Input TRS:
    1: a__U11(tt(),M,N) -> a__U12(tt(),M,N)
    2: a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
    3: a__plus(N,0()) -> mark(N)
    4: a__plus(N,s(M)) -> a__U11(tt(),M,N)
    5: mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
    6: mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
    7: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    8: mark(tt()) -> tt()
    9: mark(s(X)) -> s(mark(X))
    10: mark(0()) -> 0()
    11: a__U11(X1,X2,X3) -> U11(X1,X2,X3)
    12: a__U12(X1,X2,X3) -> U12(X1,X2,X3)
    13: a__plus(X1,X2) -> plus(X1,X2)
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... removes: 3
a__plus(x1,x2)	weight: (/ 8961 4) + 2 * x1 + x2
   U11(x1,x2,x3)	weight: (/ 4481 2) + x1 + x2 + 2 * x3
     s(x1)	weight: (/ 1 4) + x1
   U12(x1,x2,x3)	weight: (/ 4481 2) + 2 * x1 + x2 + 2 * x3
     0()	weight: 0
  mark(x1)	weight: x1
a__U11(x1,x2,x3)	weight: (/ 4481 2) + x1 + x2 + 2 * x3
a__U12(x1,x2,x3)	weight: (/ 4481 2) + 2 * x1 + x2 + 2 * x3
  plus(x1,x2)	weight: (/ 8961 4) + 2 * x1 + x2
    tt()	weight: 0
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... removes: 4 1 2
a__plus(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
   U11(x1,x2,x3)	weight: (/ 24561 2) + x1 + 2 * x2 + x3
     s(x1)	weight: (/ 49119 4) + x1
   U12(x1,x2,x3)	weight: (/ 49121 4) + x1 + 2 * x2 + x3
     0()	weight: 0
  mark(x1)	weight: x1
a__U11(x1,x2,x3)	weight: (/ 24561 2) + x1 + 2 * x2 + x3
a__U12(x1,x2,x3)	weight: (/ 49121 4) + x1 + 2 * x2 + x3
  plus(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
    tt()	weight: 0
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... removes: 12 9 6
a__plus(x1,x2)	weight: x1 + x2
   U11(x1,x2,x3)	weight: x1 + x2 + x3
     s(x1)	weight: (/ 1 4) + x1
   U12(x1,x2,x3)	weight: (/ 49121 4) + x1 + 2 * x2 + x3
     0()	weight: 0
  mark(x1)	weight: 2 * x1
a__U11(x1,x2,x3)	weight: x1 + x2 + x3
a__U12(x1,x2,x3)	weight: (/ 24561 2) + x1 + 2 * x2 + x3
  plus(x1,x2)	weight: x1 + x2
    tt()	weight: 0
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... removes: 5 11
a__plus(x1,x2)	weight: x1 + x2
   U11(x1,x2,x3)	weight: (/ 1 4) + x1 + x2 + x3
     s(x1)	weight: (/ 3 8) + x1
   U12(x1,x2,x3)	weight: (/ 98237 8) + x1 + 2 * x2 + x3
     0()	weight: 0
  mark(x1)	weight: 2 * x1
a__U11(x1,x2,x3)	weight: (/ 3 8) + x1 + x2 + x3
a__U12(x1,x2,x3)	weight: (/ 49119 4) + x1 + 2 * x2 + x3
  plus(x1,x2)	weight: x1 + x2
    tt()	weight: 0
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 8 10 7 13
a__plus(x1,x2)	weight: (/ 1 2) + x1 + x2
   U11(x1,x2,x3)	weight: x1 + x2 + x3
     s(x1)	weight: (/ 1 8) + x1
   U12(x1,x2,x3)	weight: x1 + 2 * x2 + x3
     0()	weight: 0
  mark(x1)	weight: (/ 1 8) + 2 * x1
a__U11(x1,x2,x3)	weight: (/ 1 8) + 2 * x1 + x2 + x3
a__U12(x1,x2,x3)	weight: (/ 7 8) + x1 + 2 * x2 + x3
  plus(x1,x2)	weight: (/ 3 8) + x1 + x2
    tt()	weight: 0
Number of strict rules: 0
YES