i(0) -> 0

i(i(

i(+(

+(0,

+(

+(i(

+(

+(

+(+(

+(+(

R

↳Removing Redundant Rules

Removing the following rules from

i(0) -> 0

i(+(x,y)) -> +(i(x), i(y))

+(0,y) ->y

+(x, 0) ->x

+(+(x, i(y)),y) ->x

+(+(x,y), i(y)) ->x

where the Polynomial interpretation:

was used.

_{ }^{ }POL(i(x)_{1})= 2·x _{1}_{ }^{ }_{ }^{ }POL(0)= 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

+(x, +(y,z)) -> +(+(x,y),z)

+(x, i(x)) -> 0

+(i(x),x) -> 0

where the Polynomial interpretation:

was used.

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

Not all Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳Removing Redundant Rules

Removing the following rules from

i(i(x)) ->x

where the Polynomial interpretation:

was used.

_{ }^{ }POL(i(x)_{1})= 1 + x _{1}_{ }^{ }

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