f(

g(h(

g(h(

R

↳Removing Redundant Rules

Removing the following rules from

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

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

where the Polynomial interpretation:

was used.

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

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

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

where the Polynomial interpretation:

was used.

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