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