and(not(not(

R

↳Dependency Pair Analysis

AND(not(not(x)),y, not(z)) -> AND(y, band(x,z),x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**AND(not(not( x)), y, not(z)) -> AND(y, band(x, z), x)**

and(not(not(x)),y, not(z)) -> and(y, band(x,z),x)

innermost

The following dependency pair can be strictly oriented:

AND(not(not(x)),y, not(z)) -> AND(y, band(x,z),x)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(not(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(AND(x)_{1}, x_{2}, x_{3})= 1 + x _{1}+ x_{2}+ x_{3}_{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

AND(x,_{1}x,_{2}x) -> AND(_{3}x,_{1}x,_{2}x)_{3}

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

band(x,_{1}x) ->_{2}x_{2}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

and(not(not(x)),y, not(z)) -> and(y, band(x,z),x)

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes