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. 



   R
     ↳Removing Redundant Rules for Innermost Termination



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)


   R
     ↳RRRI
       →TRS2
         ↳Removing Redundant Rules



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(x1, x2))=  x1 + x2  
was used.

All Rules of R can be deleted. 


   R
     ↳RRRI
       →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