Input TRS:
    1: active(from(X)) -> mark(cons(X,from(s(X))))
    2: active(head(cons(X,XS))) -> mark(X)
    3: active(2nd(cons(X,XS))) -> mark(head(XS))
    4: active(take(0(),XS)) -> mark(nil())
    5: active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS)))
    6: active(sel(0(),cons(X,XS))) -> mark(X)
    7: active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS))
    8: mark(from(X)) -> active(from(mark(X)))
    9: mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    10: mark(s(X)) -> active(s(mark(X)))
    11: mark(head(X)) -> active(head(mark(X)))
    12: mark(2nd(X)) -> active(2nd(mark(X)))
    13: mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
    14: mark(0()) -> active(0())
    15: mark(nil()) -> active(nil())
    16: mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
    17: from(mark(X)) -> from(X)
    18: from(active(X)) -> from(X)
    19: cons(mark(X1),X2) -> cons(X1,X2)
    20: cons(X1,mark(X2)) -> cons(X1,X2)
    21: cons(active(X1),X2) -> cons(X1,X2)
    22: cons(X1,active(X2)) -> cons(X1,X2)
    23: s(mark(X)) -> s(X)
    24: s(active(X)) -> s(X)
    25: head(mark(X)) -> head(X)
    26: head(active(X)) -> head(X)
    27: 2nd(mark(X)) -> 2nd(X)
    28: 2nd(active(X)) -> 2nd(X)
    29: take(mark(X1),X2) -> take(X1,X2)
    30: take(X1,mark(X2)) -> take(X1,X2)
    31: take(active(X1),X2) -> take(X1,X2)
    32: take(X1,active(X2)) -> take(X1,X2)
    33: sel(mark(X1),X2) -> sel(X1,X2)
    34: sel(X1,mark(X2)) -> sel(X1,X2)
    35: sel(active(X1),X2) -> sel(X1,X2)
    36: sel(X1,active(X2)) -> sel(X1,X2)
Number of strict rules: 36
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(head(cons(X,XS))) -> #mark(X)
   #2: #take(mark(X1),X2) -> #take(X1,X2)
   #3: #sel(active(X1),X2) -> #sel(X1,X2)
   #4: #active(sel(0(),cons(X,XS))) -> #mark(X)
   #5: #mark(take(X1,X2)) -> #active(take(mark(X1),mark(X2)))
   #6: #mark(take(X1,X2)) -> #take(mark(X1),mark(X2))
   #7: #mark(take(X1,X2)) -> #mark(X1)
   #8: #mark(take(X1,X2)) -> #mark(X2)
   #9: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2))
   #10: #mark(cons(X1,X2)) -> #cons(mark(X1),X2)
   #11: #mark(cons(X1,X2)) -> #mark(X1)
   #12: #mark(head(X)) -> #active(head(mark(X)))
   #13: #mark(head(X)) -> #head(mark(X))
   #14: #mark(head(X)) -> #mark(X)
   #15: #s(active(X)) -> #s(X)
   #16: #s(mark(X)) -> #s(X)
   #17: #mark(2nd(X)) -> #active(2nd(mark(X)))
   #18: #mark(2nd(X)) -> #2nd(mark(X))
   #19: #mark(2nd(X)) -> #mark(X)
   #20: #take(active(X1),X2) -> #take(X1,X2)
   #21: #mark(0()) -> #active(0())
   #22: #take(X1,mark(X2)) -> #take(X1,X2)
   #23: #head(mark(X)) -> #head(X)
   #24: #cons(X1,mark(X2)) -> #cons(X1,X2)
   #25: #active(sel(s(N),cons(X,XS))) -> #mark(sel(N,XS))
   #26: #active(sel(s(N),cons(X,XS))) -> #sel(N,XS)
   #27: #mark(s(X)) -> #active(s(mark(X)))
   #28: #mark(s(X)) -> #s(mark(X))
   #29: #mark(s(X)) -> #mark(X)
   #30: #sel(mark(X1),X2) -> #sel(X1,X2)
   #31: #active(take(s(N),cons(X,XS))) -> #mark(cons(X,take(N,XS)))
   #32: #active(take(s(N),cons(X,XS))) -> #cons(X,take(N,XS))
   #33: #active(take(s(N),cons(X,XS))) -> #take(N,XS)
   #34: #2nd(active(X)) -> #2nd(X)
   #35: #cons(X1,active(X2)) -> #cons(X1,X2)
   #36: #sel(X1,mark(X2)) -> #sel(X1,X2)
   #37: #2nd(mark(X)) -> #2nd(X)
   #38: #from(mark(X)) -> #from(X)
   #39: #take(X1,active(X2)) -> #take(X1,X2)
   #40: #cons(mark(X1),X2) -> #cons(X1,X2)
   #41: #head(active(X)) -> #head(X)
   #42: #sel(X1,active(X2)) -> #sel(X1,X2)
   #43: #cons(active(X1),X2) -> #cons(X1,X2)
   #44: #mark(sel(X1,X2)) -> #active(sel(mark(X1),mark(X2)))
   #45: #mark(sel(X1,X2)) -> #sel(mark(X1),mark(X2))
   #46: #mark(sel(X1,X2)) -> #mark(X1)
   #47: #mark(sel(X1,X2)) -> #mark(X2)
   #48: #active(2nd(cons(X,XS))) -> #mark(head(XS))
   #49: #active(2nd(cons(X,XS))) -> #head(XS)
   #50: #active(from(X)) -> #mark(cons(X,from(s(X))))
   #51: #active(from(X)) -> #cons(X,from(s(X)))
   #52: #active(from(X)) -> #from(s(X))
   #53: #active(from(X)) -> #s(X)
   #54: #mark(from(X)) -> #active(from(mark(X)))
   #55: #mark(from(X)) -> #from(mark(X))
   #56: #mark(from(X)) -> #mark(X)
   #57: #mark(nil()) -> #active(nil())
   #58: #active(take(0(),XS)) -> #mark(nil())
   #59: #from(active(X)) -> #from(X)
Number of SCCs: 8, DPs: 40, edges: 231
	SCC { #38 #59 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: x1
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #38 #59
Number of SCCs: 7, DPs: 38, edges: 227
	SCC { #15 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #15 #16
Number of SCCs: 6, DPs: 36, edges: 223
	SCC { #34 #37 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(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
   nil()	weight: 0
 #2nd(x1)	weight: x1
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #34 #37
Number of SCCs: 5, DPs: 34, edges: 219
	SCC { #23 #41 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(x1)	weight: x1
#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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #23 #41
Number of SCCs: 4, DPs: 32, edges: 215
	SCC { #2 #20 #22 #39 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: x2
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #22 #39
Number of SCCs: 4, DPs: 30, edges: 203
	SCC { #2 #20 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: x1
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #20
Number of SCCs: 3, DPs: 28, edges: 199
	SCC { #24 #35 #40 #43 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x2
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #24 #35
Number of SCCs: 4, DPs: 26, edges: 187
	SCC { #40 #43 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #40 #43
Number of SCCs: 3, DPs: 24, edges: 183
	SCC { #3 #30 #36 #42 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #3 #30
Number of SCCs: 4, DPs: 22, edges: 171
	SCC { #36 #42 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   2nd(x1)	weight: 0
#head(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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #36 #42
Number of SCCs: 3, DPs: 20, edges: 167
	SCC { #1 #4 #5 #7 #8 #11 #12 #14 #17 #19 #25 #29 #31 #44 #46..48 #50 #54 #56 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: max{(/ 3 8) + x2, (/ 1 2) + x1}
   2nd(x1)	weight: (/ 1 4) + x1
#head(x1)	weight: 0
#mark(x1)	weight: x1
     0()	weight: (/ 1 8)
 #sel(x1,x2)	weight: 0
  from(x1)	weight: (/ 3 8) + x1
   sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 8) + x1}
   #s(x1)	weight: 0
   nil()	weight: (/ 1 2)
 #2nd(x1)	weight: 0
  mark(x1)	weight: x1
#from(x1)	weight: 0
active(x1)	weight: x1
  head(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
#active(x1)	weight: x1
    Usable rules: { 1..36 }
    Removed DPs: #1 #4 #7 #8 #11 #14 #19 #46..48 #56
Number of SCCs: 5, DPs: 3, edges: 3
	SCC { #29 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: (/ 1 4)
   2nd(x1)	weight: (/ 1 4)
#head(x1)	weight: 0
#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
   nil()	weight: 0
 #2nd(x1)	weight: 0
  mark(x1)	weight: (/ 1 4)
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2)
  head(x1)	weight: (/ 1 4)
  cons(x1,x2)	weight: (/ 1 4)
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #29
Number of SCCs: 4, DPs: 2, edges: 2
	SCC { #25 #44 }
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:
#take(x1,x2)	weight: x2	status: []	precedence above:
  take(x1,x2)	weight: x2	status: []	precedence above: #mark sel nil mark active head cons #active
   2nd(x1)	weight: (/ 5 16) + x1	status: [x1]	precedence above: head
#head(x1)	weight: (/ 1 16)	status: []	precedence above:
#mark(x1)	weight: (/ 1 16) + x1	status: [x1]	precedence above: #active
     0()	weight: (/ 1 16)	status: []	precedence above: #mark mark active head #active
 #sel(x1,x2)	weight: (/ 1 16) + x2 + x1	status: [x2,x1]	precedence above:
  from(x1)	weight: (/ 1 4) + x1	status: []	precedence above: s #mark sel mark active head cons #active
   sel(x1,x2)	weight: (/ 1 16) + x2 + x1	status: [x1]	precedence above: #mark mark active head #active
   #s(x1)	weight: x1	status: []	precedence above:
   nil()	weight: 0	status: []	precedence above: take #mark sel mark active head cons #active
 #2nd(x1)	weight: (/ 1 16)	status: []	precedence above:
  mark(x1)	weight: x1	status: x1
#from(x1)	weight: (/ 1 16)	status: []	precedence above:
active(x1)	weight: x1	status: x1
  head(x1)	weight: (/ 1 4) + x1	status: [x1]	precedence above:
  cons(x1,x2)	weight: max{x2, (/ 3 16) + x1}	status: [x1]	precedence above: #mark sel mark active head #active
#active(x1)	weight: (/ 1 16) + x1	status: [x1]	precedence above: #mark
    Usable rules: { 1..36 }
    Removed DPs: #25
Number of SCCs: 3, DPs: 0, edges: 0
YES