Term Rewriting System R:
[y, x, f]
app(app(plus, 0), y) -> y
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
app(app(app(curry, f), x), y) -> app(app(f, x), y)
add -> app(curry, plus)

Innermost Termination of R to be shown.



   R
Removing Redundant Rules



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

app(app(plus, 0), y) -> y

where the Polynomial interpretation:
  POL(plus)=  0  
  POL(0)=  1  
  POL(curry)=  0  
  POL(s)=  0  
  POL(app(x1, x2))=  x1 + x2  
  POL(add)=  0  
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:

add -> app(curry, plus)

where the Polynomial interpretation:
  POL(plus)=  0  
  POL(curry)=  0  
  POL(s)=  0  
  POL(app(x1, x2))=  x1 + x2  
  POL(add)=  1  
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:

app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
app(app(app(curry, f), x), y) -> app(app(f, x), y)

where the Polynomial interpretation:
  POL(plus)=  0  
  POL(curry)=  4  
  POL(s)=  0  
  POL(app(x1, x2))=  1 + 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