YES
Input TRS:
      1: a(h(),h(),h(),x) -> s(x)
      2: a(l,x,s(y),h()) -> a(l,x,y,s(h()))
      3: a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
      4: a(l,s(x),h(),z) -> a(l,x,z,z)
      5: a(s(l),h(),h(),z) -> a(l,z,h(),z)
      6: +(x,h()) -> x
      7: +(h(),x) -> x
      8: +(s(x),s(y)) -> s(s(+(x,y)))
      9: +(+(x,y),z) -> +(x,+(y,z))
      10: s(h()) -> 1()
      11: app(nil(),k) -> k
      12: app(l,nil()) -> l
      13: app(cons(x,l),k) -> cons(x,app(l,k))
      14: sum(cons(x,nil())) -> cons(x,nil())
      15: sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l))
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Uncurrying sum
      1: a(h(),h(),h(),x) -> s(x)
      2: a(l,x,s(y),h()) -> a(l,x,y,s(h()))
      3: a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
      4: a(l,s(x),h(),z) -> a(l,x,z,z)
      5: a(s(l),h(),h(),z) -> a(l,z,h(),z)
      6: +(x,h()) -> x
      7: +(h(),x) -> x
      8: +(s(x),s(y)) -> s(s(+(x,y)))
      9: +(+(x,y),z) -> +(x,+(y,z))
      10: s(h()) -> 1()
      11: app(nil(),k) -> k
      12: app(l,nil()) -> l
      13: app(cons(x,l),k) -> cons(x,app(l,k))
      14: sum^1_cons(x,nil()) -> cons(x,nil())
      15: sum^1_cons(x,cons(y,l)) -> sum^1_cons(a(x,y,h(),h()),l)
      16: sum(cons(_1,_2)) ->= sum^1_cons(_1,_2)
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #a(l,x,s(y),h()) -> #a(l,x,y,s(h()))
     #2: #a(l,x,s(y),h()) -> #s(h())
     #3: #app(cons(x,l),k) -> #app(l,k)
     #4: #+(+(x,y),z) -> #+(x,+(y,z))
     #5: #+(+(x,y),z) -> #+(y,z)
     #6: #a(s(l),h(),h(),z) -> #a(l,z,h(),z)
     #7: #sum(cons(_1,_2)) ->? #sum^1_cons(_1,_2)
     #8: #a(l,x,s(y),s(z)) -> #a(l,x,y,a(l,x,s(y),z))
     #9: #a(l,x,s(y),s(z)) -> #a(l,x,s(y),z)
     #10: #a(h(),h(),h(),x) -> #s(x)
     #11: #+(s(x),s(y)) -> #s(s(+(x,y)))
     #12: #+(s(x),s(y)) -> #s(+(x,y))
     #13: #+(s(x),s(y)) -> #+(x,y)
     #14: #sum^1_cons(x,cons(y,l)) -> #sum^1_cons(a(x,y,h(),h()),l)
     #15: #sum^1_cons(x,cons(y,l)) -> #a(x,y,h(),h())
     #16: #a(l,s(x),h(),z) -> #a(l,x,z,z)
Number of SCCs: 4, DPs: 10
  SCC { #3 }
POLO(Sum)... succeeded.
      a 	w: 0
      h 	w: 0
      1 	w: 0
      s 	w: 0
      sum^1_cons	w: 0
      sum	w: 0
      #s 	w: 0
      nil	w: 0
      #sum^1_cons	w: 0
      #app	w: x1
      cons	w: x2 + 1
      #a 	w: 0
      + 	w: 0
      #sum	w: 0
      #+ 	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 3, DPs: 9
  SCC { #14 }
POLO(Sum)... succeeded.
      a 	w: x1 + x4 + 21240
      h 	w: 1
      1 	w: 21241
      s 	w: x1 + 21239
      sum^1_cons	w: 0
      sum	w: 0
      #s 	w: 0
      nil	w: 0
      #sum^1_cons	w: x2
      #app	w: 0
      cons	w: x1 + x2 + 1
      #a 	w: 0
      + 	w: 0
      #sum	w: 0
      #+ 	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #14
Number of SCCs: 2, DPs: 8
  SCC { #4 #5 #13 }
POLO(Sum)... succeeded.
      a 	w: x1 + x4 + 21240
      h 	w: 1
      1 	w: 3
      s 	w: x1 + 1
      sum^1_cons	w: 0
      sum	w: 0
      #s 	w: 0
      nil	w: 0
      #sum^1_cons	w: 0
      #app	w: 0
      cons	w: 1
      #a 	w: 0
      + 	w: x1 + x2 + 1
      #sum	w: 0
      #+ 	w: x1
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #4 #5 #13
Number of SCCs: 1, DPs: 5
  SCC { #1 #6 #8 #9 #16 }
POLO(Sum)... succeeded.
      a 	w: x1 + x4 + 21240
      h 	w: 1
      1 	w: 3
      s 	w: x1 + 1
      sum^1_cons	w: 0
      sum	w: 0
      #s 	w: 0
      nil	w: 0
      #sum^1_cons	w: 0
      #app	w: 0
      cons	w: 1
      #a 	w: x1
      + 	w: x1 + x2 + 1
      #sum	w: 0
      #+ 	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 1, DPs: 4
  SCC { #1 #8 #9 #16 }
POLO(Sum)... succeeded.
      a 	w: x1 + x4 + 21240
      h 	w: 1
      1 	w: 3
      s 	w: x1 + 1
      sum^1_cons	w: 0
      sum	w: 0
      #s 	w: 0
      nil	w: 0
      #sum^1_cons	w: 0
      #app	w: 0
      cons	w: 1
      #a 	w: x2
      + 	w: x1 + x2 + 40651
      #sum	w: 0
      #+ 	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #16
Number of SCCs: 1, DPs: 3
  SCC { #1 #8 #9 }
POLO(Sum)... succeeded.
      a 	w: x1 + x4 + 21240
      h 	w: 1
      1 	w: 2
      s 	w: x1 + 1
      sum^1_cons	w: 0
      sum	w: 0
      #s 	w: 0
      nil	w: 0
      #sum^1_cons	w: 0
      #app	w: 0
      cons	w: 1
      #a 	w: x3
      + 	w: x1 + x2 + 36466
      #sum	w: 0
      #+ 	w: 0
      app	w: 0
    USABLE RULES: { 10 }
    Removed DPs: #1 #8
Number of SCCs: 1, DPs: 1
  SCC { #9 }
POLO(Sum)... POLO(max)... succeeded.
      a 	w: 0
      h 	w: 1
      1 	w: 3
      s 	w: x1 + 1
      sum^1_cons	w: 0
      sum	w: 0
      #s 	w: 0
      nil	w: 0
      #sum^1_cons	w: 0
      #app	w: 0
      cons	w: 0
      #a 	w: max(x4 + 7720)
      + 	w: 0
      #sum	w: 0
      #+ 	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 0, DPs: 0