or(

and(

not(not(

not(and(

not(or(

R

↳Dependency Pair Analysis

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

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)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

or(x,x) ->x

and(x,x) ->x

not(not(x)) ->x

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

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

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 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:

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

↳Dependency Graph

or(x,x) ->x

and(x,x) ->x

not(not(x)) ->x

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

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes