YES
Input TRS:
      1: active(from(X)) -> mark(cons(X,from(s(X))))
      2: active(first(0(),Z)) -> mark(nil())
      3: active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
      4: active(sel(0(),cons(X,Z))) -> mark(X)
      5: active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
      6: active(from(X)) -> from(active(X))
      7: active(cons(X1,X2)) -> cons(active(X1),X2)
      8: active(s(X)) -> s(active(X))
      9: active(first(X1,X2)) -> first(active(X1),X2)
      10: active(first(X1,X2)) -> first(X1,active(X2))
      11: active(sel(X1,X2)) -> sel(active(X1),X2)
      12: active(sel(X1,X2)) -> sel(X1,active(X2))
      13: from(mark(X)) -> mark(from(X))
      14: cons(mark(X1),X2) -> mark(cons(X1,X2))
      15: s(mark(X)) -> mark(s(X))
      16: first(mark(X1),X2) -> mark(first(X1,X2))
      17: first(X1,mark(X2)) -> mark(first(X1,X2))
      18: sel(mark(X1),X2) -> mark(sel(X1,X2))
      19: sel(X1,mark(X2)) -> mark(sel(X1,X2))
      20: proper(from(X)) -> from(proper(X))
      21: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      22: proper(s(X)) -> s(proper(X))
      23: proper(first(X1,X2)) -> first(proper(X1),proper(X2))
      24: proper(0()) -> ok(0())
      25: proper(nil()) -> ok(nil())
      26: proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
      27: from(ok(X)) -> ok(from(X))
      28: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      29: s(ok(X)) -> ok(s(X))
      30: first(ok(X1),ok(X2)) -> ok(first(X1,X2))
      31: sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
      32: top(mark(X)) -> top(proper(X))
      33: top(ok(X)) -> top(active(X))
Number of strict rules: 33
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #s(ok(X)) -> #s(X)
     #2: #active(from(X)) -> #from(active(X))
     #3: #active(from(X)) -> #active(X)
     #4: #from(mark(X)) -> #from(X)
     #5: #active(first(X1,X2)) -> #first(active(X1),X2)
     #6: #active(first(X1,X2)) -> #active(X1)
     #7: #active(sel(X1,X2)) -> #sel(active(X1),X2)
     #8: #active(sel(X1,X2)) -> #active(X1)
     #9: #proper(first(X1,X2)) -> #first(proper(X1),proper(X2))
     #10: #proper(first(X1,X2)) -> #proper(X1)
     #11: #proper(first(X1,X2)) -> #proper(X2)
     #12: #active(sel(X1,X2)) -> #sel(X1,active(X2))
     #13: #active(sel(X1,X2)) -> #active(X2)
     #14: #sel(ok(X1),ok(X2)) -> #sel(X1,X2)
     #15: #cons(mark(X1),X2) -> #cons(X1,X2)
     #16: #first(ok(X1),ok(X2)) -> #first(X1,X2)
     #17: #proper(from(X)) -> #from(proper(X))
     #18: #proper(from(X)) -> #proper(X)
     #19: #active(cons(X1,X2)) -> #cons(active(X1),X2)
     #20: #active(cons(X1,X2)) -> #active(X1)
     #21: #active(first(X1,X2)) -> #first(X1,active(X2))
     #22: #active(first(X1,X2)) -> #active(X2)
     #23: #top(ok(X)) -> #top(active(X))
     #24: #top(ok(X)) -> #active(X)
     #25: #active(sel(s(X),cons(Y,Z))) -> #sel(X,Z)
     #26: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
     #27: #proper(s(X)) -> #s(proper(X))
     #28: #proper(s(X)) -> #proper(X)
     #29: #from(ok(X)) -> #from(X)
     #30: #first(X1,mark(X2)) -> #first(X1,X2)
     #31: #top(mark(X)) -> #top(proper(X))
     #32: #top(mark(X)) -> #proper(X)
     #33: #sel(X1,mark(X2)) -> #sel(X1,X2)
     #34: #proper(sel(X1,X2)) -> #sel(proper(X1),proper(X2))
     #35: #proper(sel(X1,X2)) -> #proper(X1)
     #36: #proper(sel(X1,X2)) -> #proper(X2)
     #37: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
     #38: #proper(cons(X1,X2)) -> #proper(X1)
     #39: #proper(cons(X1,X2)) -> #proper(X2)
     #40: #first(mark(X1),X2) -> #first(X1,X2)
     #41: #active(first(s(X),cons(Y,Z))) -> #cons(Y,first(X,Z))
     #42: #active(first(s(X),cons(Y,Z))) -> #first(X,Z)
     #43: #active(from(X)) -> #cons(X,from(s(X)))
     #44: #active(from(X)) -> #from(s(X))
     #45: #active(from(X)) -> #s(X)
     #46: #active(s(X)) -> #s(active(X))
     #47: #active(s(X)) -> #active(X)
     #48: #s(mark(X)) -> #s(X)
     #49: #sel(mark(X1),X2) -> #sel(X1,X2)
Number of SCCs: 8, DPs: 29
  SCC { #4 #29 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      top	w: 0
      #top	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      from	w: 0
      sel	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      mark	w: x1 + 1
      first	w: 0
      #proper	w: 0
      #from	w: x1
      active	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #4 #29
Number of SCCs: 7, DPs: 27
  SCC { #1 #48 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      top	w: 0
      #top	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      from	w: 0
      sel	w: 0
      #s 	w: x1
      #first	w: 0
      nil	w: 0
      mark	w: x1 + 1
      first	w: 0
      #proper	w: 0
      #from	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #48
Number of SCCs: 6, DPs: 25
  SCC { #23 #31 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #cons	s: 1
      s 	s: [1]	p: 1	w: x1
      top	s: []	p: 0	w: 1
      #top	s: [1]	p: 0	w: x1 + 1
      proper	s: 1
      ok	s: 1
      0 	s: []	p: 2	w: 38608
      #sel	s: []	p: 0	w: 1
      from	s: [1]	p: 4	w: x1 + 2243
      sel	s: [1,2]	p: 3	w: x1 + x2 + 2241
      #s 	s: []	p: 0	w: 1
      #first	s: 1
      nil	s: []	p: 2	w: 38607
      mark	s: [1]	p: 1	w: x1
      first	s: [1,2]	p: 3	w: x1 + x2 + 2242
      #proper	s: []	p: 0	w: 1
      #from	s: []	p: 0	w: 1
      active	s: 1
      cons	s: [1]	p: 2	w: max(x1 + 2242, x2)
      #active	s: []	p: 0	w: 1
    USABLE RULES: { 1..31 }
    Removed DPs: #31
Number of SCCs: 6, DPs: 24
  SCC { #23 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      top	w: 0
      #top	w: x1
      proper	w: 3
      ok	w: x1 + 2
      0 	w: 1
      #sel	w: 0
      from	w: x1
      sel	w: x1
      #s 	w: 0
      #first	w: 0
      nil	w: 1
      mark	w: 0
      first	w: x1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 1
      cons	w: x1
      #active	w: 0
    USABLE RULES: { 1..31 }
    Removed DPs: #23
Number of SCCs: 5, DPs: 23
  SCC { #15 #26 }
POLO(Sum)... succeeded.
      #cons	w: x2
      s 	w: x1
      top	w: 0
      #top	w: x1
      proper	w: 2
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: 0
      from	w: x1
      sel	w: x1
      #s 	w: 0
      #first	w: 0
      nil	w: 1
      mark	w: 0
      first	w: x1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 1
      cons	w: x1
      #active	w: 0
    USABLE RULES: { 1..31 }
    Removed DPs: #26
Number of SCCs: 5, DPs: 22
  SCC { #15 }
POLO(Sum)... succeeded.
      #cons	w: x1
      s 	w: x1
      top	w: 0
      #top	w: 0
      proper	w: 4
      ok	w: x1 + 1
      0 	w: 3
      #sel	w: 0
      from	w: x1
      sel	w: x1
      #s 	w: 0
      #first	w: 0
      nil	w: 1
      mark	w: x1 + 1
      first	w: x1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 1
      cons	w: x1
      #active	w: 0
    USABLE RULES: { 1 2 13..15 24 25 27..29 }
    Removed DPs: #15
Number of SCCs: 4, DPs: 21
  SCC { #14 #33 #49 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      top	w: 0
      #top	w: 0
      proper	w: 2
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: x1 + x2
      from	w: x1
      sel	w: x1
      #s 	w: 0
      #first	w: 0
      nil	w: 1
      mark	w: x1 + 1
      first	w: x1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 1
      cons	w: x1
      #active	w: 0
    USABLE RULES: { 1 2 13..15 24 25 27..29 }
    Removed DPs: #14 #33 #49
Number of SCCs: 3, DPs: 18
  SCC { #16 #30 #40 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      top	w: 0
      #top	w: 0
      proper	w: 2
      ok	w: x1 + 1
      0 	w: 1
      #sel	w: 0
      from	w: x1
      sel	w: x1
      #s 	w: 0
      #first	w: x1
      nil	w: 1
      mark	w: x1 + 1
      first	w: x1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 1
      cons	w: x1
      #active	w: 0
    USABLE RULES: { 1 2 13..15 24 25 27..29 }
    Removed DPs: #16 #40
Number of SCCs: 3, DPs: 16
  SCC { #30 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1
      top	w: 0
      #top	w: 0
      proper	w: 32572
      ok	w: x1 + 1
      0 	w: 32571
      #sel	w: 0
      from	w: x1
      sel	w: x1
      #s 	w: 0
      #first	w: x2
      nil	w: 32571
      mark	w: x1 + 1
      first	w: x1
      #proper	w: 0
      #from	w: 0
      active	w: x1 + 3578
      cons	w: x1
      #active	w: 0
    USABLE RULES: { 1 2 13..15 24 25 27..29 }
    Removed DPs: #30
Number of SCCs: 2, DPs: 15
  SCC { #3 #6 #8 #13 #20 #22 #47 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      top	w: 0
      #top	w: 0
      proper	w: x1
      ok	w: x1
      0 	w: 22071
      #sel	w: 0
      from	w: x1 + 1
      sel	w: x1 + x2 + 1
      #s 	w: 0
      #first	w: 0
      nil	w: 1
      mark	w: x1 + 36351
      first	w: x1 + x2 + 1
      #proper	w: 0
      #from	w: 0
      active	w: 36354
      cons	w: x1 + x2 + 1
      #active	w: x1
    USABLE RULES: { 2 13..15 24 25 27..29 }
    Removed DPs: #3 #6 #8 #13 #20 #22 #47
Number of SCCs: 1, DPs: 8
  SCC { #10 #11 #18 #28 #35 #36 #38 #39 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: x1 + 1
      top	w: 0
      #top	w: 0
      proper	w: x1
      ok	w: x1
      0 	w: 1
      #sel	w: 0
      from	w: x1 + 1
      sel	w: x1 + x2 + 3
      #s 	w: 0
      #first	w: 0
      nil	w: 1
      mark	w: x1 + 1
      first	w: x1 + x2 + 2
      #proper	w: x1
      #from	w: 0
      active	w: 4
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { 2 13..15 24 25 27..29 }
    Removed DPs: #10 #11 #18 #28 #35 #36 #38 #39
Number of SCCs: 0, DPs: 0