and(

and(

and(

and(false,

and(

or(or(

or(

or(true,

or(

or(

or(

R

↳Dependency Pair Analysis

AND(x, or(y,z)) -> OR(and(x,y), and(x,z))

AND(x, or(y,z)) -> AND(x,y)

AND(x, or(y,z)) -> AND(x,z)

AND(x, and(y,y)) -> AND(x,y)

OR(x, or(y,y)) -> OR(x,y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**AND( x, or(y, z)) -> AND(x, z)**

and(x, or(y,z)) -> or(and(x,y), and(x,z))

and(x, and(y,y)) -> and(x,y)

and(x, true) ->x

and(false,y) -> false

and(x,x) ->x

or(or(x,y), and(y,z)) -> or(x,y)

or(x, and(x,y)) ->x

or(true,y) -> true

or(x, false) ->x

or(x,x) ->x

or(x, or(y,y)) -> or(x,y)

innermost

The following dependency pairs can be strictly oriented:

AND(x, or(y,z)) -> AND(x,z)

AND(x, or(y,z)) -> AND(x,y)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(or(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(AND(x)_{1}, x_{2})= x _{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

and(x, or(y,z)) -> or(and(x,y), and(x,z))

and(x, and(y,y)) -> and(x,y)

and(x, true) ->x

and(false,y) -> false

and(x,x) ->x

or(or(x,y), and(y,z)) -> or(x,y)

or(x, and(x,y)) ->x

or(true,y) -> true

or(x, false) ->x

or(x,x) ->x

or(x, or(y,y)) -> or(x,y)

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes