YES
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 POLO(bPol) ... removes: 4 8 1 3 5 10 7 9 6 2
      and	w: 2 * x1 + 2 * x2 + 5855
      false	w: 1
      true	w: 30613
      if	w: x1 + x2 + x3 + 5853
      = 	w: 2 * x1 + 2 * x2 + 42323
      or	w: 2 * x1 + 2 * x2 + 36467
      implies	w: 2 * x1 + x2 + 36467
      not	w: x1 + 36468
Number of strict rules: 0