YES
Input TRS:
      1: bsort(nil()) -> nil()
      2: bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
      3: bubble(nil()) -> nil()
      4: bubble(.(x,nil())) -> .(x,nil())
      5: bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
      6: last(nil()) -> 0()
      7: last(.(x,nil())) -> x
      8: last(.(x,.(y,z))) -> last(.(y,z))
      9: butlast(nil()) -> nil()
      10: butlast(.(x,nil())) -> nil()
      11: butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Uncurrying butlast last bubble
      1: bsort(nil()) -> nil()
      2: bsort(.(x,y)) -> last^1_.(bubble^1_.(x,y),bsort(butlast(bubble^1_.(x,y))))
      3: bubble^1_nil() -> nil()
      4: bubble^1_.(x,nil()) -> .(x,nil())
      5: bubble^1_.(x,.(y,z)) -> if(<=(x,y),.(y,bubble^1_.(x,z)),.(x,bubble^1_.(y,z)))
      6: last^1_nil() -> 0()
      7: last^1_.(x,nil()) -> x
      8: last^1_.(x,.(y,z)) -> last^1_.(y,z)
      9: butlast^1_nil() -> nil()
      10: butlast^1_.(x,nil()) -> nil()
      11: butlast^1_.(x,.(y,z)) -> .(x,butlast^1_.(y,z))
      12: bubble(nil()) ->= bubble^1_nil()
      13: bubble(.(_1,_2)) ->= bubble^1_.(_1,_2)
      14: last(nil()) ->= last^1_nil()
      15: last(.(_1,_2)) ->= last^1_.(_1,_2)
      16: butlast(nil()) ->= butlast^1_nil()
      17: butlast(.(_1,_2)) ->= butlast^1_.(_1,_2)
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #bsort(.(x,y)) -> #last^1_.(bubble^1_.(x,y),bsort(butlast(bubble^1_.(x,y))))
     #2: #bsort(.(x,y)) -> #bubble^1_.(x,y)
     #3: #bsort(.(x,y)) -> #bsort(butlast(bubble^1_.(x,y)))
     #4: #bsort(.(x,y)) -> #butlast(bubble^1_.(x,y))
     #5: #bsort(.(x,y)) -> #bubble^1_.(x,y)
     #6: #bubble(.(_1,_2)) ->? #bubble^1_.(_1,_2)
     #7: #butlast^1_.(x,.(y,z)) -> #butlast^1_.(y,z)
     #8: #bubble(nil()) ->? #bubble^1_nil()
     #9: #last(nil()) ->? #last^1_nil()
     #10: #bubble^1_.(x,.(y,z)) -> #bubble^1_.(x,z)
     #11: #bubble^1_.(x,.(y,z)) -> #bubble^1_.(y,z)
     #12: #butlast(.(_1,_2)) ->? #butlast^1_.(_1,_2)
     #13: #butlast(nil()) ->? #butlast^1_nil()
     #14: #last^1_.(x,.(y,z)) -> #last^1_.(y,z)
     #15: #last(.(_1,_2)) ->? #last^1_.(_1,_2)
Number of SCCs: 4, DPs: 5
  SCC { #14 }
POLO(Sum)... succeeded.
      #butlast^1_nil	w: 0
      #bubble	w: 0
      butlast^1_nil	w: 0
      #butlast	w: 0
      bubble^1_nil	w: 0
      <=	w: 0
      #bsort	w: 0
      #last^1_.	w: x2
      butlast	w: 0
      butlast^1_.	w: 0
      bubble^1_.	w: 0
      #bubble^1_nil	w: 0
      last^1_nil	w: 0
      #last	w: 0
      #last^1_nil	w: 0
      if	w: 0
      0 	w: 0
      last	w: 0
      nil	w: 0
      . 	w: x2 + 1
      bubble	w: 0
      bsort	w: 0
      #butlast^1_.	w: 0
      last^1_.	w: 0
      #bubble^1_.	w: 0
    USABLE RULES: { }
    Removed DPs: #14
Number of SCCs: 3, DPs: 4
  SCC { #7 }
POLO(Sum)... succeeded.
      #butlast^1_nil	w: 0
      #bubble	w: 0
      butlast^1_nil	w: 0
      #butlast	w: 0
      bubble^1_nil	w: 0
      <=	w: 0
      #bsort	w: 0
      #last^1_.	w: 0
      butlast	w: 0
      butlast^1_.	w: 0
      bubble^1_.	w: 0
      #bubble^1_nil	w: 0
      last^1_nil	w: 0
      #last	w: 0
      #last^1_nil	w: 0
      if	w: 0
      0 	w: 0
      last	w: 0
      nil	w: 0
      . 	w: x2 + 1
      bubble	w: 0
      bsort	w: 0
      #butlast^1_.	w: x2
      last^1_.	w: 0
      #bubble^1_.	w: 0
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 2, DPs: 3
  SCC { #3 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      #butlast^1_nil	w: 0
      #bubble	w: max(x1 - 1, 0)
      butlast^1_nil	w: 0
      #butlast	w: max(x1 - 1, 0)
      bubble^1_nil	w: 0
      <=	w: max(x1 - 1, 0)
      #bsort	w: max(x1 - 3, 0)
      #last^1_.	w: 0
      butlast	w: max(x1 - 3, 0)
      butlast^1_.	w: max(x1 + x2 + 1, 0)
      bubble^1_.	w: max(x1 + 5, 0)
      #bubble^1_nil	w: 0
      last^1_nil	w: 0
      #last	w: 0
      #last^1_nil	w: 0
      if	w: 0
      0 	w: 0
      last	w: 0
      nil	w: 1
      . 	w: max(x1 + x2 + 4, 0)
      bubble	w: max(x1 - 1, 0)
      bsort	w: max(x1 - 1, 0)
      #butlast^1_.	w: max(x1 - 1, 0)
      last^1_.	w: 0
      #bubble^1_.	w: max(x1 - 1, 0)
    USABLE RULES: { 4 5 10 11 17 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2
  SCC { #10 #11 }
POLO(Sum)... succeeded.
      #butlast^1_nil	w: 0
      #bubble	w: 0
      butlast^1_nil	w: 0
      #butlast	w: 0
      bubble^1_nil	w: 0
      <=	w: 1
      #bsort	w: 0
      #last^1_.	w: 0
      butlast	w: 0
      butlast^1_.	w: x1 + x2 + 1
      bubble^1_.	w: x1 + x2 + 11798
      #bubble^1_nil	w: 0
      last^1_nil	w: 0
      #last	w: 0
      #last^1_nil	w: 0
      if	w: x2
      0 	w: 0
      last	w: 0
      nil	w: 1
      . 	w: x1 + x2 + 1
      bubble	w: 0
      bsort	w: 0
      #butlast^1_.	w: 0
      last^1_.	w: 0
      #bubble^1_.	w: x2
    USABLE RULES: { 4 5 }
    Removed DPs: #10 #11
Number of SCCs: 0, DPs: 0