Input TRS:
    1: active(first(0(),X)) -> mark(nil())
    2: active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
    3: active(from(X)) -> mark(cons(X,from(s(X))))
    4: mark(first(X1,X2)) -> active(first(mark(X1),mark(X2)))
    5: mark(0()) -> active(0())
    6: mark(nil()) -> active(nil())
    7: mark(s(X)) -> active(s(mark(X)))
    8: mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    9: mark(from(X)) -> active(from(mark(X)))
    10: first(mark(X1),X2) -> first(X1,X2)
    11: first(X1,mark(X2)) -> first(X1,X2)
    12: first(active(X1),X2) -> first(X1,X2)
    13: first(X1,active(X2)) -> first(X1,X2)
    14: s(mark(X)) -> s(X)
    15: s(active(X)) -> s(X)
    16: cons(mark(X1),X2) -> cons(X1,X2)
    17: cons(X1,mark(X2)) -> cons(X1,X2)
    18: cons(active(X1),X2) -> cons(X1,X2)
    19: cons(X1,active(X2)) -> cons(X1,X2)
    20: from(mark(X)) -> from(X)
    21: from(active(X)) -> from(X)
Number of strict rules: 21
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(first(s(X),cons(Y,Z))) -> #mark(cons(Y,first(X,Z)))
   #2: #active(first(s(X),cons(Y,Z))) -> #cons(Y,first(X,Z))
   #3: #active(first(s(X),cons(Y,Z))) -> #first(X,Z)
   #4: #mark(nil()) -> #active(nil())
   #5: #first(X1,active(X2)) -> #first(X1,X2)
   #6: #mark(from(X)) -> #active(from(mark(X)))
   #7: #mark(from(X)) -> #from(mark(X))
   #8: #mark(from(X)) -> #mark(X)
   #9: #first(X1,mark(X2)) -> #first(X1,X2)
   #10: #first(active(X1),X2) -> #first(X1,X2)
   #11: #s(mark(X)) -> #s(X)
   #12: #from(mark(X)) -> #from(X)
   #13: #mark(s(X)) -> #active(s(mark(X)))
   #14: #mark(s(X)) -> #s(mark(X))
   #15: #mark(s(X)) -> #mark(X)
   #16: #first(mark(X1),X2) -> #first(X1,X2)
   #17: #mark(0()) -> #active(0())
   #18: #cons(X1,mark(X2)) -> #cons(X1,X2)
   #19: #cons(X1,active(X2)) -> #cons(X1,X2)
   #20: #from(active(X)) -> #from(X)
   #21: #cons(mark(X1),X2) -> #cons(X1,X2)
   #22: #active(from(X)) -> #mark(cons(X,from(s(X))))
   #23: #active(from(X)) -> #cons(X,from(s(X)))
   #24: #active(from(X)) -> #from(s(X))
   #25: #active(from(X)) -> #s(X)
   #26: #active(first(0(),X)) -> #mark(nil())
   #27: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2))
   #28: #mark(cons(X1,X2)) -> #cons(mark(X1),X2)
   #29: #mark(cons(X1,X2)) -> #mark(X1)
   #30: #s(active(X)) -> #s(X)
   #31: #mark(first(X1,X2)) -> #active(first(mark(X1),mark(X2)))
   #32: #mark(first(X1,X2)) -> #first(mark(X1),mark(X2))
   #33: #mark(first(X1,X2)) -> #mark(X1)
   #34: #mark(first(X1,X2)) -> #mark(X2)
   #35: #cons(active(X1),X2) -> #cons(X1,X2)
Number of SCCs: 5, DPs: 21, edges: 79
	SCC { #12 #20 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
#first(x1,x2)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
 first(x1,x2)	weight: 0
#from(x1)	weight: x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #12 #20
Number of SCCs: 4, DPs: 19, edges: 75
	SCC { #11 #30 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: x1
#first(x1,x2)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
 first(x1,x2)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #11 #30
Number of SCCs: 3, DPs: 17, edges: 71
	SCC { #18 #19 #21 #35 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x2
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
#first(x1,x2)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
 first(x1,x2)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #18 #19
Number of SCCs: 3, DPs: 15, edges: 59
	SCC { #21 #35 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
#first(x1,x2)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
 first(x1,x2)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #21 #35
Number of SCCs: 2, DPs: 13, edges: 55
	SCC { #5 #9 #10 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
#first(x1,x2)	weight: x2
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
 first(x1,x2)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5 #9
Number of SCCs: 3, DPs: 11, edges: 43
	SCC { #10 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
#first(x1,x2)	weight: x1
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
 first(x1,x2)	weight: 0
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #10 #16
Number of SCCs: 2, DPs: 9, edges: 39
	SCC { #1 #6 #8 #15 #22 #29 #31 #33 #34 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#mark(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
  from(x1)	weight: (/ 70711 4) + x1
   #s(x1)	weight: 0
#first(x1,x2)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: x1
 first(x1,x2)	weight: (/ 1 4) + x1 + x2
#from(x1)	weight: 0
active(x1)	weight: x1
  cons(x1,x2)	weight: (/ 70709 4) + x1
#active(x1)	weight: x1
    Usable rules: { 1..21 }
    Removed DPs: #1 #6 #8 #15 #22 #29 #31 #33 #34
Number of SCCs: 2, DPs: 0, edges: 0
YES