Input TRS:
    1: active(zeros()) -> mark(cons(0(),zeros()))
    2: active(tail(cons(X,XS))) -> mark(XS)
    3: active(cons(X1,X2)) -> cons(active(X1),X2)
    4: active(tail(X)) -> tail(active(X))
    5: cons(mark(X1),X2) -> mark(cons(X1,X2))
    6: tail(mark(X)) -> mark(tail(X))
    7: proper(zeros()) -> ok(zeros())
    8: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    9: proper(0()) -> ok(0())
    10: proper(tail(X)) -> tail(proper(X))
    11: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    12: tail(ok(X)) -> ok(tail(X))
    13: top(mark(X)) -> top(proper(X))
    14: top(ok(X)) -> top(active(X))
Number of strict rules: 14
Direct Order(PosReal,>,Poly) ... removes: 2
   top(x1)	weight: 2 * x1
 zeros()	weight: 0
  tail(x1)	weight: 18458 + x1
proper(x1)	weight: x1
    ok(x1)	weight: x1
     0()	weight: 0
  mark(x1)	weight: x1
active(x1)	weight: x1
  cons(x1,x2)	weight: x1 + x2
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #tail(mark(X)) -> #tail(X)
   #2: #top(mark(X)) -> #top(proper(X))
   #3: #top(mark(X)) -> #proper(X)
   #4: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
   #5: #tail(ok(X)) -> #tail(X)
   #6: #top(ok(X)) -> #top(active(X))
   #7: #top(ok(X)) -> #active(X)
   #8: #proper(tail(X)) -> #tail(proper(X))
   #9: #proper(tail(X)) -> #proper(X)
   #10: #cons(mark(X1),X2) -> #cons(X1,X2)
   #11: #active(cons(X1,X2)) -> #cons(active(X1),X2)
   #12: #active(cons(X1,X2)) -> #active(X1)
   #13: #active(zeros()) -> #cons(0(),zeros())
   #14: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
   #15: #proper(cons(X1,X2)) -> #proper(X1)
   #16: #proper(cons(X1,X2)) -> #proper(X2)
   #17: #active(tail(X)) -> #tail(active(X))
   #18: #active(tail(X)) -> #active(X)
Number of SCCs: 5, DPs: 11, edges: 25
	SCC { #1 #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
#tail(x1)	weight: x1
  mark(x1)	weight: (/ 1 2) + x1
#proper(x1)	weight: 0
active(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #5
Number of SCCs: 4, DPs: 9, edges: 21
	SCC { #12 #18 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: (/ 1 2) + x1
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2)
     0()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 2)
#proper(x1)	weight: 0
active(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x1
#active(x1)	weight: x1
    Usable rules: { }
    Removed DPs: #12 #18
Number of SCCs: 3, DPs: 7, edges: 17
	SCC { #2 #6 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#cons(x1,x2)	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: x1
 zeros()	weight: (/ 1 2)
  tail(x1)	weight: (/ 1 8) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: (/ 1 8)
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 3 8) + x1
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: max{0, (/ 1 8) + x1}
#active(x1)	weight: 0
    Usable rules: { 1 3..12 }
    Removed DPs: #2 #6
Number of SCCs: 2, DPs: 5, edges: 13
	SCC { #4 #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x2
   top(x1)	weight: 0
 #top(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4)
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 3 4)
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 2)
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 2, DPs: 4, edges: 10
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x1
   top(x1)	weight: 0
 #top(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4)
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #9 #15 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: (/ 1 2) + x1
proper(x1)	weight: 0
    ok(x1)	weight: 0
     0()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#proper(x1)	weight: x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: x1 + x2
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 2, DPs: 2, edges: 4
	SCC { #15 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
 zeros()	weight: 0
  tail(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: 0
    ok(x1)	weight: 0
     0()	weight: 0
#tail(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#proper(x1)	weight: x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #15 #16
Number of SCCs: 1, DPs: 0, edges: 0
YES