f(f(

f(

f(

f(

f(g(

R

↳Removing Redundant Rules

Removing the following rules from

f(f(x,y,z),u, f(x,y,v)) -> f(x,y, f(z,u,v))

f(x,y,y) ->y

f(x,y, g(y)) ->x

f(x,x,y) ->x

f(g(x),x,y) ->y

where the Polynomial interpretation:

was used.

_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(f(x)_{1}, x_{2}, x_{3})= 1 + x _{1}+ x_{2}+ x_{3}_{ }^{ }

All Rules of

R

↳RRRPolo

→TRS2

↳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

↳OC

→TRS3

↳Dependency Pair Analysis

Duration:

0:00 minutes