+(

+(

+(0, s(

s(+(0,

R

↳Removing Redundant Rules

Removing the following rules from

+(x, 0) ->x

+(0, s(y)) -> s(y)

s(+(0,y)) -> s(y)

where the Polynomial interpretation:

was used.

_{ }^{ }POL(0)= 1 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 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

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

where the Polynomial interpretation:

was used.

_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(+(x)_{1}, x_{2})= x _{1}+ 2·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