not(true) -> false

not(false) -> true

odd(0) -> false

odd(s(

+(

+(

+(s(

R

↳Removing Redundant Rules

Removing the following rules from

not(true) -> false

not(false) -> true

where the Polynomial interpretation:

was used.

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(odd(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(false)= 0 _{ }^{ }_{ }^{ }POL(true)= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(not(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(+(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

+(x, 0) ->x

odd(0) -> false

where the Polynomial interpretation:

was used.

_{ }^{ }POL(0)= 1 _{ }^{ }_{ }^{ }POL(odd(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(false)= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(not(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(+(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(x),y) -> s(+(x,y))

odd(s(x)) -> not(odd(x))

where the Polynomial interpretation:

was used.

_{ }^{ }POL(odd(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(not(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(+(x)_{1}, x_{2})= 2·x _{1}+ x_{2}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳RRRPolo

...

→TRS4

↳Removing Redundant Rules

Removing the following rules from

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

where the Polynomial interpretation:

was used.

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

All Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳RRRPolo

...

→TRS5

↳Dependency Pair Analysis

Duration:

0:00 minutes