g(

g(

f(s(

R

↳Dependency Pair Analysis

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Instantiation Transformation

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

g(x,y) ->x

g(x,y) ->y

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

On this DP problem, an Instantiation SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

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

F(s(x0), s(x'''), s(x''')) -> F(s(x'''),x0, s(x0))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Polynomial Ordering

**F(s( x0), s(x'''), s(x''')) -> F(s(x'''), x0, s(x0))**

g(x,y) ->x

g(x,y) ->y

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

The following dependency pair can be strictly oriented:

F(s(x0), s(x'''), s(x''')) -> F(s(x'''),x0, s(x0))

Additionally, the following rules can be oriented:

g(x,y) ->x

g(x,y) ->y

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(f(x)_{1}, x_{2}, x_{3})= 0 _{ }^{ }_{ }^{ }POL(F(x)_{1}, x_{2}, x_{3})= x _{1}+ x_{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

g(x,y) ->x

g(x,y) ->y

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes