Input TRS:
    1: active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
    2: active(f(X1,X2)) -> f(active(X1),X2)
    3: active(g(X)) -> g(active(X))
    4: f(mark(X1),X2) -> mark(f(X1,X2))
    5: g(mark(X)) -> mark(g(X))
    6: proper(f(X1,X2)) -> f(proper(X1),proper(X2))
    7: proper(g(X)) -> g(proper(X))
    8: f(ok(X1),ok(X2)) -> ok(f(X1,X2))
    9: g(ok(X)) -> ok(g(X))
    10: top(mark(X)) -> top(proper(X))
    11: top(ok(X)) -> top(active(X))
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... removes: 8 1 10 11 2
   top(x1)	weight: x1
     f(x1,x2)	weight: (/ 1 8) + x1 + x2
proper(x1)	weight: x1
    ok(x1)	weight: (/ 3 8) + 2 * x1
  mark(x1)	weight: (/ 1 8) + x1
active(x1)	weight: (/ 1 4) + 2 * x1
     g(x1)	weight: x1
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... removes: 9
   top(x1)	weight: x1
     f(x1,x2)	weight: (/ 1 8) + x1 + x2
proper(x1)	weight: x1
    ok(x1)	weight: (/ 1 8) + x1
  mark(x1)	weight: x1
active(x1)	weight: x1
     g(x1)	weight: 2 * x1
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... removes: 6
   top(x1)	weight: x1
     f(x1,x2)	weight: (/ 1 8) + x1 + x2
proper(x1)	weight: 2 * x1
    ok(x1)	weight: (/ 1 8) + x1
  mark(x1)	weight: (/ 1 8) + x1
active(x1)	weight: x1
     g(x1)	weight: x1
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 4
   top(x1)	weight: x1
     f(x1,x2)	weight: (/ 1 8) + 2 * x1 + x2
proper(x1)	weight: 2 * x1
    ok(x1)	weight: (/ 1 8) + x1
  mark(x1)	weight: (/ 1 8) + x1
active(x1)	weight: x1
     g(x1)	weight: x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 5
   top(x1)	weight: x1
     f(x1,x2)	weight: (/ 1 8) + 2 * x1 + x2
proper(x1)	weight: x1
    ok(x1)	weight: (/ 1 8) + x1
  mark(x1)	weight: (/ 1 8) + x1
active(x1)	weight: x1
     g(x1)	weight: 2 * x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 3
   top(x1)	weight: x1
     f(x1,x2)	weight: (/ 1 16) + 2 * x1 + x2
proper(x1)	weight: (/ 1 16) + x1
    ok(x1)	weight: (/ 1 16) + x1
  mark(x1)	weight: (/ 1 4) + x1
active(x1)	weight: (/ 1 16) + 2 * x1
     g(x1)	weight: (/ 1 16) + x1
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... removes: 7
   top(x1)	weight: x1
     f(x1,x2)	weight: (/ 1 16) + 2 * x1 + x2
proper(x1)	weight: (/ 1 16) + 2 * x1
    ok(x1)	weight: (/ 1 16) + x1
  mark(x1)	weight: (/ 1 4) + x1
active(x1)	weight: (/ 1 16) + 2 * x1
     g(x1)	weight: (/ 1 16) + x1
Number of strict rules: 0
YES