f(

f(

f(

f(

g1(

g1(

g2(

g2(

h(

R

↳Removing Redundant Rules

Removing the following rules from

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

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

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

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

where the Polynomial interpretation:

was used.

_{ }^{ }POL(g2(x)_{1}, x_{2}, x_{3}, x_{4})= x _{1}+ x_{2}+ x_{3}+ x_{4}_{ }^{ }_{ }^{ }POL(h(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(a)= 0 _{ }^{ }_{ }^{ }POL(f(x)_{1}, x_{2}, x_{3}, x_{4}, x_{5})= 1 + 2·x _{1}+ 2·x_{2}+ x_{3}+ x_{4}+ x_{5}_{ }^{ }_{ }^{ }POL(g1(x)_{1}, x_{2}, x_{3}, x_{4})= x _{1}+ x_{2}+ x_{3}+ x_{4}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

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

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

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

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

where the Polynomial interpretation:

was used.

_{ }^{ }POL(g2(x)_{1}, x_{2}, x_{3}, x_{4})= x _{1}+ x_{2}+ x_{3}+ x_{4}_{ }^{ }_{ }^{ }POL(h(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(a)= 1 _{ }^{ }_{ }^{ }POL(g1(x)_{1}, x_{2}, x_{3}, x_{4})= x _{1}+ x_{2}+ x_{3}+ x_{4}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳Removing Redundant Rules

Removing the following rules from

h(x,x) ->x

where the Polynomial interpretation:

was used.

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

All Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳RRRPolo

...

→TRS4

↳Dependency Pair Analysis

Duration:

0:00 minutes