and(

and(

not(not(

implies(false,

implies(

implies(not(

R

↳Removing Redundant Rules

Removing the following rules from

and(x, false) -> false

and(x, not(false)) ->x

not(not(x)) ->x

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

where the Polynomial interpretation:

was used.

_{ }^{ }POL(and(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(false)= 0 _{ }^{ }_{ }^{ }POL(implies(x)_{1}, x_{2})= 1 + 2·x _{1}+ 2·x_{2}_{ }^{ }_{ }^{ }POL(not(x)_{1})= 1 + 2·x _{1}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

implies(x, false) -> not(x)

implies(false,y) -> not(false)

where the Polynomial interpretation:

was used.

_{ }^{ }POL(false)= 0 _{ }^{ }_{ }^{ }POL(implies(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(not(x)_{1})= x _{1}_{ }^{ }

All Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳Overlay and local confluence Check

The TRS is overlay and locally confluent (all critical pairs are trivially joinable).Hence, we can switch to innermost.

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳OC

...

→TRS4

↳Dependency Pair Analysis

Duration:

0:00 minutes