YES
Input TRS:
      1: dbl(0()) -> 0()
      2: dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
      3: dbls(nil()) -> nil()
      4: dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
      5: sel(0(),cons(X,Y)) -> activate(X)
      6: sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
      7: indx(nil(),X) -> nil()
      8: indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
      9: from(X) -> cons(activate(X),n__from(n__s(activate(X))))
      10: s(X) -> n__s(X)
      11: dbl(X) -> n__dbl(X)
      12: dbls(X) -> n__dbls(X)
      13: sel(X1,X2) -> n__sel(X1,X2)
      14: indx(X1,X2) -> n__indx(X1,X2)
      15: from(X) -> n__from(X)
      16: activate(n__s(X)) -> s(X)
      17: activate(n__dbl(X)) -> dbl(X)
      18: activate(n__dbls(X)) -> dbls(X)
      19: activate(n__sel(X1,X2)) -> sel(X1,X2)
      20: activate(n__indx(X1,X2)) -> indx(X1,X2)
      21: activate(n__from(X)) -> from(X)
      22: activate(X) -> X
Number of strict rules: 22
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #dbl(s(X)) -> #s(n__s(n__dbl(activate(X))))
     #2: #dbl(s(X)) -> #activate(X)
     #3: #sel(s(X),cons(Y,Z)) -> #sel(activate(X),activate(Z))
     #4: #sel(s(X),cons(Y,Z)) -> #activate(X)
     #5: #sel(s(X),cons(Y,Z)) -> #activate(Z)
     #6: #from(X) -> #activate(X)
     #7: #from(X) -> #activate(X)
     #8: #activate(n__indx(X1,X2)) -> #indx(X1,X2)
     #9: #sel(0(),cons(X,Y)) -> #activate(X)
     #10: #activate(n__dbl(X)) -> #dbl(X)
     #11: #activate(n__sel(X1,X2)) -> #sel(X1,X2)
     #12: #activate(n__from(X)) -> #from(X)
     #13: #activate(n__s(X)) -> #s(X)
     #14: #indx(cons(X,Y),Z) -> #activate(X)
     #15: #indx(cons(X,Y),Z) -> #activate(Z)
     #16: #indx(cons(X,Y),Z) -> #activate(Y)
     #17: #indx(cons(X,Y),Z) -> #activate(Z)
     #18: #dbls(cons(X,Y)) -> #activate(X)
     #19: #dbls(cons(X,Y)) -> #activate(Y)
     #20: #activate(n__dbls(X)) -> #dbls(X)
Number of SCCs: 1, DPs: 18
  SCC { #2..12 #14..20 }
POLO(Sum)... POLO(max)... succeeded.
      s 	w: x1
      dbls	w: x1 + 32287
      activate	w: x1
      dbl	w: x1 + 32287
      indx	w: max(x1 + 5513, x2 + 11026)
      n__indx	w: max(x1 + 5513, x2 + 11026)
      n__from	w: x1 + 8367
      #dbl	w: x1 + 16305
      #activate	w: x1 + 16304
      #dbls	w: x1 + 16305
      n__dbls	w: x1 + 32287
      n__s	w: x1
      n__dbl	w: x1 + 32287
      0 	w: 1
      #sel	w: max(x1 + 16304, x2 + 16304)
      #indx	w: max(x1 + 21816, x2 + 16305)
      sel	w: max(x1 + 5513, x2)
      from	w: x1 + 8367
      #s 	w: 0
      nil	w: 11027
      n__sel	w: max(x1 + 5513, x2)
      #from	w: x1 + 24670
      cons	w: max(x1 + 5512, x2)
    USABLE RULES: { 1..22 }
    Removed DPs: #2 #6..10 #12 #14..20
Number of SCCs: 1, DPs: 4
  SCC { #3..5 #11 }
POLO(Sum)... POLO(max)... succeeded.
      s 	w: x1
      dbls	w: x1 + 1
      activate	w: x1
      dbl	w: x1 + 1
      indx	w: max(x1 + 2999, x2 + 3001)
      n__indx	w: max(x1 + 2999, x2 + 3001)
      n__from	w: x1 + 20977
      #dbl	w: 16305
      #activate	w: x1 + 46572
      #dbls	w: 16305
      n__dbls	w: x1 + 1
      n__s	w: x1
      n__dbl	w: x1 + 1
      0 	w: 1
      #sel	w: max(x1 + 49571, x2 + 46572)
      #indx	w: 0
      sel	w: max(x1 + 2999, x2)
      from	w: x1 + 20977
      #s 	w: 0
      nil	w: 3002
      n__sel	w: max(x1 + 2999, x2)
      #from	w: 24670
      cons	w: max(x1 + 1, x2)
    USABLE RULES: { 1..22 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 3
  SCC { #3 #5 #11 }
POLO(Sum)... POLO(max)... succeeded.
      s 	w: x1
      dbls	w: x1 + 1
      activate	w: x1
      dbl	w: x1 + 1
      indx	w: max(x1 + 1326, x2 + 1328)
      n__indx	w: max(x1 + 1326, x2 + 1328)
      n__from	w: x1 + 53255
      #dbl	w: 16305
      #activate	w: x1 + 4688
      #dbls	w: 16305
      n__dbls	w: x1 + 1
      n__s	w: x1
      n__dbl	w: x1 + 1
      0 	w: 38607
      #sel	w: max(x1 + 4687, x2 + 4689)
      #indx	w: 0
      sel	w: max(x1 + 1326, x2 + 1)
      from	w: x1 + 53255
      #s 	w: 0
      nil	w: 1329
      n__sel	w: max(x1 + 1326, x2 + 1)
      #from	w: 24670
      cons	w: max(x1 + 1, x2)
    USABLE RULES: { 1..22 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 1
  SCC { #3 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 2	w: x1
      dbls	s: [1]	p: 5	w: x1 + 57802
      activate	s: [1]	p: 1	w: x1
      dbl	s: [1]	p: 3	w: x1 + 25907
      indx	s: []	p: 4	w: x1 + x2 + 31895
      n__indx	s: []	p: 4	w: x1 + x2 + 31895
      n__from	s: []	p: 4	w: x1 + 58180
      #dbl	s: []	p: 0	w: 1
      #activate	s: 1
      #dbls	s: 1
      n__dbls	s: [1]	p: 5	w: x1 + 57802
      n__s	s: [1]	p: 2	w: x1
      n__dbl	s: [1]	p: 3	w: x1 + 25907
      0 	s: []	p: 0	w: 2998
      #sel	s: 1
      #indx	s: [1,2]	p: 0	w: x1 + x2 + 1
      sel	s: []	p: 5	w: x1 + x2 + 31893
      from	s: []	p: 4	w: x1 + 58180
      #s 	s: 1
      nil	s: []	p: 4	w: 36336
      n__sel	s: []	p: 5	w: x1 + x2 + 31893
      #from	s: []	p: 0	w: 1
      cons	s: []	p: 4	w: max(x1 + 31894, x2)
    USABLE RULES: { 1..22 }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0