concat(leaf,

concat(cons(

lessleaves(

lessleaves(leaf, cons(

lessleaves(cons(

R

↳Removing Redundant Rules

Removing the following rules from

concat(leaf,Y) ->Y

lessleaves(X, leaf) -> false

lessleaves(leaf, cons(W,Z)) -> true

where the Polynomial interpretation:

was used.

_{ }^{ }POL(cons(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(false)= 0 _{ }^{ }_{ }^{ }POL(lessleaves(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(true)= 0 _{ }^{ }_{ }^{ }POL(leaf)= 1 _{ }^{ }_{ }^{ }POL(concat(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

lessleaves(cons(U,V), cons(W,Z)) -> lessleaves(concat(U,V), concat(W,Z))

where the Polynomial interpretation:

was used.

_{ }^{ }POL(cons(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(lessleaves(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(concat(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

concat(cons(U,V),Y) -> cons(U, concat(V,Y))

where the Polynomial interpretation:

was used.

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

All Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳RRRPolo

...

→TRS4

↳Dependency Pair Analysis

Duration:

0:00 minutes