MAYBE
Input TRS:
      1: a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
      2: a__sel(0(),cons(X,Z)) -> mark(X)
      3: a__first(0(),Z) -> nil()
      4: a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
      5: a__from(X) -> cons(mark(X),from(s(X)))
      6: a__sel1(s(X),cons(Y,Z)) -> a__sel1(mark(X),mark(Z))
      7: a__sel1(0(),cons(X,Z)) -> a__quote(X)
      8: a__first1(0(),Z) -> nil1()
      9: a__first1(s(X),cons(Y,Z)) -> cons1(a__quote(Y),a__first1(mark(X),mark(Z)))
      10: a__quote(0()) -> 01()
      11: a__quote1(cons(X,Z)) -> cons1(a__quote(X),a__quote1(Z))
      12: a__quote1(nil()) -> nil1()
      13: a__quote(s(X)) -> s1(a__quote(X))
      14: a__quote(sel(X,Z)) -> a__sel1(mark(X),mark(Z))
      15: a__quote1(first(X,Z)) -> a__first1(mark(X),mark(Z))
      16: a__unquote(01()) -> 0()
      17: a__unquote(s1(X)) -> s(a__unquote(mark(X)))
      18: a__unquote1(nil1()) -> nil()
      19: a__unquote1(cons1(X,Z)) -> a__fcons(a__unquote(mark(X)),a__unquote1(mark(Z)))
      20: a__fcons(X,Z) -> cons(mark(X),Z)
      21: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
      22: mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
      23: mark(from(X)) -> a__from(mark(X))
      24: mark(sel1(X1,X2)) -> a__sel1(mark(X1),mark(X2))
      25: mark(quote(X)) -> a__quote(X)
      26: mark(first1(X1,X2)) -> a__first1(mark(X1),mark(X2))
      27: mark(quote1(X)) -> a__quote1(X)
      28: mark(unquote(X)) -> a__unquote(mark(X))
      29: mark(unquote1(X)) -> a__unquote1(mark(X))
      30: mark(fcons(X1,X2)) -> a__fcons(mark(X1),mark(X2))
      31: mark(s(X)) -> s(mark(X))
      32: mark(cons(X1,X2)) -> cons(mark(X1),X2)
      33: mark(0()) -> 0()
      34: mark(nil()) -> nil()
      35: mark(nil1()) -> nil1()
      36: mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2))
      37: mark(01()) -> 01()
      38: mark(s1(X)) -> s1(mark(X))
      39: a__sel(X1,X2) -> sel(X1,X2)
      40: a__first(X1,X2) -> first(X1,X2)
      41: a__from(X) -> from(X)
      42: a__sel1(X1,X2) -> sel1(X1,X2)
      43: a__quote(X) -> quote(X)
      44: a__first1(X1,X2) -> first1(X1,X2)
      45: a__quote1(X) -> quote1(X)
      46: a__unquote(X) -> unquote(X)
      47: a__unquote1(X) -> unquote1(X)
      48: a__fcons(X1,X2) -> fcons(X1,X2)
Number of strict rules: 48
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a__sel(0(),cons(X,Z)) -> #mark(X)
     #2: #mark(unquote1(X)) -> #a__unquote1(mark(X))
     #3: #mark(unquote1(X)) -> #mark(X)
     #4: #mark(s1(X)) -> #mark(X)
     #5: #a__sel1(s(X),cons(Y,Z)) -> #a__sel1(mark(X),mark(Z))
     #6: #a__sel1(s(X),cons(Y,Z)) -> #mark(X)
     #7: #a__sel1(s(X),cons(Y,Z)) -> #mark(Z)
     #8: #a__quote(s(X)) -> #a__quote(X)
     #9: #a__first1(s(X),cons(Y,Z)) -> #a__quote(Y)
     #10: #a__first1(s(X),cons(Y,Z)) -> #a__first1(mark(X),mark(Z))
     #11: #a__first1(s(X),cons(Y,Z)) -> #mark(X)
     #12: #a__first1(s(X),cons(Y,Z)) -> #mark(Z)
     #13: #a__quote1(cons(X,Z)) -> #a__quote(X)
     #14: #a__quote1(cons(X,Z)) -> #a__quote1(Z)
     #15: #mark(sel1(X1,X2)) -> #a__sel1(mark(X1),mark(X2))
     #16: #mark(sel1(X1,X2)) -> #mark(X1)
     #17: #mark(sel1(X1,X2)) -> #mark(X2)
     #18: #mark(from(X)) -> #a__from(mark(X))
     #19: #mark(from(X)) -> #mark(X)
     #20: #mark(s(X)) -> #mark(X)
     #21: #a__quote(sel(X,Z)) -> #a__sel1(mark(X),mark(Z))
     #22: #a__quote(sel(X,Z)) -> #mark(X)
     #23: #a__quote(sel(X,Z)) -> #mark(Z)
     #24: #mark(fcons(X1,X2)) -> #a__fcons(mark(X1),mark(X2))
     #25: #mark(fcons(X1,X2)) -> #mark(X1)
     #26: #mark(fcons(X1,X2)) -> #mark(X2)
     #27: #mark(quote(X)) -> #a__quote(X)
     #28: #a__fcons(X,Z) -> #mark(X)
     #29: #a__sel1(0(),cons(X,Z)) -> #a__quote(X)
     #30: #a__from(X) -> #mark(X)
     #31: #mark(unquote(X)) -> #a__unquote(mark(X))
     #32: #mark(unquote(X)) -> #mark(X)
     #33: #mark(first(X1,X2)) -> #a__first(mark(X1),mark(X2))
     #34: #mark(first(X1,X2)) -> #mark(X1)
     #35: #mark(first(X1,X2)) -> #mark(X2)
     #36: #mark(quote1(X)) -> #a__quote1(X)
     #37: #a__unquote(s1(X)) -> #a__unquote(mark(X))
     #38: #a__unquote(s1(X)) -> #mark(X)
     #39: #mark(cons(X1,X2)) -> #mark(X1)
     #40: #a__unquote1(cons1(X,Z)) -> #a__fcons(a__unquote(mark(X)),a__unquote1(mark(Z)))
     #41: #a__unquote1(cons1(X,Z)) -> #a__unquote(mark(X))
     #42: #a__unquote1(cons1(X,Z)) -> #mark(X)
     #43: #a__unquote1(cons1(X,Z)) -> #a__unquote1(mark(Z))
     #44: #a__unquote1(cons1(X,Z)) -> #mark(Z)
     #45: #mark(first1(X1,X2)) -> #a__first1(mark(X1),mark(X2))
     #46: #mark(first1(X1,X2)) -> #mark(X1)
     #47: #mark(first1(X1,X2)) -> #mark(X2)
     #48: #mark(cons1(X1,X2)) -> #mark(X1)
     #49: #mark(cons1(X1,X2)) -> #mark(X2)
     #50: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
     #51: #mark(sel(X1,X2)) -> #mark(X1)
     #52: #mark(sel(X1,X2)) -> #mark(X2)
     #53: #a__sel(s(X),cons(Y,Z)) -> #a__sel(mark(X),mark(Z))
     #54: #a__sel(s(X),cons(Y,Z)) -> #mark(X)
     #55: #a__sel(s(X),cons(Y,Z)) -> #mark(Z)
     #56: #a__quote1(first(X,Z)) -> #a__first1(mark(X),mark(Z))
     #57: #a__quote1(first(X,Z)) -> #mark(X)
     #58: #a__quote1(first(X,Z)) -> #mark(Z)
     #59: #a__first(s(X),cons(Y,Z)) -> #mark(Y)
Number of SCCs: 1, DPs: 59
  SCC { #1..59 }
POLO(Sum)... POLO(max)... succeeded.
      #a__quote	w: x1 + 1145
      01	w: 1
      s 	w: x1
      unquote1	w: x1 + 14685
      a__first1	w: max(x1 + 15, x2 + 4)
      #a__from	w: x1 + 1146
      #a__fcons	w: max(x1 + 1146, x2 + 1)
      #a__first	w: max(x2 + 1155)
      a__from	w: x1 + 12
      #a__first1	w: max(x1 + 1159, x2 + 1146)
      #a__unquote	w: x1 + 15826
      a__unquote	w: x1 + 14682
      a__sel1	w: max(x1 + 20561, x2 + 4)
      a__fcons	w: max(x1 + 12, x2)
      cons1	w: max(x1 + 11, x2)
      #mark	w: x1 + 1145
      0 	w: 1
      a__quote	w: x1 + 5
      from	w: x1 + 12
      sel	w: max(x1 + 20556, x2 + 20542)
      #a__sel1	w: max(x1 + 1146, x2 + 1149)
      nil	w: 11
      quote1	w: x1 + 6
      #a__quote1	w: x1 + 1150
      #a__sel	w: max(x1 + 21700, x2 + 21687)
      mark	w: x1
      nil1	w: 6
      a__sel	w: max(x1 + 20556, x2 + 20542)
      first	w: max(x1 + 9, x2 + 11)
      a__first	w: max(x1 + 9, x2 + 11)
      first1	w: max(x1 + 15, x2 + 4)
      a__unquote1	w: x1 + 14685
      #a__unquote1	w: x1 + 15829
      quote	w: x1 + 5
      cons	w: max(x1 + 12, x2)
      sel1	w: max(x1 + 20561, x2 + 4)
      a__quote1	w: x1 + 6
      s1	w: x1
      unquote	w: x1 + 14682
      fcons	w: max(x1 + 12, x2)
    USABLE RULES: { 1..48 }
    Removed DPs: #1..3 #6 #7 #9 #11..13 #16..19 #21..25 #27..36 #38..42 #44..48 #51 #52 #54 #55 #57..59
Number of SCCs: 8, DPs: 11
  SCC { #8 }
POLO(Sum)... succeeded.
      #a__quote	w: x1
      01	w: 2
      s 	w: x1 + 1
      unquote1	w: 1
      a__first1	w: 5
      #a__from	w: 0
      #a__fcons	w: 0
      #a__first	w: 0
      a__from	w: 2
      #a__first1	w: 0
      #a__unquote	w: 0
      a__unquote	w: x1 + 4187
      a__sel1	w: 11824
      a__fcons	w: 2
      cons1	w: 6
      #mark	w: 0
      0 	w: 4190
      a__quote	w: x1 + 2
      from	w: x1 + 3
      sel	w: x2 + 11821
      #a__sel1	w: 0
      nil	w: 2
      quote1	w: 3
      #a__quote1	w: 0
      #a__sel	w: 0
      mark	w: 1
      nil1	w: 6
      a__sel	w: x2 + 1
      first	w: 2
      a__first	w: x2 + 1
      first1	w: 6
      a__unquote1	w: 0
      #a__unquote1	w: 0
      quote	w: 3
      cons	w: x2 + 3
      sel1	w: x2 + 11825
      a__quote1	w: x1 + 2
      s1	w: 243
      unquote	w: 4188
      fcons	w: x1 + x2 + 3
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 7, DPs: 10
  SCC { #37 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      #a__quote	w: max(x1 - 1, 0)
      01	w: 28885
      s 	w: max(x1 + 2, 0)
      unquote1	w: max(x1 + 63414, 0)
      a__first1	w: max(x2 - 3, 0)
      #a__from	w: 0
      #a__fcons	w: 0
      #a__first	w: max(x2 - 1, 0)
      a__from	w: max(x1 - 19163, 0)
      #a__first1	w: max(x1 - 1, 0)
      #a__unquote	w: max(x1 - 1, 0)
      a__unquote	w: max(x1 + 2, 0)
      a__sel1	w: max(x1 + x2 + 2, 0)
      a__fcons	w: max(x1 + 34519, x2 - 2, 0)
      cons1	w: max(x1 - 28893, x2 - 2, 0)
      #mark	w: max(x1 - 1, 0)
      0 	w: 28887
      a__quote	w: max(x1 + 1, 0)
      from	w: max(x1 - 19163, 0)
      sel	w: max(x1 + x2 + 1, 0)
      #a__sel1	w: 0
      nil	w: 4
      quote1	w: max(x1 - 4, 0)
      #a__quote1	w: 0
      #a__sel	w: max(x1 - 1, 0)
      mark	w: max(x1, 0)
      nil1	w: 0
      a__sel	w: max(x1 + x2 + 1, 0)
      first	w: max(x2 + 4, 0)
      a__first	w: max(x2 + 4, 0)
      first1	w: max(x2 - 3, 0)
      a__unquote1	w: max(x1 + 63414, 0)
      #a__unquote1	w: 0
      quote	w: max(x1 + 1, 0)
      cons	w: max(x1 - 28888, x2 - 2, 0)
      sel1	w: max(x1 + x2 + 2, 0)
      a__quote1	w: max(x1 - 4, 0)
      s1	w: max(x1 + 2, 0)
      unquote	w: max(x1 + 2, 0)
      fcons	w: max(x1 + 34519, x2 - 2, 0)
    USABLE RULES: { 1..48 }
    Removed DPs: #37
Number of SCCs: 6, DPs: 9
  SCC { #14 }
POLO(Sum)... succeeded.
      #a__quote	w: 0
      01	w: 2
      s 	w: 2
      unquote1	w: x1 + 2
      a__first1	w: 982
      #a__from	w: 0
      #a__fcons	w: 0
      #a__first	w: 0
      a__from	w: 2
      #a__first1	w: 0
      #a__unquote	w: 0
      a__unquote	w: x1 + 1
      a__sel1	w: x1 + 1
      a__fcons	w: x1 + 1
      cons1	w: x1 + x2 + 1
      #mark	w: 0
      0 	w: 4
      a__quote	w: x1 + 6
      from	w: 32530
      sel	w: x1 + x2 + 3
      #a__sel1	w: 0
      nil	w: 5
      quote1	w: x1 + 979
      #a__quote1	w: x1
      #a__sel	w: 0
      mark	w: 1
      nil1	w: 984
      a__sel	w: 2
      first	w: x1 + x2 + 3
      a__first	w: x1 + x2
      first1	w: x1 + x2 + 983
      a__unquote1	w: x1 + 1
      #a__unquote1	w: 0
      quote	w: 7
      cons	w: x2 + 4
      sel1	w: x2 + 2
      a__quote1	w: x1 + 978
      s1	w: x1 + 3
      unquote	w: x1 + 2
      fcons	w: 2
    USABLE RULES: { }
    Removed DPs: #14
Number of SCCs: 5, DPs: 8
  SCC { #43 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.