Term Rewriting System R:
[Y, U, V, X, W, Z]
concat(leaf, Y) -> Y
concat(cons(U, V), Y) -> cons(U, concat(V, Y))
lessleaves(X, leaf) -> false
lessleaves(leaf, cons(W, Z)) -> true
lessleaves(cons(U, V), cons(W, Z)) -> lessleaves(concat(U, V), concat(W, Z))

Innermost Termination of R to be shown. 



   R
     ↳Removing Redundant Rules



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

concat(leaf, Y) -> Y
lessleaves(X, leaf) -> false
lessleaves(leaf, cons(W, Z)) -> true

where the Polynomial interpretation:
  POL(cons(x1, x2))=  x1 + x2  
  POL(false)=  0  
  POL(lessleaves(x1, x2))=  x1 + x2  
  POL(true)=  0  
  POL(leaf)=  1  
  POL(concat(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
         ↳Removing Redundant Rules



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

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

where the Polynomial interpretation:
  POL(cons(x1, x2))=  1 + x1 + x2  
  POL(lessleaves(x1, x2))=  x1 + x2  
  POL(concat(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:

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

where the Polynomial interpretation:
  POL(cons(x1, x2))=  1 + x1 + x2  
  POL(concat(x1, x2))=  2·x1 + x2  
was used.

All Rules of R can be deleted. 


   R
     ↳RRRPolo
       →TRS2
         ↳RRRPolo
           →TRS3
             ↳RRRPolo
             ...
               →TRS4
                 ↳Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

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