f(0) -> s(0)

f(s(0)) -> s(s(0))

f(s(0)) -> *(s(s(0)), f(0))

f(+(

f(+(

R

↳Removing Redundant Rules

Removing the following rules from

f(0) -> s(0)

f(s(0)) -> s(s(0))

where the Polynomial interpretation:

was used.

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

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

f(+(x,y)) -> *(f(x), f(y))

where the Polynomial interpretation:

was used.

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

Not all Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳Removing Redundant Rules

Removing the following rules from

f(+(x, s(0))) -> +(s(s(0)), f(x))

where the Polynomial interpretation:

was used.

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

Not 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

F(s(0)) -> F(0)

Duration:

0:00 minutes