Term Rewriting System R:
[YS, X, XS, Y, L]
app(nil, YS) -> YS
app(cons(X), YS) -> cons(X)
from(X) -> cons(X)
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
prefix(L) -> cons(nil)

Termination of R to be shown. 



   R
     ↳Removing Redundant Rules



Removing the following rules from R which fullfill a polynomial ordering:

app(nil, YS) -> YS
app(cons(X), YS) -> cons(X)
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil

where the Polynomial interpretation:
  POL(from(x1))=  x1  
  POL(cons(x1))=  x1  
  POL(nil)=  0  
  POL(app(x1, x2))=  1 + x1 + x2  
  POL(prefix(x1))=  x1  
  POL(zWadr(x1, x2))=  1 + x1 + x2  
was used.

Not all Rules of R can be deleted, so we still have to regard a part of R. 


   R
     ↳RRRPolo
       →TRS2
         ↳Removing Redundant Rules



Removing the following rules from R which fullfill a polynomial ordering:

prefix(L) -> cons(nil)

where the Polynomial interpretation:
  POL(from(x1))=  x1  
  POL(cons(x1))=  x1  
  POL(nil)=  0  
  POL(app(x1, x2))=  x1 + x2  
  POL(prefix(x1))=  1 + x1  
  POL(zWadr(x1, x2))=  x1 + x2  
was used.

Not all Rules of R can be deleted, so we still have to regard a part of R. 


   R
     ↳RRRPolo
       →TRS2
         ↳RRRPolo
           →TRS3
             ↳Removing Redundant Rules



Removing the following rules from R which fullfill a polynomial ordering:

from(X) -> cons(X)

where the Polynomial interpretation:
  POL(from(x1))=  1 + x1  
  POL(cons(x1))=  x1  
  POL(app(x1, x2))=  x1 + x2  
  POL(zWadr(x1, x2))=  x1 + x2  
was used.

Not all Rules of R can be deleted, so we still have to regard a part of R. 


   R
     ↳RRRPolo
       →TRS2
         ↳RRRPolo
           →TRS3
             ↳RRRPolo
             ...
               →TRS4
                 ↳Removing Redundant Rules



Removing the following rules from R which fullfill a polynomial ordering:

zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))

where the Polynomial interpretation:
  POL(cons(x1))=  x1  
  POL(app(x1, x2))=  x1 + x2  
  POL(zWadr(x1, x2))=  1 + x1 + x2  
was used.

All Rules of R can be deleted. 


   R
     ↳RRRPolo
       →TRS2
         ↳RRRPolo
           →TRS3
             ↳RRRPolo
             ...
               →TRS5
                 ↳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
             ...
               →TRS6
                 ↳Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

Termination of R successfully shown.
Duration:
0:00 minutes