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

Termination of R to be shown. 



   R
     ↳Removing Redundant Rules



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

f(g(f(a), h(a, f(a)))) -> f(h(g(f(a), a), g(f(a), f(a))))

where the Polynomial interpretation:
  POL(g(x1, x2))=  x1 + 2·x2  
  POL(h(x1, x2))=  1 + x1 + x2  
  POL(a)=  0  
  POL(f(x1))=  x1  
was used.

All Rules of R can be deleted. 


   R
     ↳RRRPolo
       →TRS2
         ↳Overlay and local confluence Check



The TRS is overlay and locally confluent (all critical pairs are trivially joinable).Hence, we can switch to innermost. 


   R
     ↳RRRPolo
       →TRS2
         ↳OC
           →TRS3
             ↳Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

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