p(

p(

p(

R

↳Removing Redundant Rules

Removing the following rules from

p(m,n, s(r)) -> p(m,r,n)

p(m, s(n), 0) -> p(0,n,m)

where the Polynomial interpretation:

was used.

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(p(x)_{1}, x_{2}, x_{3})= x _{1}+ x_{2}+ x_{3}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

p(m, 0, 0) ->m

where the Polynomial interpretation:

was used.

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(p(x)_{1}, x_{2}, x_{3})= 1 + x _{1}+ x_{2}+ x_{3}_{ }^{ }

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