Input TRS:
    1: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
    2: active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
    3: active(plus(N,0())) -> mark(N)
    4: active(plus(N,s(M))) -> mark(U11(tt(),M,N))
    5: active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
    6: active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
    7: active(s(X)) -> s(active(X))
    8: active(plus(X1,X2)) -> plus(active(X1),X2)
    9: active(plus(X1,X2)) -> plus(X1,active(X2))
    10: U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
    11: U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
    12: s(mark(X)) -> mark(s(X))
    13: plus(mark(X1),X2) -> mark(plus(X1,X2))
    14: plus(X1,mark(X2)) -> mark(plus(X1,X2))
    15: proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
    16: proper(tt()) -> ok(tt())
    17: proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
    18: proper(s(X)) -> s(proper(X))
    19: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
    20: proper(0()) -> ok(0())
    21: U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
    22: U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
    23: s(ok(X)) -> ok(s(X))
    24: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
    25: top(mark(X)) -> top(proper(X))
    26: top(ok(X)) -> top(active(X))
Number of strict rules: 26
Direct Order(PosReal,>,Poly) ... removes: 3
   U11(x1,x2,x3)	weight: (/ 74067 2) + x1 + x2 + x3
     s(x1)	weight: (/ 1 4) + x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: (/ 74067 2) + x1 + x2 + x3
proper(x1)	weight: x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: x1
  plus(x1,x2)	weight: (/ 148133 4) + x1 + x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 25
Direct Order(PosReal,>,Poly) ... removes: 2
   U11(x1,x2,x3)	weight: (/ 34291 4) + x1 + 2 * x2 + x3
     s(x1)	weight: (/ 1 4) + x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: (/ 34291 4) + x1 + 2 * x2 + x3
proper(x1)	weight: x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: x1
  plus(x1,x2)	weight: (/ 34289 4) + x1 + 2 * x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 24
Direct Order(PosReal,>,Poly) ... removes: 4 1
   U11(x1,x2,x3)	weight: (/ 1 4) + x1 + 2 * x2 + x3
     s(x1)	weight: (/ 1 8) + x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: (/ 3 16) + x1 + 2 * x2 + x3
proper(x1)	weight: x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: x1
  plus(x1,x2)	weight: (/ 1 16) + x1 + 2 * x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 22
Direct Order(PosReal,>,Poly) ... removes: 10 25
   U11(x1,x2,x3)	weight: 2 * x1 + x2 + x3
     s(x1)	weight: x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: x1 + x2 + x3
proper(x1)	weight: x1
    ok(x1)	weight: 2 * x1
     0()	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: x1 + x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 20
Direct Order(PosReal,>,Poly) ... removes: 14
   U11(x1,x2,x3)	weight: 2 * x1 + x2 + x3
     s(x1)	weight: (/ 1 8) + x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: x1 + x2 + x3
proper(x1)	weight: x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: (/ 3 8) + x1
  plus(x1,x2)	weight: x1 + 2 * x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 19
Direct Order(PosReal,>,Poly) ... removes: 15
   U11(x1,x2,x3)	weight: (/ 1681 2) + x1 + x2 + x3
     s(x1)	weight: x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: x1 + x2 + x3
proper(x1)	weight: 2 * x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: 841 + x1
  plus(x1,x2)	weight: x1 + 2 * x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 18
Direct Order(PosReal,>,Poly) ... removes: 12
   U11(x1,x2,x3)	weight: x1 + x2 + x3
     s(x1)	weight: 2 * x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: x1 + x2 + x3
proper(x1)	weight: x1
    ok(x1)	weight: 2 * x1
     0()	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: x1 + x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 17
Direct Order(PosReal,>,Poly) ... removes: 11 13
   U11(x1,x2,x3)	weight: x1 + x2 + x3
     s(x1)	weight: (/ 1 8) + x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: 2 * x1 + x2 + x3
proper(x1)	weight: x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: (/ 1 8) + x1
  plus(x1,x2)	weight: (/ 1 8) + 2 * x1 + x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 15
Direct Order(PosReal,>,Poly) ... removes: 18
   U11(x1,x2,x3)	weight: x1 + x2 + x3
     s(x1)	weight: (/ 1 4) + x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: x1 + x2 + x3
proper(x1)	weight: 2 * x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
  plus(x1,x2)	weight: x1 + x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 14
Direct Order(PosReal,>,Poly) ... removes: 16 20
   U11(x1,x2,x3)	weight: x1 + x2 + x3
     s(x1)	weight: x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: (/ 1 4) + x1 + x2 + x3
proper(x1)	weight: (/ 1 8) + 2 * x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: x1
  plus(x1,x2)	weight: (/ 1 8) + x1 + x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... removes: 19 17
   U11(x1,x2,x3)	weight: (/ 1 8) + x1 + x2 + x3
     s(x1)	weight: x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: (/ 3 8) + x1 + x2 + x3
proper(x1)	weight: (/ 1 8) + 2 * x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: (/ 1 8) + x1
  plus(x1,x2)	weight: (/ 1 4) + x1 + x2
active(x1)	weight: x1
    tt()	weight: 0
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... removes: 8 21 26 22 5 7 23 24 9 6
   U11(x1,x2,x3)	weight: (/ 5 16) + x1 + x2 + x3
     s(x1)	weight: (/ 1 8) + 2 * x1
   top(x1)	weight: x1
   U12(x1,x2,x3)	weight: (/ 21 16) + 2 * x1 + 2 * x2 + 2 * x3
proper(x1)	weight: (/ 3 16) + 2 * x1
    ok(x1)	weight: (/ 11 40) + 2 * x1
     0()	weight: 0
  mark(x1)	weight: (/ 23 16) + x1
  plus(x1,x2)	weight: (/ 9 16) + 2 * x1 + 2 * x2
active(x1)	weight: (/ 1 16) + 2 * x1
    tt()	weight: 0
Number of strict rules: 0
YES