 1,z))

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

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

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

g(x,_{1}x) -> g(_{2}x,_{1}x)_{2}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

**F(0, 1, x) -> F(s(x), x, x)**

g(x,y) ->x

g(x,y) ->y

f(0, 1,x) -> f(s(x),x,x)

f(x,y, s(z)) -> s(f(0, 1,z))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes