g(0, f(

g(

g(s(

g(f(

R

↳Removing Redundant Rules

Removing the following rules from

g(0, f(x,x)) ->x

where the Polynomial interpretation:

was used.

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(g(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }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(s(x),y) -> g(f(x,y), 0)

g(x, s(y)) -> g(f(x,y), 0)

where the Polynomial interpretation:

was used.

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

Not all Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳Removing Redundant Rules

Removing the following rules from

g(f(x,y), 0) -> f(g(x, 0), g(y, 0))

where the Polynomial interpretation:

was used.

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(g(x)_{1}, x_{2})= 2·x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(f(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }

All Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳RRRPolo

...

→TRS4

↳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

↳RRRPolo

...

→TRS5

↳Dependency Pair Analysis

Duration:

0:00 minutes