YES
Input TRS:
      1: app(app(map(),f),nil()) -> nil()
      2: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
      3: app(app(minus(),x),0()) -> x
      4: app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),app(p(),app(s(),x))),app(p(),app(s(),y)))
      5: app(p(),app(s(),x)) -> x
      6: app(app(div(),0()),app(s(),y)) -> 0()
      7: app(app(div(),app(s(),x)),app(s(),y)) -> app(s(),app(app(div(),app(app(minus(),x),app(id(),y))),app(s(),y)))
      8: app(id(),x) -> x
      9: app(id(),x) -> app(s(),app(s(),app(s(),x)))
      10: app(id(),app(p(),x)) -> app(id(),app(s(),app(id(),x)))
Number of strict rules: 10
Direct POLO(bPol) ... failed.
Uncurrying app
      1: app^2_map(f,nil()) -> nil()
      2: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
      3: app^2_minus(x,0()) -> x
      4: app^2_minus(app^1_s(x),app^1_s(y)) -> app^2_minus(app^1_p(app^1_s(x)),app^1_p(app^1_s(y)))
      5: app^1_p(app^1_s(x)) -> x
      6: app^2_div(0(),app^1_s(y)) -> 0()
      7: app^2_div(app^1_s(x),app^1_s(y)) -> app^1_s(app^2_div(app^2_minus(x,app^1_id(y)),app^1_s(y)))
      8: app^1_id(x) -> x
      9: app^1_id(x) -> app^1_s(app^1_s(app^1_s(x)))
      10: app^1_id(app^1_p(x)) -> app^1_id(app^1_s(app^1_id(x)))
      11: app(p(),_1) ->= app^1_p(_1)
      12: app(cons(),_1) ->= app^1_cons(_1)
      13: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
      14: app(div(),_1) ->= app^1_div(_1)
      15: app(app^1_div(_1),_2) ->= app^2_div(_1,_2)
      16: app(id(),_1) ->= app^1_id(_1)
      17: app(s(),_1) ->= app^1_s(_1)
      18: app(minus(),_1) ->= app^1_minus(_1)
      19: app(app^1_minus(_1),_2) ->= app^2_minus(_1,_2)
      20: app(map(),_1) ->= app^1_map(_1)
      21: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
Number of strict rules: 10
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
     #2: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
     #3: #app(p(),_1) ->? #app^1_p(_1)
     #4: #app^2_div(app^1_s(x),app^1_s(y)) -> #app^2_div(app^2_minus(x,app^1_id(y)),app^1_s(y))
     #5: #app^2_div(app^1_s(x),app^1_s(y)) -> #app^2_minus(x,app^1_id(y))
     #6: #app^2_div(app^1_s(x),app^1_s(y)) -> #app^1_id(y)
     #7: #app^1_id(app^1_p(x)) -> #app^1_id(app^1_s(app^1_id(x)))
     #8: #app^1_id(app^1_p(x)) -> #app^1_id(x)
     #9: #app(app^1_minus(_1),_2) ->? #app^2_minus(_1,_2)
     #10: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
     #11: #app(id(),_1) ->? #app^1_id(_1)
     #12: #app(app^1_div(_1),_2) ->? #app^2_div(_1,_2)
     #13: #app^2_minus(app^1_s(x),app^1_s(y)) -> #app^2_minus(app^1_p(app^1_s(x)),app^1_p(app^1_s(y)))
     #14: #app^2_minus(app^1_s(x),app^1_s(y)) -> #app^1_p(app^1_s(x))
     #15: #app^2_minus(app^1_s(x),app^1_s(y)) -> #app^1_p(app^1_s(y))
Number of SCCs: 4, DPs: 6
  SCC { #8 }
POLO(Sum)... succeeded.
      app^1_div	w: 0
      #app^2_minus	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: 0
      #app^1_p	w: 0
      minus	w: 0
      div	w: 0
      app^1_id	w: 0
      app^1_p	w: x1 + 1
      p 	w: 0
      0 	w: 0
      nil	w: 0
      #app	w: 0
      #app^2_div	w: 0
      app^2_minus	w: 0
      map	w: 0
      #app^1_id	w: x1
      app^2_div	w: 0
      cons	w: 0
      id	w: 0
      app^1_minus	w: 0
      app^1_map	w: 0
      app^2_cons	w: 0
      app^1_s	w: 0
      app^2_map	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 3, DPs: 5
  SCC { #4 }
POLO(Sum)... succeeded.
      app^1_div	w: 0
      #app^2_minus	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: 0
      #app^1_p	w: 0
      minus	w: 0
      div	w: 0
      app^1_id	w: 1
      app^1_p	w: x1
      p 	w: 0
      0 	w: 1
      nil	w: 0
      #app	w: 0
      #app^2_div	w: x1
      app^2_minus	w: x1 + 23676
      map	w: 0
      #app^1_id	w: 0
      app^2_div	w: 0
      cons	w: 0
      id	w: 0
      app^1_minus	w: 0
      app^1_map	w: 0
      app^2_cons	w: 0
      app^1_s	w: x1 + 23677
      app^2_map	w: 0
      app	w: 0
    USABLE RULES: { 3..5 }
    Removed DPs: #4
Number of SCCs: 2, DPs: 4
  SCC { #13 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      app^1_div	w: max(x1 - 1, 0)
      #app^2_minus	w: max(x1 + x2 + 2, 0)
      s 	w: 0
      app^1_cons	w: max(x1 - 1, 0)
      #app^2_map	w: max(x2 - 1, 0)
      #app^1_p	w: max(x1 - 1, 0)
      minus	w: 0
      div	w: 0
      app^1_id	w: max(x1 - 1, 0)
      app^1_p	w: max(x1 - 3, 0)
      p 	w: 0
      0 	w: 0
      nil	w: 0
      #app	w: max(x1 - 1, 0)
      #app^2_div	w: max(x1 - 1, 0)
      app^2_minus	w: 0
      map	w: 0
      #app^1_id	w: max(x1 - 1, 0)
      app^2_div	w: max(x1 - 1, 0)
      cons	w: 0
      id	w: 0
      app^1_minus	w: max(x1 - 1, 0)
      app^1_map	w: 0
      app^2_cons	w: max(x2 - 1, 0)
      app^1_s	w: max(x1 + 5, 0)
      app^2_map	w: max(x1 - 1, 0)
      app	w: max(x1 - 1, 0)
    USABLE RULES: { 5 }
    Removed DPs: #13
Number of SCCs: 1, DPs: 3
  SCC { #1 #2 #10 }
POLO(Sum)... succeeded.
      app^1_div	w: 0
      #app^2_minus	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: x1 + 1
      #app^1_p	w: 0
      minus	w: 0
      div	w: 0
      app^1_id	w: 1
      app^1_p	w: 0
      p 	w: 0
      0 	w: 1
      nil	w: 0
      #app	w: x1
      #app^2_div	w: 0
      app^2_minus	w: 23676
      map	w: 0
      #app^1_id	w: 0
      app^2_div	w: 0
      cons	w: 0
      id	w: 0
      app^1_minus	w: 0
      app^1_map	w: x1 + 2
      app^2_cons	w: 1
      app^1_s	w: x1 + 1143
      app^2_map	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #10
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... succeeded.
      app^1_div	w: 0
      #app^2_minus	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: x2 + 1
      #app^1_p	w: 0
      minus	w: 0
      div	w: 0
      app^1_id	w: 1
      app^1_p	w: 0
      p 	w: 0
      0 	w: 1
      nil	w: 0
      #app	w: 0
      #app^2_div	w: 0
      app^2_minus	w: 23676
      map	w: 0
      #app^1_id	w: 0
      app^2_div	w: 0
      cons	w: 0
      id	w: 0
      app^1_minus	w: 0
      app^1_map	w: 2
      app^2_cons	w: x2 + 1
      app^1_s	w: x1 + 282
      app^2_map	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0