Input TRS:
    1: not(x) -> if(x,false(),true())
    2: and(x,y) -> if(x,y,false())
    3: or(x,y) -> if(x,true(),y)
    4: implies(x,y) -> if(x,y,true())
    5: =(x,x) -> true()
    6: =(x,y) -> if(x,y,not(y))
    7: if(true(),x,y) -> x
    8: if(false(),x,y) -> y
    9: if(x,x,if(x,false(),true())) -> true()
    10: =(x,y) -> if(x,y,if(y,false(),true()))
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3 5 10 7 9 6 2
   and(x1,x2)	weight: (/ 1 4) + x1 + x2
 false()	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: (/ 1 8) + x1 + x2 + x3
     =(x1,x2)	weight: (/ 1 2) + 2 * x1 + 2 * x2
    or(x1,x2)	weight: (/ 1 4) + x1 + x2
implies(x1,x2)	weight: (/ 1 4) + x1 + x2
   not(x1)	weight: (/ 1 4) + x1
Number of strict rules: 0
YES