merge(

merge(nil,

merge(++(

merge(++(

R

↳Removing Redundant Rules

Removing the following rules from

merge(x, nil) ->x

merge(nil,y) ->y

where the Polynomial interpretation:

was used.

_{ }^{ }POL(v)= 0 _{ }^{ }_{ }^{ }POL(merge(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(++(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(nil)= 1 _{ }^{ }_{ }^{ }POL(u)= 0 _{ }^{ }

Not all Rules of

R

↳RRRPolo

→TRS2

↳Removing Redundant Rules

Removing the following rules from

merge(++(x,y), ++(u, v)) -> ++(x, merge(y, ++(u, v)))

where the Polynomial interpretation:

was used.

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

Not all Rules of

R

↳RRRPolo

→TRS2

↳RRRPolo

→TRS3

↳Removing Redundant Rules

Removing the following rules from

merge(++(x,y), ++(u, v)) -> ++(u, merge(++(x,y), v))

where the Polynomial interpretation:

was used.

_{ }^{ }POL(v)= 1 _{ }^{ }_{ }^{ }POL(merge(x)_{1}, x_{2})= x _{1}+ 2·x_{2}_{ }^{ }_{ }^{ }POL(++(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(u)= 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