Term Rewriting System R:
[x, y]
f(x, y) -> x
g(a) -> h(a, b, a)
i(x) -> f(x, x)
h(x, x, y) -> g(x)

Innermost Termination of R to be shown.



   R
Removing Redundant Rules



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

f(x, y) -> x

where the Polynomial interpretation:
  POL(i(x1))=  1 + 2·x1  
  POL(g(x1))=  x1  
  POL(b)=  0  
  POL(h(x1, x2, x3))=  x1 + x2 + x3  
  POL(a)=  0  
  POL(f(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:

i(x) -> f(x, x)

where the Polynomial interpretation:
  POL(i(x1))=  1 + 2·x1  
  POL(g(x1))=  x1  
  POL(b)=  0  
  POL(h(x1, x2, x3))=  x1 + x2 + x3  
  POL(a)=  0  
  POL(f(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
Dependency Pair Analysis



R contains the following Dependency Pairs:

H(x, x, y) -> G(x)
G(a) -> H(a, b, a)

R contains no SCCs.

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