Input TRS:
    1: a__and(true(),X) -> mark(X)
    2: a__and(false(),Y) -> false()
    3: a__if(true(),X,Y) -> mark(X)
    4: a__if(false(),X,Y) -> mark(Y)
    5: a__add(0(),X) -> mark(X)
    6: a__add(s(X),Y) -> s(add(X,Y))
    7: a__first(0(),X) -> nil()
    8: a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
    9: a__from(X) -> cons(X,from(s(X)))
    10: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    11: mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
    12: mark(add(X1,X2)) -> a__add(mark(X1),X2)
    13: mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
    14: mark(from(X)) -> a__from(X)
    15: mark(true()) -> true()
    16: mark(false()) -> false()
    17: mark(0()) -> 0()
    18: mark(s(X)) -> s(X)
    19: mark(nil()) -> nil()
    20: mark(cons(X1,X2)) -> cons(X1,X2)
    21: a__and(X1,X2) -> and(X1,X2)
    22: a__if(X1,X2,X3) -> if(X1,X2,X3)
    23: a__add(X1,X2) -> add(X1,X2)
    24: a__first(X1,X2) -> first(X1,X2)
    25: a__from(X) -> from(X)
Number of strict rules: 25
Direct Order(PosReal,>,Poly) ... removes: 18 4 15 8 1 3 16 21 19 17 22 5 10 7 20 25 14 12 23 24 11 9 13 6 2
     s(x1)	weight: (/ 1 16) + x1
a__from(x1)	weight: (/ 10587 8) + 2 * x1
   and(x1,x2)	weight: (/ 1 8) + x1 + x2
a__add(x1,x2)	weight: (/ 3 16) + x1 + 2 * x2
 false()	weight: 0
  true()	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: (/ 147657 8) + x1 + x2 + x3
  from(x1)	weight: (/ 21171 16) + x1
   nil()	weight: 0
  mark(x1)	weight: (/ 1 16) + 2 * x1
 first(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
a__first(x1,x2)	weight: (/ 5 16) + x1 + 2 * x2
  cons(x1,x2)	weight: (/ 1 16) + x1 + x2
   add(x1,x2)	weight: (/ 1 8) + x1 + x2
a__and(x1,x2)	weight: (/ 3 16) + x1 + 2 * x2
 a__if(x1,x2,x3)	weight: (/ 295315 16) + x1 + 2 * x2 + 2 * x3
Number of strict rules: 0
YES