EQUATIONS: 
f(f(x,y),z) = f(x,f(y,z))
f(a1(),y) = y
f(a2(),y) = y
f(a3(),y) = y
f(x,i1(x)) = a1()
f(x,i2(x)) = a2()
f(x,i3(x)) = a3()

COMPLETE TRS:
RULES:
f(f(x,y),z) -> f(x,f(y,z))
f(a1(),y) -> y
f(a2(),y) -> y
f(a3(),y) -> y
f(x,i1(x)) -> a1()
i1(a1()) -> a1()
i1(a2()) -> a1()
i1(a3()) -> a1()
f(i1(x),f(x,y)) -> y
i2(x) -> f(i1(x),a2())
i3(x) -> f(i1(x),a3())
f(y,f(i1(y),x)) -> x
i1(i1(x)) -> f(x,a1())
i1(f(y,x)) -> f(i1(x),i1(y))
f(i1(x),a1()) -> i1(x)

SUCCESS
MaxTRS: 2 
Search time: 3.17 seconds