YES
Did not drop rules.
Inlined conditions for 0 rules.
Left-inlined conditions for 0 rules.
Due to Ifrit-method removed 2 infeasible rules:
  f(c(x),c(c(y))) -> a(a(x)) 
   | c(f(x,y)) ->* c(a(b()))
  f(c(c(c(x))),y) -> a(y) 
   | c(f(c(x)
        ,c(c(y)))) ->* c(a(a(b())))
Did not use redundant rules method.
INFEASIBLE because

problem obtained from input
is proven infeasible
using TCAP on
|(c(f(c(c(x1)),y))
 ,c(f(c(x1)
     ,c(c(c(c(y))))))) ->* |(c(a(b()))
                            ,c(a(a(b()))))

where | is used as a fresh function symbol, since it is illegal in the input format.