minus(minus(

minux(+(

+(minus(

+(+(

R

↳Removing Redundant Rules

Removing the following rules from

minus(minus(x)) ->x

+(minus(x), +(x,y)) ->y

+(+(x,y), minus(y)) ->x

where the Polynomial interpretation:

was used.

_{ }^{ }POL(minus(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(minux(x)_{1})= 2 + x _{1}_{ }^{ }_{ }^{ }POL(+(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

minux(+(x,y)) -> +(minus(y), minus(x))

where the Polynomial interpretation:

was used.

_{ }^{ }POL(minus(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(minux(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(+(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }

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