MAYBE
Input TRS:
      1: app(app(app(fold(),f),x),nil()) -> x
      2: app(app(app(fold(),f),x),app(app(cons(),y),z)) -> app(app(f,y),app(app(app(fold(),f),x),z))
      3: app(app(plus(),0()),y) -> y
      4: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
      5: app(app(times(),0()),y) -> 0()
      6: app(app(times(),app(s(),x)),y) -> app(app(plus(),app(app(times(),x),y)),y)
      7: sum() -> app(app(fold(),add()),0())
      8: prod() -> app(app(fold(),mul()),app(s(),0()))
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying app
      1: app^3_fold(f,x,nil()) -> x
      2: app^3_fold(f,x,app^2_cons(y,z)) -> app(app(f,y),app^3_fold(f,x,z))
      3: app^2_plus(0(),y) -> y
      4: app^2_plus(app^1_s(x),y) -> app^1_s(app^2_plus(x,y))
      5: app^2_times(0(),y) -> 0()
      6: app^2_times(app^1_s(x),y) -> app^2_plus(app^2_times(x,y),y)
      7: sum() -> app^2_fold(add(),0())
      8: prod() -> app^2_fold(mul(),app^1_s(0()))
      9: app(plus(),_1) ->= app^1_plus(_1)
      10: app(app^1_plus(_1),_2) ->= app^2_plus(_1,_2)
      11: app(cons(),_1) ->= app^1_cons(_1)
      12: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
      13: app(times(),_1) ->= app^1_times(_1)
      14: app(app^1_times(_1),_2) ->= app^2_times(_1,_2)
      15: app(s(),_1) ->= app^1_s(_1)
      16: app(fold(),_1) ->= app^1_fold(_1)
      17: app(app^1_fold(_1),_2) ->= app^2_fold(_1,_2)
      18: app(app^2_fold(_1,_2),_3) ->= app^3_fold(_1,_2,_3)
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #app^3_fold(f,x,app^2_cons(y,z)) -> #app(app(f,y),app^3_fold(f,x,z))
     #2: #app^3_fold(f,x,app^2_cons(y,z)) -> #app(f,y)
     #3: #app^3_fold(f,x,app^2_cons(y,z)) -> #app^3_fold(f,x,z)
     #4: #app^2_times(app^1_s(x),y) -> #app^2_plus(app^2_times(x,y),y)
     #5: #app^2_times(app^1_s(x),y) -> #app^2_times(x,y)
     #6: #app(app^1_times(_1),_2) ->? #app^2_times(_1,_2)
     #7: #app(app^1_plus(_1),_2) ->? #app^2_plus(_1,_2)
     #8: #app^2_plus(app^1_s(x),y) -> #app^2_plus(x,y)
     #9: #app(app^2_fold(_1,_2),_3) ->? #app^3_fold(_1,_2,_3)
Number of SCCs: 3, DPs: 6
  SCC { #5 }
POLO(Sum)... succeeded.
      mul	w: 0
      prod	w: 0
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      app^2_fold	w: 0
      #prod	w: 0
      app^1_fold	w: 0
      #app^2_plus	w: 0
      sum	w: 0
      app^3_fold	w: 0
      app^2_plus	w: 0
      0 	w: 0
      times	w: 0
      nil	w: 0
      #app	w: 0
      #app^3_fold	w: 0
      fold	w: 0
      plus	w: 0
      cons	w: 0
      add	w: 0
      app^1_times	w: 0
      #app^2_times	w: x1
      #sum	w: 0
      app^2_cons	w: 0
      app^1_s	w: x1 + 1
      app	w: 0
      app^2_times	w: 0
    USABLE RULES: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 5
  SCC { #8 }
POLO(Sum)... succeeded.
      mul	w: 0
      prod	w: 0
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      app^2_fold	w: 0
      #prod	w: 0
      app^1_fold	w: 0
      #app^2_plus	w: x1
      sum	w: 0
      app^3_fold	w: 0
      app^2_plus	w: 0
      0 	w: 0
      times	w: 0
      nil	w: 0
      #app	w: 0
      #app^3_fold	w: 0
      fold	w: 0
      plus	w: 0
      cons	w: 0
      add	w: 0
      app^1_times	w: 0
      #app^2_times	w: 0
      #sum	w: 0
      app^2_cons	w: 0
      app^1_s	w: x1 + 1
      app	w: 0
      app^2_times	w: 0
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 4
  SCC { #1..3 #9 }
POLO(Sum)... POLO(max)... succeeded.
      mul	w: 0
      prod	w: 0
      s 	w: 0
      app^1_cons	w: x1
      app^1_plus	w: 1
      app^2_fold	w: max(x1 + 20821, x2)
      #prod	w: 0
      app^1_fold	w: x1
      #app^2_plus	w: 0
      sum	w: 0
      app^3_fold	w: max(x1 + 41642, x2 + 20538, x3)
      app^2_plus	w: max(x2)
      0 	w: 0
      times	w: 0
      nil	w: 0
      #app	w: max(x1 + 37885, x2 + 17064)
      #app^3_fold	w: max(x1 + 58706, x2 + 37884, x3 + 17064)
      fold	w: 0
      plus	w: 0
      cons	w: 0
      add	w: 0
      app^1_times	w: 1
      #app^2_times	w: 0
      #sum	w: 0
      app^2_cons	w: max(x1 + 20821, x2)
      app^1_s	w: 0
      app	w: max(x1 + 20821, x2)
      app^2_times	w: max(x2)
    USABLE RULES: { 1..6 9..18 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 3
  SCC { #1 #3 #9 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.