Input TRS:
    1: f(X) -> if(X,c(),n__f(n__true()))
    2: if(true(),X,Y) -> X
    3: if(false(),X,Y) -> activate(Y)
    4: f(X) -> n__f(X)
    5: true() -> n__true()
    6: activate(n__f(X)) -> f(activate(X))
    7: activate(n__true()) -> true()
    8: activate(X) -> X
Number of Rules: 8
Direct QWPOS(Pol) ... orients all.
	I(if) = x1 + 2 * x2 + x3	sigma(if) = [1,2,3]
	I(c) = 0
	I(f) = x1 + 2	sigma(f) = [1]
	I(activate) = x1 + 2	sigma(activate) = [1]
	I(n__f) = x1 + 2	sigma(n__f) = [1]
	I(true) = 1
	I(false) = 3
	I(n__true) = 0
    PREC: true = n__true > c = activate > f = false > if = n__f
Number of Rules: 0