Input TRS:
    1: active(from(X)) -> mark(cons(X,from(s(X))))
    2: active(length(nil())) -> mark(0())
    3: active(length(cons(X,Y))) -> mark(s(length1(Y)))
    4: active(length1(X)) -> mark(length(X))
    5: active(from(X)) -> from(active(X))
    6: active(cons(X1,X2)) -> cons(active(X1),X2)
    7: active(s(X)) -> s(active(X))
    8: from(mark(X)) -> mark(from(X))
    9: cons(mark(X1),X2) -> mark(cons(X1,X2))
    10: s(mark(X)) -> mark(s(X))
    11: proper(from(X)) -> from(proper(X))
    12: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    13: proper(s(X)) -> s(proper(X))
    14: proper(length(X)) -> length(proper(X))
    15: proper(nil()) -> ok(nil())
    16: proper(0()) -> ok(0())
    17: proper(length1(X)) -> length1(proper(X))
    18: from(ok(X)) -> ok(from(X))
    19: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    20: s(ok(X)) -> ok(s(X))
    21: length(ok(X)) -> ok(length(X))
    22: length1(ok(X)) -> ok(length1(X))
    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(cons(X1,X2)) -> #cons(active(X1),X2)
   #2: #active(cons(X1,X2)) -> #active(X1)
   #3: #proper(s(X)) -> #s(proper(X))
   #4: #proper(s(X)) -> #proper(X)
   #5: #cons(mark(X1),X2) -> #cons(X1,X2)
   #6: #proper(from(X)) -> #from(proper(X))
   #7: #proper(from(X)) -> #proper(X)
   #8: #top(ok(X)) -> #top(active(X))
   #9: #top(ok(X)) -> #active(X)
   #10: #top(mark(X)) -> #top(proper(X))
   #11: #top(mark(X)) -> #proper(X)
   #12: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
   #13: #proper(cons(X1,X2)) -> #proper(X1)
   #14: #proper(cons(X1,X2)) -> #proper(X2)
   #15: #proper(length(X)) -> #length(proper(X))
   #16: #proper(length(X)) -> #proper(X)
   #17: #s(ok(X)) -> #s(X)
   #18: #active(s(X)) -> #s(active(X))
   #19: #active(s(X)) -> #active(X)
   #20: #s(mark(X)) -> #s(X)
   #21: #active(from(X)) -> #from(active(X))
   #22: #active(from(X)) -> #active(X)
   #23: #length1(ok(X)) -> #length1(X)
   #24: #proper(length1(X)) -> #length1(proper(X))
   #25: #proper(length1(X)) -> #proper(X)
   #26: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
   #27: #length(ok(X)) -> #length(X)
   #28: #active(length(cons(X,Y))) -> #s(length1(Y))
   #29: #active(length(cons(X,Y))) -> #length1(Y)
   #30: #active(from(X)) -> #cons(X,from(s(X)))
   #31: #active(from(X)) -> #from(s(X))
   #32: #active(from(X)) -> #s(X)
   #33: #from(mark(X)) -> #from(X)
   #34: #active(length1(X)) -> #length(X)
   #35: #from(ok(X)) -> #from(X)
Number of SCCs: 8, DPs: 19, edges: 63
	SCC { #27 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#length1(x1)	weight: 0
   top(x1)	weight: 0
length1(x1)	weight: 0
 #top(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: 0
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: x1
    Usable rules: { }
    Removed DPs: #27
Number of SCCs: 7, DPs: 18, edges: 62
	SCC { #23 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#length1(x1)	weight: x1
   top(x1)	weight: 0
length1(x1)	weight: 0
 #top(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: 0
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #23
Number of SCCs: 6, DPs: 17, edges: 61
	SCC { #17 #20 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#length1(x1)	weight: 0
   top(x1)	weight: 0
length1(x1)	weight: 0
 #top(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: x1
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #17 #20
Number of SCCs: 5, DPs: 15, edges: 57
	SCC { #33 #35 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#length1(x1)	weight: 0
   top(x1)	weight: 0
length1(x1)	weight: 0
 #top(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#proper(x1)	weight: 0
#from(x1)	weight: x1
active(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #33 #35
Number of SCCs: 4, DPs: 13, edges: 53
	SCC { #8 #10 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
#cons(x1,x2)	weight: 0; 0
     s(x1)	weight: (/ 1 8) + x1_1; x1_1
#length1(x1)	weight: 0; 0
   top(x1)	weight: 0; 0
length1(x1)	weight: (/ 3 8) + x1_2; (/ 1 8) + x1_2
 #top(x1)	weight: x1_1; x1_1
proper(x1)	weight: (/ 1 4) + x1_1; (/ 1 4) + x1_2
    ok(x1)	weight: (/ 1 4) + x1_1; (/ 1 4) + x1_2
     0()	weight: 0; (/ 1 8)
  from(x1)	weight: (/ 1 4) + x1_1; (/ 1 8) + x1_2
   #s(x1)	weight: 0; 0
   nil()	weight: 0; (/ 1 8)
  mark(x1)	weight: (/ 3 8) + x1_1; (/ 1 8)
#proper(x1)	weight: 0; 0
#from(x1)	weight: 0; 0
active(x1)	weight: (/ 1 8) + x1_1; (/ 1 8) + x1_1 + x1_2
  cons(x1,x2)	weight: x1_1; (/ 5 8) + x2_2
#active(x1)	weight: 0; 0
length(x1)	weight: (/ 1 8) + x1_2; (/ 1 8) + x1_2
#length(x1)	weight: 0; 0
    Usable rules: { 1..22 }
    Removed DPs: #8 #10
Number of SCCs: 3, DPs: 11, edges: 49
	SCC { #5 #26 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x2
     s(x1)	weight: (/ 1 2)
#length1(x1)	weight: 0
   top(x1)	weight: 0
length1(x1)	weight: (/ 1 2)
 #top(x1)	weight: 0
proper(x1)	weight: (/ 1 4)
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 2)
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 3 4)
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4)
  cons(x1,x2)	weight: (/ 1 4) + x1
#active(x1)	weight: 0
length(x1)	weight: (/ 1 2)
#length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #26
Number of SCCs: 3, DPs: 10, edges: 46
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
#length1(x1)	weight: 0
   top(x1)	weight: 0
length1(x1)	weight: (/ 1 2)
 #top(x1)	weight: 0
proper(x1)	weight: (/ 1 4)
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4)
  cons(x1,x2)	weight: x1
#active(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 9, edges: 45
	SCC { #2 #19 #22 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#length1(x1)	weight: 0
   top(x1)	weight: 0
length1(x1)	weight: (/ 1 2)
 #top(x1)	weight: 0
proper(x1)	weight: (/ 1 4)
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 4) + x1
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#proper(x1)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4)
  cons(x1,x2)	weight: (/ 1 4) + x1
#active(x1)	weight: x1
length(x1)	weight: 0
#length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #19 #22
Number of SCCs: 2, DPs: 6, edges: 36
	SCC { #4 #7 #13 #14 #16 #25 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#length1(x1)	weight: 0
   top(x1)	weight: 0
length1(x1)	weight: (/ 1 4) + x1
 #top(x1)	weight: 0
proper(x1)	weight: (/ 1 4)
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 4) + x1
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 3 4) + x1
#proper(x1)	weight: x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
#active(x1)	weight: 0
length(x1)	weight: x1
#length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #7 #13 #14 #25
Number of SCCs: 2, DPs: 1, edges: 1
	SCC { #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#length1(x1)	weight: 0
   top(x1)	weight: 0
length1(x1)	weight: (/ 1 4) + x1
 #top(x1)	weight: 0
proper(x1)	weight: (/ 1 4)
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
  from(x1)	weight: (/ 1 4) + x1
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 3 4) + x1
#proper(x1)	weight: x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
#active(x1)	weight: 0
length(x1)	weight: (/ 1 4) + x1
#length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #16
Number of SCCs: 1, DPs: 0, edges: 0
YES