g(f(

g(h(

g(

R

↳Removing Redundant Rules

Removing the following rules from

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

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

where the Polynomial interpretation:

was used.

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

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

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

where the Polynomial interpretation:

was used.

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