s(a) -> a

s(s(

s(f(

s(g(

f(

f(a,

f(g(

g(a, a) -> a

R

↳Removing Redundant Rules

Removing the following rules from

s(a) -> a

f(x, a) ->x

f(a,y) ->y

g(a, a) -> a

where the Polynomial interpretation:

was used.

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

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

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

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

where the Polynomial interpretation:

was used.

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

s(s(x)) ->x

where the Polynomial interpretation:

was used.

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

Not all Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳RRRPolo

...

→TRS4

↳Removing Redundant Rules

Removing the following rules from

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

where the Polynomial interpretation:

was used.

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

All Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳RRRPolo

...

→TRS5

↳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

...

→TRS6

↳Dependency Pair Analysis

Duration:

0:00 minutes