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

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

**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 that need to be oriented.

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳AFS

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

↳AFS

→DP Problem 2

↳Argument Filtering and 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)

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

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

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

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

NOT(x) -> NOT(_{1}x)_{1}

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳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