Term Rewriting System R:

   [x, y, z]
   +(+(x, y), z) -> +(x, +(y, z))
   +(f(x), f(y)) -> f(+(x, y))
   +(f(x), +(f(y), z)) -> +(f(+(x, y)), z)

Termination of R to be shown.


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

   +(f(x), f(y)) -> f(+(x, y))
   +(f(x), +(f(y), z)) -> +(f(+(x, y)), z)

where the Polynomial interpretation:
POL(+(x_1, x_2)) = x_1 + x_2
POL(f(x_1)) = 1 + x_1
was used. 



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


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

   +(+(x, y), z) -> +(x, +(y, z))

where the Polynomial interpretation:
POL(+(x_1, x_2)) = 1 + 2*x_1 + x_2
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.402 seconds.