Input TRS:
    1: a__from(X) -> cons(mark(X),from(s(X)))
    2: a__head(cons(X,XS)) -> mark(X)
    3: a__2nd(cons(X,XS)) -> a__head(mark(XS))
    4: a__take(|0|(),XS) -> nil()
    5: a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
    6: a__sel(|0|(),cons(X,XS)) -> mark(X)
    7: a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS))
    8: mark(from(X)) -> a__from(mark(X))
    9: mark(head(X)) -> a__head(mark(X))
    10: mark(|2nd|(X)) -> a__2nd(mark(X))
    11: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    12: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    13: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    14: mark(s(X)) -> s(mark(X))
    15: mark(|0|()) -> |0|()
    16: mark(nil()) -> nil()
    17: a__from(X) -> from(X)
    18: a__head(X) -> head(X)
    19: a__2nd(X) -> |2nd|(X)
    20: a__take(X1,X2) -> take(X1,X2)
    21: a__sel(X1,X2) -> sel(X1,X2)
Number of strict rules: 21
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__head(cons(X,XS)) -> #mark(X)
   #2: #a__sel(|0|(),cons(X,XS)) -> #mark(X)
   #3: #mark(cons(X1,X2)) -> #mark(X1)
   #4: #mark(head(X)) -> #a__head(mark(X))
   #5: #mark(head(X)) -> #mark(X)
   #6: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2))
   #7: #mark(take(X1,X2)) -> #mark(X1)
   #8: #mark(take(X1,X2)) -> #mark(X2)
   #9: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #10: #mark(sel(X1,X2)) -> #mark(X1)
   #11: #mark(sel(X1,X2)) -> #mark(X2)
   #12: #mark(s(X)) -> #mark(X)
   #13: #a__sel(s(N),cons(X,XS)) -> #a__sel(mark(N),mark(XS))
   #14: #a__sel(s(N),cons(X,XS)) -> #mark(N)
   #15: #a__sel(s(N),cons(X,XS)) -> #mark(XS)
   #16: #mark(|2nd|(X)) -> #a__2nd(mark(X))
   #17: #mark(|2nd|(X)) -> #mark(X)
   #18: #a__take(s(N),cons(X,XS)) -> #mark(X)
   #19: #a__2nd(cons(X,XS)) -> #a__head(mark(XS))
   #20: #a__2nd(cons(X,XS)) -> #mark(XS)
   #21: #a__from(X) -> #mark(X)
   #22: #mark(from(X)) -> #a__from(mark(X))
   #23: #mark(from(X)) -> #mark(X)
Number of SCCs: 1, DPs: 23, edges: 238
	SCC { #1..23 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
   |0|()	weight: (/ 1 8)
     s(x1)	weight: x1
#a__head(x1)	weight: (/ 1 8) + x1
#a__from(x1)	weight: (/ 3 8) + x1
a__from(x1)	weight: (/ 1 4) + x1
  take(x1,x2)	weight: max{x2, x1}
 |2nd|(x1)	weight: (/ 1 4) + x1
a__2nd(x1)	weight: (/ 1 4) + x1
#a__take(x1,x2)	weight: max{0, (/ 1 8) + x2}
#a__2nd(x1)	weight: (/ 3 8) + x1
#mark(x1)	weight: (/ 1 4) + x1
  from(x1)	weight: (/ 1 4) + x1
   sel(x1,x2)	weight: max{x2, (/ 1 8) + x1}
   nil()	weight: (/ 1 8)
#a__sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 3 8) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{x2, (/ 1 8) + x1}
  head(x1)	weight: x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
a__take(x1,x2)	weight: max{x2, x1}
a__head(x1)	weight: x1
    Usable rules: { 1..21 }
    Removed DPs: #1..4 #6 #10 #14 #16..23
Number of SCCs: 1, DPs: 8, edges: 40
	SCC { #5 #7..9 #11..13 #15 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
   |0|()	weight: (/ 1 8)
     s(x1)	weight: x1
#a__head(x1)	weight: (/ 1 8) + x1
#a__from(x1)	weight: (/ 3 8) + x1
a__from(x1)	weight: (/ 1 4) + x1
  take(x1,x2)	weight: max{x2, (/ 1 8) + x1}
 |2nd|(x1)	weight: (/ 1 4) + x1
a__2nd(x1)	weight: (/ 1 4) + x1
#a__take(x1,x2)	weight: max{0, (/ 1 8) + x2}
#a__2nd(x1)	weight: (/ 3 8) + x1
#mark(x1)	weight: (/ 1 8) + x1
  from(x1)	weight: (/ 1 4) + x1
   sel(x1,x2)	weight: max{x2, (/ 1 4) + x1}
   nil()	weight: (/ 1 4)
#a__sel(x1,x2)	weight: max{(/ 1 8) + x2, (/ 1 4) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{x2, (/ 1 4) + x1}
  head(x1)	weight: x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
a__take(x1,x2)	weight: max{x2, (/ 1 8) + x1}
a__head(x1)	weight: x1
    Usable rules: { 1..21 }
    Removed DPs: #7
Number of SCCs: 1, DPs: 7, edges: 29
	SCC { #5 #8 #9 #11..13 #15 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
   |0|()	weight: (/ 1 8)
     s(x1)	weight: x1
#a__head(x1)	weight: (/ 1 8) + x1
#a__from(x1)	weight: (/ 3 8) + x1
a__from(x1)	weight: (/ 1 4) + x1
  take(x1,x2)	weight: max{x2, (/ 1 8) + x1}
 |2nd|(x1)	weight: (/ 1 4) + x1
a__2nd(x1)	weight: (/ 1 4) + x1
#a__take(x1,x2)	weight: max{0, (/ 1 8) + x2}
#a__2nd(x1)	weight: (/ 3 8) + x1
#mark(x1)	weight: (/ 1 4) + x1
  from(x1)	weight: (/ 1 4) + x1
   sel(x1,x2)	weight: max{x2, (/ 1 4) + x1}
   nil()	weight: (/ 1 4)
#a__sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 8) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{x2, (/ 1 4) + x1}
  head(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
a__take(x1,x2)	weight: max{x2, (/ 1 8) + x1}
a__head(x1)	weight: (/ 1 8) + x1
    Usable rules: { 1..21 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 6, edges: 20
	SCC { #8 #9 #11..13 #15 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
   |0|()	weight: (/ 1 8)
     s(x1)	weight: x1
#a__head(x1)	weight: (/ 1 8) + x1
#a__from(x1)	weight: (/ 3 8) + x1
a__from(x1)	weight: (/ 1 4) + x1
  take(x1,x2)	weight: max{x2, (/ 1 8) + x1}
 |2nd|(x1)	weight: (/ 1 4) + x1
a__2nd(x1)	weight: (/ 1 4) + x1
#a__take(x1,x2)	weight: max{0, (/ 1 8) + x2}
#a__2nd(x1)	weight: (/ 3 8) + x1
#mark(x1)	weight: (/ 1 4) + x1
  from(x1)	weight: (/ 1 4) + x1
   sel(x1,x2)	weight: max{(/ 3 8) + x2, (/ 5 8) + x1}
   nil()	weight: (/ 1 4)
#a__sel(x1,x2)	weight: max{(/ 3 8) + x2, (/ 3 4) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{(/ 3 8) + x2, (/ 5 8) + x1}
  head(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
a__take(x1,x2)	weight: max{x2, (/ 1 8) + x1}
a__head(x1)	weight: (/ 1 8) + x1
    Usable rules: { 1..21 }
    Removed DPs: #9 #11 #15
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #8 #12 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 8) + x1
#a__head(x1)	weight: (/ 1 8)
#a__from(x1)	weight: (/ 1 8)
a__from(x1)	weight: (/ 3 8)
  take(x1,x2)	weight: (/ 1 8) + x1 + x2
 |2nd|(x1)	weight: (/ 1 4)
a__2nd(x1)	weight: (/ 1 8) + x1
#a__take(x1,x2)	weight: 0
#a__2nd(x1)	weight: (/ 1 8)
#mark(x1)	weight: (/ 3 8) + x1
  from(x1)	weight: (/ 1 2)
   sel(x1,x2)	weight: (/ 1 4) + x1 + x2
   nil()	weight: 0
#a__sel(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 4)
a__sel(x1,x2)	weight: (/ 1 8) + x1
  head(x1)	weight: (/ 7 8) + x1
  cons(x1,x2)	weight: (/ 1 2)
a__take(x1,x2)	weight: x1 + x2
a__head(x1)	weight: (/ 3 4)
    Usable rules: { }
    Removed DPs: #8 #12
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #13 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
   |0|()	weight: (/ 1 8)
     s(x1)	weight: max{0, (/ 3 8) + x1}
#a__head(x1)	weight: 0
#a__from(x1)	weight: 0
a__from(x1)	weight: max{0, (/ 1 2) + x1}
  take(x1,x2)	weight: max{0, (/ 1 8) + x2}
 |2nd|(x1)	weight: max{0, (/ 3 4) + x1}
a__2nd(x1)	weight: max{0, (/ 3 4) + x1}
#a__take(x1,x2)	weight: 0
#a__2nd(x1)	weight: 0
#mark(x1)	weight: 0
  from(x1)	weight: max{0, (/ 1 2) + x1}
   sel(x1,x2)	weight: max{0, (/ 1 8) + x2 + x1}
   nil()	weight: (/ 1 8)
#a__sel(x1,x2)	weight: max{0, (/ 1 8) + x1}
  mark(x1)	weight: max{0, x1}
a__sel(x1,x2)	weight: max{0, (/ 1 8) + x2 + x1}
  head(x1)	weight: max{0, (/ 3 8) + x1}
  cons(x1,x2)	weight: max{0, (/ 1 4) + x1, (- (/ 3 8)) + x2}
a__take(x1,x2)	weight: max{0, (/ 1 8) + x2}
a__head(x1)	weight: max{0, (/ 3 8) + x1}
    Usable rules: { 1..21 }
    Removed DPs: #13
Number of SCCs: 0, DPs: 0, edges: 0
YES