f(

f(

f(

f(

g1(

g1(

g2(

g2(

h(

R

↳Removing Redundant Rules

Removing the following rules from

f(x,y) -> g1(x,x,y)

f(x,y) -> g1(y,x,x)

f(x,y) -> g2(x,y,y)

f(x,y) -> g2(y,y,x)

where the Polynomial interpretation:

was used.

_{ }^{ }POL(g2(x)_{1}, x_{2}, x_{3})= x _{1}+ x_{2}+ x_{3}_{ }^{ }_{ }^{ }POL(h(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(f(x)_{1}, x_{2})= 1 + 2·x _{1}+ 2·x_{2}_{ }^{ }_{ }^{ }POL(g1(x)_{1}, x_{2}, x_{3})= x _{1}+ x_{2}+ x_{3}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

h(x,x) ->x

where the Polynomial interpretation:

was used.

_{ }^{ }POL(g2(x)_{1}, x_{2}, x_{3})= 1 + x _{1}+ x_{2}+ x_{3}_{ }^{ }_{ }^{ }POL(h(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(g1(x)_{1}, x_{2}, x_{3})= 1 + x _{1}+ x_{2}+ x_{3}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳Removing Redundant Rules

Removing the following rules from

g1(y,x,x) -> h(x,y)

g1(x,x,y) -> h(x,y)

where the Polynomial interpretation:

was used.

_{ }^{ }POL(g2(x)_{1}, x_{2}, x_{3})= x _{1}+ x_{2}+ x_{3}_{ }^{ }_{ }^{ }POL(h(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(g1(x)_{1}, x_{2}, x_{3})= 1 + x _{1}+ x_{2}+ x_{3}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳RRRPolo

...

→TRS4

↳Removing Redundant Rules

Removing the following rules from

g2(x,y,y) -> h(x,y)

g2(y,y,x) -> h(x,y)

where the Polynomial interpretation:

was used.

_{ }^{ }POL(g2(x)_{1}, x_{2}, x_{3})= 1 + x _{1}+ x_{2}+ x_{3}_{ }^{ }_{ }^{ }POL(h(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }

All Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳RRRPolo

...

→TRS5

↳Dependency Pair Analysis

Duration:

0:00 minutes