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

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

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

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)

The following dependency pair can be strictly oriented:

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

There are no usable rules w.r.t. to the AFS 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:

OR(x,_{1}x) -> OR(_{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

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)

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

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

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)

The following dependency pairs can be strictly oriented:

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

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

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

There are no usable rules w.r.t. to the AFS 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}

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 2

↳AFS

→DP Problem 4

↳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)

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes