Input TRS:
    1: a__dbl(0()) -> 0()
    2: a__dbl(s(X)) -> s(s(dbl(X)))
    3: a__dbls(nil()) -> nil()
    4: a__dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
    5: a__sel(0(),cons(X,Y)) -> mark(X)
    6: a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
    7: a__indx(nil(),X) -> nil()
    8: a__indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
    9: a__from(X) -> cons(X,from(s(X)))
    10: mark(dbl(X)) -> a__dbl(mark(X))
    11: mark(dbls(X)) -> a__dbls(mark(X))
    12: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    13: mark(indx(X1,X2)) -> a__indx(mark(X1),X2)
    14: mark(from(X)) -> a__from(X)
    15: mark(0()) -> 0()
    16: mark(s(X)) -> s(X)
    17: mark(nil()) -> nil()
    18: mark(cons(X1,X2)) -> cons(X1,X2)
    19: a__dbl(X) -> dbl(X)
    20: a__dbls(X) -> dbls(X)
    21: a__sel(X1,X2) -> sel(X1,X2)
    22: a__indx(X1,X2) -> indx(X1,X2)
    23: a__from(X) -> from(X)
Number of strict rules: 23
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__sel(s(X),cons(Y,Z)) -> #a__sel(mark(X),mark(Z))
   #2: #a__sel(s(X),cons(Y,Z)) -> #mark(X)
   #3: #a__sel(s(X),cons(Y,Z)) -> #mark(Z)
   #4: #mark(indx(X1,X2)) -> #a__indx(mark(X1),X2)
   #5: #mark(indx(X1,X2)) -> #mark(X1)
   #6: #mark(dbls(X)) -> #a__dbls(mark(X))
   #7: #mark(dbls(X)) -> #mark(X)
   #8: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #9: #mark(sel(X1,X2)) -> #mark(X1)
   #10: #mark(sel(X1,X2)) -> #mark(X2)
   #11: #mark(from(X)) -> #a__from(X)
   #12: #mark(dbl(X)) -> #a__dbl(mark(X))
   #13: #mark(dbl(X)) -> #mark(X)
   #14: #a__sel(0(),cons(X,Y)) -> #mark(X)
Number of SCCs: 1, DPs: 10, edges: 56
	SCC { #1..3 #5 #7..10 #13 #14 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: x1
#a__from(x1)	weight: 0
  dbls(x1)	weight: (/ 1 8) + x1
a__indx(x1,x2)	weight: max{(/ 5 8) + x2, (/ 3 8) + x1}
a__from(x1)	weight: (/ 1 8) + x1
#a__indx(x1,x2)	weight: 0
   dbl(x1)	weight: (/ 1 8) + x1
  indx(x1,x2)	weight: max{(/ 5 8) + x2, (/ 3 8) + x1}
a__dbl(x1)	weight: (/ 1 8) + x1
#a__dbls(x1)	weight: 0
#mark(x1)	weight: x1
     0()	weight: (/ 1 8)
   sel(x1,x2)	weight: max{(/ 1 2) + x2, (/ 3 8) + x1}
  from(x1)	weight: (/ 1 8) + x1
   nil()	weight: (/ 3 4)
#a__dbl(x1)	weight: 0
#a__sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 8) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{(/ 1 2) + x2, (/ 3 8) + x1}
a__dbls(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: max{x2, (/ 1 8) + x1}
    Usable rules: { 1..23 }
    Removed DPs: #2 #3 #5 #7..10 #13 #14
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
     s(x1)	weight: x1	status: [x1]	precedence above: dbls a__indx indx sel nil #a__sel mark a__sel a__dbls cons
#a__from(x1)	weight: (/ 1 4)	status: []	precedence above:
  dbls(x1)	weight: (/ 1 2) + x1	status: [x1]	precedence above: a__indx indx sel nil #a__sel mark a__sel a__dbls cons
a__indx(x1,x2)	weight: (/ 1 2) + x2	status: [x2]	precedence above: indx sel nil a__sel cons
a__from(x1)	weight: (/ 1 2) + x1	status: []	precedence above: s dbls a__indx indx sel from nil #a__sel mark a__sel a__dbls cons
#a__indx(x1,x2)	weight: (/ 1 4) + x2	status: [x2]	precedence above:
   dbl(x1)	weight: x1	status: [x1]	precedence above: s dbls a__indx indx a__dbl sel nil #a__sel mark a__sel a__dbls cons
  indx(x1,x2)	weight: (/ 1 2) + x2	status: [x2]	precedence above: a__indx sel nil a__sel cons
a__dbl(x1)	weight: x1	status: [x1]	precedence above: s dbls a__indx dbl indx sel nil #a__sel mark a__sel a__dbls cons
#a__dbls(x1)	weight: x1	status: []	precedence above:
#mark(x1)	weight: x1	status: []	precedence above:
     0()	weight: (/ 1 4)	status: []	precedence above:
   sel(x1,x2)	weight: x2	status: []	precedence above: a__sel
  from(x1)	weight: (/ 1 2) + x1	status: []	precedence above: s dbls a__indx a__from indx sel nil #a__sel mark a__sel a__dbls cons
   nil()	weight: 0	status: []	precedence above:
#a__dbl(x1)	weight: (/ 1 4)	status: []	precedence above:
#a__sel(x1,x2)	weight: x1	status: x1
  mark(x1)	weight: x1	status: x1
a__sel(x1,x2)	weight: x2	status: []	precedence above: sel
a__dbls(x1)	weight: (/ 1 2) + x1	status: [x1]	precedence above: dbls a__indx indx sel nil #a__sel mark a__sel cons
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}	status: []	precedence above: sel a__sel
    Usable rules: { 1..23 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES