YES
Input TRS:
      1: active(dbl(0())) -> mark(0())
      2: active(dbl(s(X))) -> mark(s(s(dbl(X))))
      3: active(dbls(nil())) -> mark(nil())
      4: active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
      5: active(sel(0(),cons(X,Y))) -> mark(X)
      6: active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
      7: active(indx(nil(),X)) -> mark(nil())
      8: active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
      9: active(from(X)) -> mark(cons(X,from(s(X))))
      10: active(dbl(X)) -> dbl(active(X))
      11: active(dbls(X)) -> dbls(active(X))
      12: active(sel(X1,X2)) -> sel(active(X1),X2)
      13: active(sel(X1,X2)) -> sel(X1,active(X2))
      14: active(indx(X1,X2)) -> indx(active(X1),X2)
      15: dbl(mark(X)) -> mark(dbl(X))
      16: dbls(mark(X)) -> mark(dbls(X))
      17: sel(mark(X1),X2) -> mark(sel(X1,X2))
      18: sel(X1,mark(X2)) -> mark(sel(X1,X2))
      19: indx(mark(X1),X2) -> mark(indx(X1,X2))
      20: proper(dbl(X)) -> dbl(proper(X))
      21: proper(0()) -> ok(0())
      22: proper(s(X)) -> s(proper(X))
      23: proper(dbls(X)) -> dbls(proper(X))
      24: proper(nil()) -> ok(nil())
      25: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      26: proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
      27: proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
      28: proper(from(X)) -> from(proper(X))
      29: dbl(ok(X)) -> ok(dbl(X))
      30: s(ok(X)) -> ok(s(X))
      31: dbls(ok(X)) -> ok(dbls(X))
      32: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      33: sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
      34: indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
      35: from(ok(X)) -> ok(from(X))
      36: top(mark(X)) -> top(proper(X))
      37: top(ok(X)) -> top(active(X))
Number of strict rules: 37
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #active(dbl(s(X))) -> #s(s(dbl(X)))
     #2: #active(dbl(s(X))) -> #s(dbl(X))
     #3: #active(dbl(s(X))) -> #dbl(X)
     #4: #dbl(ok(X)) -> #dbl(X)
     #5: #from(ok(X)) -> #from(X)
     #6: #top(ok(X)) -> #top(active(X))
     #7: #top(ok(X)) -> #active(X)
     #8: #active(sel(s(X),cons(Y,Z))) -> #sel(X,Z)
     #9: #active(sel(X1,X2)) -> #sel(X1,active(X2))
     #10: #active(sel(X1,X2)) -> #active(X2)
     #11: #active(from(X)) -> #cons(X,from(s(X)))
     #12: #active(from(X)) -> #from(s(X))
     #13: #active(from(X)) -> #s(X)
     #14: #active(dbls(X)) -> #dbls(active(X))
     #15: #active(dbls(X)) -> #active(X)
     #16: #proper(dbls(X)) -> #dbls(proper(X))
     #17: #proper(dbls(X)) -> #proper(X)
     #18: #active(sel(X1,X2)) -> #sel(active(X1),X2)
     #19: #active(sel(X1,X2)) -> #active(X1)
     #20: #dbls(ok(X)) -> #dbls(X)
     #21: #active(indx(X1,X2)) -> #indx(active(X1),X2)
     #22: #active(indx(X1,X2)) -> #active(X1)
     #23: #s(ok(X)) -> #s(X)
     #24: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
     #25: #proper(cons(X1,X2)) -> #proper(X1)
     #26: #proper(cons(X1,X2)) -> #proper(X2)
     #27: #proper(dbl(X)) -> #dbl(proper(X))
     #28: #proper(dbl(X)) -> #proper(X)
     #29: #active(dbl(X)) -> #dbl(active(X))
     #30: #active(dbl(X)) -> #active(X)
     #31: #sel(ok(X1),ok(X2)) -> #sel(X1,X2)
     #32: #proper(from(X)) -> #from(proper(X))
     #33: #proper(from(X)) -> #proper(X)
     #34: #proper(s(X)) -> #s(proper(X))
     #35: #proper(s(X)) -> #proper(X)
     #36: #indx(ok(X1),ok(X2)) -> #indx(X1,X2)
     #37: #proper(indx(X1,X2)) -> #indx(proper(X1),proper(X2))
     #38: #proper(indx(X1,X2)) -> #proper(X1)
     #39: #proper(indx(X1,X2)) -> #proper(X2)
     #40: #sel(mark(X1),X2) -> #sel(X1,X2)
     #41: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
     #42: #indx(mark(X1),X2) -> #indx(X1,X2)
     #43: #proper(sel(X1,X2)) -> #sel(proper(X1),proper(X2))
     #44: #proper(sel(X1,X2)) -> #proper(X1)
     #45: #proper(sel(X1,X2)) -> #proper(X2)
     #46: #top(mark(X)) -> #top(proper(X))
     #47: #top(mark(X)) -> #proper(X)
     #48: #dbls(mark(X)) -> #dbls(X)
     #49: #active(indx(cons(X,Y),Z)) -> #cons(sel(X,Z),indx(Y,Z))
     #50: #active(indx(cons(X,Y),Z)) -> #sel(X,Z)
     #51: #active(indx(cons(X,Y),Z)) -> #indx(Y,Z)
     #52: #dbl(mark(X)) -> #dbl(X)
     #53: #active(dbls(cons(X,Y))) -> #cons(dbl(X),dbls(Y))
     #54: #active(dbls(cons(X,Y))) -> #dbl(X)
     #55: #active(dbls(cons(X,Y))) -> #dbls(Y)
     #56: #sel(X1,mark(X2)) -> #sel(X1,X2)
Number of SCCs: 10, DPs: 29
  SCC { #5 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      dbls	w: 0
      dbl	w: 0
      top	w: 0
      indx	w: 0
      #dbl	w: 0
      #dbls	w: 0
      #top	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      #indx	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      nil	w: 0
      mark	w: 0
      #proper	w: 0
      #from	w: x1
      active	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #5
Number of SCCs: 9, DPs: 28
  SCC { #23 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      dbls	w: 0
      dbl	w: 0
      top	w: 0
      indx	w: 0
      #dbl	w: 0
      #dbls	w: 0
      #top	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      #indx	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: x1
      nil	w: 0
      mark	w: 0
      #proper	w: 0
      #from	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #23
Number of SCCs: 8, DPs: 27
  SCC { #41 }
POLO(Sum)... succeeded.
      #cons	w: x2
      s 	w: 0
      dbls	w: 0
      dbl	w: 0
      top	w: 0
      indx	w: 0
      #dbl	w: 0
      #dbls	w: 0
      #top	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      #indx	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      nil	w: 0
      mark	w: 0
      #proper	w: 0
      #from	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #41
Number of SCCs: 7, DPs: 26
  SCC { #4 #52 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      dbls	w: 0
      dbl	w: 0
      top	w: 0
      indx	w: 0
      #dbl	w: x1
      #dbls	w: 0
      #top	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      #indx	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      nil	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #4 #52
Number of SCCs: 6, DPs: 24
  SCC { #20 #48 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      dbls	w: 0
      dbl	w: 0
      top	w: 0
      indx	w: 0
      #dbl	w: 0
      #dbls	w: x1
      #top	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      #indx	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      nil	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #20 #48
Number of SCCs: 5, DPs: 22
  SCC { #6 #46 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #cons	s: 1
      s 	s: [1]	p: 0	w: x1
      dbls	s: [1]	p: 2	w: x1 + 31113
      dbl	s: [1]	p: 3	w: x1 + 31112
      top	s: []	p: 0	w: 1
      indx	s: [1]	p: 6	w: x1 + x2 + 62230
      #dbl	s: []	p: 0	w: 1
      #dbls	s: []	p: 0	w: 1
      #top	s: [1]	p: 0	w: x1 + 1
      proper	s: 1
      ok	s: 1
      0 	s: []	p: 6	w: 1
      #sel	s: 2
      #indx	s: [1,2]	p: 0	w: x1 + x2 + 1
      sel	s: [1,2]	p: 3	w: x1 + x2 + 31115
      from	s: [1]	p: 4	w: x1 + 51699
      #s 	s: []	p: 0	w: 1
      nil	s: []	p: 3	w: 19791
      mark	s: [1]	p: 1	w: x1
      #proper	s: []	p: 0	w: 1
      #from	s: 1
      active	s: 1
      cons	s: []	p: 0	w: max(x1 + 31114, x2)
      #active	s: 1
    USABLE RULES: { 1..35 }
    Removed DPs: #46
Number of SCCs: 5, DPs: 21
  SCC { #6 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      dbls	w: x1 + 1
      dbl	w: x1 + 24720
      top	w: 0
      indx	w: x2 + 1
      #dbl	w: 0
      #dbls	w: 0
      #top	w: x1
      proper	w: x1 + 16164
      ok	w: x1 + 16164
      0 	w: 1
      #sel	w: 0
      #indx	w: 0
      sel	w: x1 + 28938
      from	w: x1 + 1
      #s 	w: 0
      nil	w: 1
      mark	w: 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 13359
      cons	w: x2
      #active	w: 0
    USABLE RULES: { 1..35 }
    Removed DPs: #6
Number of SCCs: 4, DPs: 20
  SCC { #36 #42 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      dbls	w: x1 + 1
      dbl	w: x1 + 1
      top	w: 0
      indx	w: x2 + 1
      #dbl	w: 0
      #dbls	w: 0
      #top	w: x1
      proper	w: x1 + 25192
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: 0
      #indx	w: x2
      sel	w: x1 + 1
      from	w: x1 + 26170
      #s 	w: 0
      nil	w: 1
      mark	w: 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 38368
      cons	w: x2
      #active	w: 0
    USABLE RULES: { 1..35 }
    Removed DPs: #36
Number of SCCs: 4, DPs: 19
  SCC { #42 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      dbls	w: x1 + 1
      dbl	w: x1 + 23491
      top	w: 0
      indx	w: x1
      #dbl	w: 0
      #dbls	w: 0
      #top	w: 0
      proper	w: x1 + 1
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: 0
      #indx	w: x1
      sel	w: x1 + 16512
      from	w: x1
      #s 	w: 0
      nil	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 26873
      cons	w: x2
      #active	w: 0
    USABLE RULES: { 1..4 7..9 15 16 19 21 24 29..32 34 35 }
    Removed DPs: #42
Number of SCCs: 3, DPs: 18
  SCC { #31 #40 #56 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      dbls	w: x1 + 1
      dbl	w: x1 + 1
      top	w: 0
      indx	w: x1
      #dbl	w: 0
      #dbls	w: 0
      #top	w: 0
      proper	w: x1 + 16513
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: x1
      #indx	w: 0
      sel	w: x1 + 1
      from	w: x1
      #s 	w: 0
      nil	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 1
      cons	w: x2
      #active	w: 0
    USABLE RULES: { 1..4 7..9 15 16 19 21 24 29..32 34 35 }
    Removed DPs: #31 #40
Number of SCCs: 3, DPs: 16
  SCC { #56 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      dbls	w: x1 + 1
      dbl	w: x1 + 1
      top	w: 0
      indx	w: x1
      #dbl	w: 0
      #dbls	w: 0
      #top	w: 0
      proper	w: x1 + 1
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: x2
      #indx	w: 0
      sel	w: x1 + 1
      from	w: x1
      #s 	w: 0
      nil	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 7156
      cons	w: x2
      #active	w: 0
    USABLE RULES: { 1..4 7..9 15 16 19 21 24 29..32 34 35 }
    Removed DPs: #56
Number of SCCs: 2, DPs: 15
  SCC { #10 #15 #19 #22 #30 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      dbls	w: x1 + 1
      dbl	w: x1 + 1
      top	w: 0
      indx	w: x1 + 1
      #dbl	w: 0
      #dbls	w: 0
      #top	w: 0
      proper	w: x1
      ok	w: 1
      0 	w: 1
      #sel	w: 0
      #indx	w: 0
      sel	w: x1 + x2 + 1
      from	w: x1
      #s 	w: 0
      nil	w: 1
      mark	w: x1 + 31249
      #proper	w: 0
      #from	w: 0
      active	w: 38405
      cons	w: x2
      #active	w: x1
    USABLE RULES: { 1 3 7 15 16 19 21 24 29..32 34 35 }
    Removed DPs: #10 #15 #19 #22 #30
Number of SCCs: 1, DPs: 10
  SCC { #17 #25 #26 #28 #33 #35 #38 #39 #44 #45 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      dbls	w: x1 + 1
      dbl	w: x1 + 1
      top	w: 0
      indx	w: x1 + x2 + 1
      #dbl	w: 0
      #dbls	w: 0
      #top	w: 0
      proper	w: x1
      ok	w: x1
      0 	w: 1
      #sel	w: 0
      #indx	w: 0
      sel	w: x1 + x2 + 1
      from	w: x1 + 1
      #s 	w: 0
      nil	w: 1
      mark	w: x1 + 1
      #proper	w: x1
      #from	w: 0
      active	w: 4
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { 1 3 7 15 16 19 21 24 29..32 34 35 }
    Removed DPs: #17 #25 #26 #28 #33 #35 #38 #39 #44 #45
Number of SCCs: 0, DPs: 0