Term Rewriting System R:
[x, y, z]
f(0, 1, x) -> f(x, x, x)
f(x, y, z) -> 2
0 -> 2
1 -> 2

Innermost Termination of R to be shown.



   R
Removing Redundant Rules for Innermost Termination



Removing the following rules from R which left hand sides contain non normal subterms

f(0, 1, x) -> f(x, x, x)


   R
RRRI
       →TRS2
Removing Redundant Rules



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

f(x, y, z) -> 2

where the Polynomial interpretation:
  POL(0)=  0  
  POL(1)=  0  
  POL(2)=  0  
  POL(f(x1, x2, x3))=  1 + x1 + x2 + x3  
was used.

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


   R
RRRI
       →TRS2
RRRPolo
           →TRS3
Removing Redundant Rules



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

1 -> 2

where the Polynomial interpretation:
  POL(0)=  0  
  POL(1)=  1  
  POL(2)=  0  
was used.

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


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



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

0 -> 2

where the Polynomial interpretation:
  POL(0)=  1  
  POL(2)=  0  
was used.

All Rules of R can be deleted.


   R
RRRI
       →TRS2
RRRPolo
           →TRS3
RRRPolo
             ...
               →TRS5
Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

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