Term Rewriting System R:
[X, Y]
f(c(X, s(Y))) -> f(c(s(X), Y))
g(c(s(X), Y)) -> f(c(X, s(Y)))

Innermost Termination of R to be shown.



   R
Removing Redundant Rules



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

f(c(X, s(Y))) -> f(c(s(X), Y))

where the Polynomial interpretation:
  POL(c(x1, x2))=  x1 + 2·x2  
  POL(g(x1))=  2·x1  
  POL(s(x1))=  1 + x1  
  POL(f(x1))=  x1  
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:

g(c(s(X), Y)) -> f(c(X, s(Y)))

where the Polynomial interpretation:
  POL(c(x1, x2))=  x1 + x2  
  POL(g(x1))=  1 + x1  
  POL(s(x1))=  x1  
  POL(f(x1))=  x1  
was used.

All Rules of R can be deleted.


   R
RRRPolo
       →TRS2
RRRPolo
           →TRS3
Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

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