Term Rewriting System R:

   [x, y, z]
   app(app(app(f, app(app(g, x), y)), x), z) -> app(app(app(f, z), z), z)
   app(app(g, x), y) -> x
   app(app(g, x), y) -> y

Innermost Termination of R to be shown.


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

   app(app(app(f, app(app(g, x), y)), x), z) -> app(app(app(f, z), z), z)

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

   app(app(g, x), y) -> x
   app(app(g, x), y) -> y

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



All Rules of R can be deleted.



Innermost Termination of R successfully shown.


Duration: 0.361 seconds.