Input TRS:
    1: active(from(X)) -> mark(cons(X,from(s(X))))
    2: active(first(0(),Z)) -> mark(nil())
    3: active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
    4: active(sel(0(),cons(X,Z))) -> mark(X)
    5: active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
    6: mark(from(X)) -> active(from(mark(X)))
    7: mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    8: mark(s(X)) -> active(s(mark(X)))
    9: mark(first(X1,X2)) -> active(first(mark(X1),mark(X2)))
    10: mark(0()) -> active(0())
    11: mark(nil()) -> active(nil())
    12: mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
    13: from(mark(X)) -> from(X)
    14: from(active(X)) -> from(X)
    15: cons(mark(X1),X2) -> cons(X1,X2)
    16: cons(X1,mark(X2)) -> cons(X1,X2)
    17: cons(active(X1),X2) -> cons(X1,X2)
    18: cons(X1,active(X2)) -> cons(X1,X2)
    19: s(mark(X)) -> s(X)
    20: s(active(X)) -> s(X)
    21: first(mark(X1),X2) -> first(X1,X2)
    22: first(X1,mark(X2)) -> first(X1,X2)
    23: first(active(X1),X2) -> first(X1,X2)
    24: first(X1,active(X2)) -> first(X1,X2)
    25: sel(mark(X1),X2) -> sel(X1,X2)
    26: sel(X1,mark(X2)) -> sel(X1,X2)
    27: sel(active(X1),X2) -> sel(X1,X2)
    28: sel(X1,active(X2)) -> sel(X1,X2)
Number of strict rules: 28
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(first(0(),Z)) -> #mark(nil())
   #2: #mark(from(X)) -> #active(from(mark(X)))
   #3: #mark(from(X)) -> #from(mark(X))
   #4: #mark(from(X)) -> #mark(X)
   #5: #from(mark(X)) -> #from(X)
   #6: #mark(first(X1,X2)) -> #active(first(mark(X1),mark(X2)))
   #7: #mark(first(X1,X2)) -> #first(mark(X1),mark(X2))
   #8: #mark(first(X1,X2)) -> #mark(X1)
   #9: #mark(first(X1,X2)) -> #mark(X2)
   #10: #mark(nil()) -> #active(nil())
   #11: #first(X1,active(X2)) -> #first(X1,X2)
   #12: #first(active(X1),X2) -> #first(X1,X2)
   #13: #mark(sel(X1,X2)) -> #active(sel(mark(X1),mark(X2)))
   #14: #mark(sel(X1,X2)) -> #sel(mark(X1),mark(X2))
   #15: #mark(sel(X1,X2)) -> #mark(X1)
   #16: #mark(sel(X1,X2)) -> #mark(X2)
   #17: #from(active(X)) -> #from(X)
   #18: #sel(mark(X1),X2) -> #sel(X1,X2)
   #19: #s(active(X)) -> #s(X)
   #20: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2))
   #21: #mark(cons(X1,X2)) -> #cons(mark(X1),X2)
   #22: #mark(cons(X1,X2)) -> #mark(X1)
   #23: #mark(0()) -> #active(0())
   #24: #active(sel(s(X),cons(Y,Z))) -> #mark(sel(X,Z))
   #25: #active(sel(s(X),cons(Y,Z))) -> #sel(X,Z)
   #26: #sel(X1,active(X2)) -> #sel(X1,X2)
   #27: #first(X1,mark(X2)) -> #first(X1,X2)
   #28: #sel(active(X1),X2) -> #sel(X1,X2)
   #29: #cons(active(X1),X2) -> #cons(X1,X2)
   #30: #s(mark(X)) -> #s(X)
   #31: #sel(X1,mark(X2)) -> #sel(X1,X2)
   #32: #first(mark(X1),X2) -> #first(X1,X2)
   #33: #cons(X1,mark(X2)) -> #cons(X1,X2)
   #34: #active(first(s(X),cons(Y,Z))) -> #mark(cons(Y,first(X,Z)))
   #35: #active(first(s(X),cons(Y,Z))) -> #cons(Y,first(X,Z))
   #36: #active(first(s(X),cons(Y,Z))) -> #first(X,Z)
   #37: #active(from(X)) -> #mark(cons(X,from(s(X))))
   #38: #active(from(X)) -> #cons(X,from(s(X)))
   #39: #active(from(X)) -> #from(s(X))
   #40: #active(from(X)) -> #s(X)
   #41: #mark(s(X)) -> #active(s(mark(X)))
   #42: #mark(s(X)) -> #s(mark(X))
   #43: #mark(s(X)) -> #mark(X)
   #44: #cons(mark(X1),X2) -> #cons(X1,X2)
   #45: #active(sel(0(),cons(X,Z))) -> #mark(X)
   #46: #cons(X1,active(X2)) -> #cons(X1,X2)
Number of SCCs: 6, DPs: 30, edges: 145
	SCC { #19 #30 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	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: #19 #30
Number of SCCs: 5, DPs: 28, edges: 141
	SCC { #5 #17 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	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: #5 #17
Number of SCCs: 4, DPs: 26, edges: 137
	SCC { #29 #33 #44 #46 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x2
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	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: #33 #46
Number of SCCs: 4, DPs: 24, edges: 125
	SCC { #29 #44 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	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: #29 #44
Number of SCCs: 3, DPs: 22, edges: 121
	SCC { #18 #26 #28 #31 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: x2
  from(x1)	weight: 0
   sel(x1,x2)	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: #26 #31
Number of SCCs: 4, DPs: 20, edges: 109
	SCC { #18 #28 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: x1
  from(x1)	weight: 0
   sel(x1,x2)	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 #28
Number of SCCs: 3, DPs: 18, edges: 105
	SCC { #11 #12 #27 #32 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	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: #12 #32
Number of SCCs: 4, DPs: 16, edges: 93
	SCC { #11 #27 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	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: #11 #27
Number of SCCs: 3, DPs: 14, edges: 89
	SCC { #2 #4 #6 #8 #9 #13 #15 #16 #22 #24 #34 #37 #43 #45 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#mark(x1)	weight: x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: (/ 1 4) + x1
   sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 8) + x1}
   #s(x1)	weight: 0
#first(x1,x2)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: x1
 first(x1,x2)	weight: max{(/ 3 8) + x2, (/ 1 4) + x1}
#from(x1)	weight: 0
active(x1)	weight: x1
  cons(x1,x2)	weight: max{x2, (/ 1 8) + x1}
#active(x1)	weight: x1
    Usable rules: { 1..28 }
    Removed DPs: #4 #8 #9 #15 #16 #22 #45
Number of SCCs: 5, DPs: 3, edges: 3
	SCC { #43 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#mark(x1)	weight: x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: (/ 1 4)
   sel(x1,x2)	weight: (/ 1 4)
   #s(x1)	weight: 0
#first(x1,x2)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 4)
 first(x1,x2)	weight: (/ 1 4)
#from(x1)	weight: 0
active(x1)	weight: (/ 1 4)
  cons(x1,x2)	weight: (/ 1 4)
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #43
Number of SCCs: 4, DPs: 2, edges: 2
	SCC { #13 #24 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
#cons(x1,x2)	weight: x2	status: [x2]	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above:
#mark(x1)	weight: x1	status: [x1]	precedence above: #active
     0()	weight: 0	status: []	precedence above:
 #sel(x1,x2)	weight: (/ 1 8) + x2	status: [x2]	precedence above:
  from(x1)	weight: (/ 1 2) + x1	status: []	precedence above: nil first cons
   sel(x1,x2)	weight: x2 + x1	status: [x1]	precedence above: #mark mark active #active
   #s(x1)	weight: x1	status: []	precedence above:
#first(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x2,x1]	precedence above:
   nil()	weight: (/ 1 8)	status: []	precedence above:
  mark(x1)	weight: x1	status: x1
 first(x1,x2)	weight: (/ 1 4) + x2	status: []	precedence above: from nil cons
#from(x1)	weight: (/ 1 8)	status: []	precedence above:
active(x1)	weight: x1	status: x1
  cons(x1,x2)	weight: max{x2, (/ 3 8) + x1}	status: []	precedence above: from nil first
#active(x1)	weight: x1	status: [x1]	precedence above: #mark
    Usable rules: { 1..28 }
    Removed DPs: #24
Number of SCCs: 3, DPs: 0, edges: 0
YES