not(and(

not(or(

and(

R

↳Dependency Pair Analysis

NOT(and(x,y)) -> NOT(x)

NOT(and(x,y)) -> NOT(y)

NOT(or(x,y)) -> AND(not(x), not(y))

NOT(or(x,y)) -> NOT(x)

NOT(or(x,y)) -> NOT(y)

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

→DP Problem 2

↳Polo

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

not(and(x,y)) -> or(not(x), not(y))

not(or(x,y)) -> and(not(x), not(y))

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

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 w.r.t. to the implicit AFS 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 3

↳Dependency Graph

→DP Problem 2

↳Polo

not(and(x,y)) -> or(not(x), not(y))

not(or(x,y)) -> and(not(x), not(y))

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

innermost

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

**NOT(or( x, y)) -> NOT(y)**

not(and(x,y)) -> or(not(x), not(y))

not(or(x,y)) -> and(not(x), not(y))

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

innermost

The following dependency pairs can be strictly oriented:

NOT(or(x,y)) -> NOT(y)

NOT(or(x,y)) -> NOT(x)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(and(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(NOT(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(or(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

→DP Problem 4

↳Polynomial Ordering

**NOT(and( x, y)) -> NOT(y)**

not(and(x,y)) -> or(not(x), not(y))

not(or(x,y)) -> and(not(x), not(y))

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

innermost

The following dependency pairs can be strictly oriented:

NOT(and(x,y)) -> NOT(y)

NOT(and(x,y)) -> NOT(x)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(and(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(NOT(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

→DP Problem 4

↳Polo

...

→DP Problem 5

↳Dependency Graph

not(and(x,y)) -> or(not(x), not(y))

not(or(x,y)) -> and(not(x), not(y))

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes