implies(not(

implies(not(

implies(

R

↳Dependency Pair Analysis

IMPLIES(not(x), or(y,z)) -> IMPLIES(y, or(x,z))

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

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

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

implies(not(x), or(y,z)) -> implies(y, or(x,z))

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

innermost

The following dependency pair can be strictly oriented:

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

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 _{2}_{ }^{ }_{ }^{ }POL(not(x)_{1})= 0 _{ }^{ }_{ }^{ }POL(IMPLIES(x)_{1}, x_{2})= x _{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

**IMPLIES(not( x), or(y, z)) -> IMPLIES(y, or(x, z))**

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

implies(not(x), or(y,z)) -> implies(y, or(x,z))

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

innermost

The following dependency pair can be strictly oriented:

IMPLIES(not(x), or(y,z)) -> IMPLIES(y, or(x,z))

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})= x _{1}_{ }^{ }_{ }^{ }POL(not(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(IMPLIES(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 3

↳Dependency Graph

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

implies(not(x), or(y,z)) -> implies(y, or(x,z))

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes