YES
Input TRS:
      1: a__f(X) -> cons(mark(X),f(g(X)))
      2: a__g(0()) -> s(0())
      3: a__g(s(X)) -> s(s(a__g(mark(X))))
      4: a__sel(0(),cons(X,Y)) -> mark(X)
      5: a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
      6: mark(f(X)) -> a__f(mark(X))
      7: mark(g(X)) -> a__g(mark(X))
      8: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
      9: mark(cons(X1,X2)) -> cons(mark(X1),X2)
      10: mark(0()) -> 0()
      11: mark(s(X)) -> s(mark(X))
      12: a__f(X) -> f(X)
      13: a__g(X) -> g(X)
      14: a__sel(X1,X2) -> sel(X1,X2)
Number of strict rules: 14
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #mark(f(X)) -> #a__f(mark(X))
     #2: #mark(f(X)) -> #mark(X)
     #3: #mark(cons(X1,X2)) -> #mark(X1)
     #4: #mark(s(X)) -> #mark(X)
     #5: #mark(g(X)) -> #a__g(mark(X))
     #6: #mark(g(X)) -> #mark(X)
     #7: #a__sel(s(X),cons(Y,Z)) -> #a__sel(mark(X),mark(Z))
     #8: #a__sel(s(X),cons(Y,Z)) -> #mark(X)
     #9: #a__sel(s(X),cons(Y,Z)) -> #mark(Z)
     #10: #a__g(s(X)) -> #a__g(mark(X))
     #11: #a__g(s(X)) -> #mark(X)
     #12: #a__f(X) -> #mark(X)
     #13: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
     #14: #mark(sel(X1,X2)) -> #mark(X1)
     #15: #mark(sel(X1,X2)) -> #mark(X2)
     #16: #a__sel(0(),cons(X,Y)) -> #mark(X)
Number of SCCs: 1, DPs: 16
  SCC { #1..16 }
POLO(Sum)... POLO(max)... succeeded.
      a__g	w: x1
      s 	w: x1
      #a__g	w: x1
      a__f	w: x1 + 2242
      f 	w: x1 + 2242
      #mark	w: x1
      0 	w: 1
      sel	w: max(x1 + 28884, x2 + 1)
      #a__sel	w: max(x1 + 28884, x2 + 1)
      mark	w: x1
      a__sel	w: max(x1 + 28884, x2 + 1)
      cons	w: max(x1 + 1, x2)
      #a__f	w: x1 + 2241
      g 	w: x1
    USABLE RULES: { 1..14 }
    Removed DPs: #1..3 #8 #9 #12 #14..16
Number of SCCs: 2, DPs: 6
  SCC { #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      a__g	s: [1]	p: 3	w: x1
      s 	s: [1]	p: 2	w: x1
      #a__g	s: []	p: 0	w: 1
      a__f	s: []	p: 2	w: x1 + 17679
      f 	s: []	p: 2	w: x1 + 17679
      #mark	s: []	p: 0	w: 1
      0 	s: []	p: 0	w: 1
      sel	s: []	p: 0	w: x2 + 43964
      #a__sel	s: 1
      mark	s: 1
      a__sel	s: []	p: 0	w: x2 + 43964
      cons	s: []	p: 0	w: max(x1 + 17678, x2)
      #a__f	s: []	p: 0	w: 1
      g 	s: [1]	p: 3	w: x1
    USABLE RULES: { 1..14 }
    Removed DPs: #7
Number of SCCs: 1, DPs: 5
  SCC { #4..6 #10 #11 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      a__g	s: [1]	p: 3	w: x1
      s 	s: [1]	p: 2	w: x1
      #a__g	s: [1]	p: 2	w: x1
      a__f	s: []	p: 2	w: x1 + 18459
      f 	s: []	p: 2	w: x1 + 18459
      #mark	s: [1]	p: 1	w: x1
      0 	s: []	p: 0	w: 1
      sel	s: []	p: 0	w: x2 + 44744
      #a__sel	s: 1
      mark	s: 1
      a__sel	s: []	p: 0	w: x2 + 44744
      cons	s: []	p: 0	w: max(x1 + 18458, x2)
      #a__f	s: []	p: 0	w: 1
      g 	s: [1]	p: 3	w: x1
    USABLE RULES: { 1..14 }
    Removed DPs: #4..6 #10 #11
Number of SCCs: 0, DPs: 0