Input TRS:
    1: active(from(X)) -> mark(cons(X,from(s(X))))
    2: active(after(0(),XS)) -> mark(XS)
    3: active(after(s(N),cons(X,XS))) -> mark(after(N,XS))
    4: active(from(X)) -> from(active(X))
    5: active(cons(X1,X2)) -> cons(active(X1),X2)
    6: active(s(X)) -> s(active(X))
    7: active(after(X1,X2)) -> after(active(X1),X2)
    8: active(after(X1,X2)) -> after(X1,active(X2))
    9: from(mark(X)) -> mark(from(X))
    10: cons(mark(X1),X2) -> mark(cons(X1,X2))
    11: s(mark(X)) -> mark(s(X))
    12: after(mark(X1),X2) -> mark(after(X1,X2))
    13: after(X1,mark(X2)) -> mark(after(X1,X2))
    14: proper(from(X)) -> from(proper(X))
    15: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    16: proper(s(X)) -> s(proper(X))
    17: proper(after(X1,X2)) -> after(proper(X1),proper(X2))
    18: proper(0()) -> ok(0())
    19: from(ok(X)) -> ok(from(X))
    20: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    21: s(ok(X)) -> ok(s(X))
    22: after(ok(X1),ok(X2)) -> ok(after(X1,X2))
    23: top(mark(X)) -> top(proper(X))
    24: top(ok(X)) -> top(active(X))
Number of strict rules: 24
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(s(X)) -> #s(active(X))
   #2: #active(s(X)) -> #active(X)
   #3: #after(X1,mark(X2)) -> #after(X1,X2)
   #4: #from(mark(X)) -> #from(X)
   #5: #s(mark(X)) -> #s(X)
   #6: #top(ok(X)) -> #top(active(X))
   #7: #top(ok(X)) -> #active(X)
   #8: #top(mark(X)) -> #top(proper(X))
   #9: #top(mark(X)) -> #proper(X)
   #10: #after(mark(X1),X2) -> #after(X1,X2)
   #11: #proper(from(X)) -> #from(proper(X))
   #12: #proper(from(X)) -> #proper(X)
   #13: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
   #14: #active(after(X1,X2)) -> #after(active(X1),X2)
   #15: #active(after(X1,X2)) -> #active(X1)
   #16: #cons(mark(X1),X2) -> #cons(X1,X2)
   #17: #active(cons(X1,X2)) -> #cons(active(X1),X2)
   #18: #active(cons(X1,X2)) -> #active(X1)
   #19: #after(ok(X1),ok(X2)) -> #after(X1,X2)
   #20: #proper(after(X1,X2)) -> #after(proper(X1),proper(X2))
   #21: #proper(after(X1,X2)) -> #proper(X1)
   #22: #proper(after(X1,X2)) -> #proper(X2)
   #23: #from(ok(X)) -> #from(X)
   #24: #s(ok(X)) -> #s(X)
   #25: #proper(s(X)) -> #s(proper(X))
   #26: #proper(s(X)) -> #proper(X)
   #27: #active(after(s(N),cons(X,XS))) -> #after(N,XS)
   #28: #active(from(X)) -> #cons(X,from(s(X)))
   #29: #active(from(X)) -> #from(s(X))
   #30: #active(from(X)) -> #s(X)
   #31: #active(after(X1,X2)) -> #after(X1,active(X2))
   #32: #active(after(X1,X2)) -> #active(X2)
   #33: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
   #34: #proper(cons(X1,X2)) -> #proper(X1)
   #35: #proper(cons(X1,X2)) -> #proper(X2)
   #36: #active(from(X)) -> #from(active(X))
   #37: #active(from(X)) -> #active(X)
Number of SCCs: 7, DPs: 22, edges: 86
	SCC { #4 #23 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
 after(x1,x2)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#after(x1,x2)	weight: 0
#proper(x1)	weight: 0
#from(x1)	weight: x1
active(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #23
Number of SCCs: 6, DPs: 20, edges: 82
	SCC { #5 #24 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
 after(x1,x2)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: x1
  mark(x1)	weight: (/ 1 2) + x1
#after(x1,x2)	weight: 0
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5 #24
Number of SCCs: 5, DPs: 18, edges: 78
	SCC { #6 #8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
#cons(x1,x2)	weight: (/ 1 4) + x1	status: [x1]	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: ok mark
   top(x1)	weight: x1	status: []	precedence above:
 #top(x1)	weight: x1	status: [x1]	precedence above:
 after(x1,x2)	weight: (/ 1 2) + x2 + x1	status: [x1,x2]	precedence above: mark
proper(x1)	weight: x1	status: x1
    ok(x1)	weight: x1	status: x1
     0()	weight: (/ 1 4)	status: []	precedence above:
  from(x1)	weight: (/ 1 2) + x1	status: [x1]	precedence above: s ok mark cons
   #s(x1)	weight: x1	status: []	precedence above:
  mark(x1)	weight: x1	status: [x1]	precedence above:
#after(x1,x2)	weight: (/ 1 4) + x2	status: [x2]	precedence above:
#proper(x1)	weight: x1	status: []	precedence above:
#from(x1)	weight: (/ 1 4)	status: []	precedence above:
active(x1)	weight: x1	status: x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}	status: [x1]	precedence above: mark
#active(x1)	weight: x1	status: []	precedence above:
    Usable rules: { 1..22 }
    Removed DPs: #8
Number of SCCs: 5, DPs: 17, edges: 75
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
   top(x1)	weight: 0
 #top(x1)	weight: x1
 after(x1,x2)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 4) + x1
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4)
#after(x1,x2)	weight: 0
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 4) + x1
#active(x1)	weight: 0
    Usable rules: { 1..13 19..22 }
    Removed DPs: #6
Number of SCCs: 4, DPs: 16, edges: 74
	SCC { #13 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x2
     s(x1)	weight: (/ 1 4) + x1
   top(x1)	weight: 0
 #top(x1)	weight: x1
 after(x1,x2)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 4) + x1
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4)
#after(x1,x2)	weight: 0
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 4) + x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #13
Number of SCCs: 5, DPs: 15, edges: 71
	SCC { #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x1
     s(x1)	weight: (/ 1 4) + x1
   top(x1)	weight: 0
 #top(x1)	weight: 0
 after(x1,x2)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 4) + x1
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#after(x1,x2)	weight: 0
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 4) + x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #16
Number of SCCs: 4, DPs: 14, edges: 70
	SCC { #3 #10 #19 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
   top(x1)	weight: 0
 #top(x1)	weight: 0
 after(x1,x2)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 4) + x1
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#after(x1,x2)	weight: x1
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 4) + x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #10 #19
Number of SCCs: 5, DPs: 12, edges: 62
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
   top(x1)	weight: 0
 #top(x1)	weight: 0
 after(x1,x2)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 4) + x1
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#after(x1,x2)	weight: x2
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 4) + x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 4, DPs: 11, edges: 61
	SCC { #2 #15 #18 #32 #37 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 8) + x1
   top(x1)	weight: 0
 #top(x1)	weight: 0
 after(x1,x2)	weight: (/ 1 8) + x1 + x2
proper(x1)	weight: (/ 1 8) + x1
    ok(x1)	weight: (/ 1 8) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 8) + x1
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 8) + x1
#after(x1,x2)	weight: 0
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 3 8) + x1
  cons(x1,x2)	weight: (/ 1 8) + x1 + x2
#active(x1)	weight: x1
    Usable rules: { }
    Removed DPs: #2 #15 #18 #32 #37
Number of SCCs: 4, DPs: 6, edges: 36
	SCC { #12 #21 #22 #26 #34 #35 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 8) + x1
   top(x1)	weight: 0
 #top(x1)	weight: 0
 after(x1,x2)	weight: (/ 1 8) + x1 + x2
proper(x1)	weight: (/ 1 8) + x1
    ok(x1)	weight: (/ 1 8) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 8) + x1
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 8) + x1
#after(x1,x2)	weight: 0
#proper(x1)	weight: x1
#from(x1)	weight: 0
active(x1)	weight: (/ 3 8) + x1
  cons(x1,x2)	weight: (/ 1 8) + x1 + x2
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #12 #21 #22 #26 #34 #35
Number of SCCs: 3, DPs: 0, edges: 0
YES