MAYBE
Input TRS:
      1: app(app(le(),0()),y) -> true()
      2: app(app(le(),app(s(),x)),0()) -> false()
      3: app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
      4: app(app(eq(),0()),0()) -> true()
      5: app(app(eq(),0()),app(s(),y)) -> false()
      6: app(app(eq(),app(s(),x)),0()) -> false()
      7: app(app(eq(),app(s(),x)),app(s(),y)) -> app(app(eq(),x),y)
      8: app(app(app(if(),true()),x),y) -> x
      9: app(app(app(if(),false()),x),y) -> y
      10: app(minsort(),nil()) -> nil()
      11: app(minsort(),app(app(cons(),x),y)) -> app(app(cons(),app(app(min(),x),y)),app(minsort(),app(app(del(),app(app(min(),x),y)),app(app(cons(),x),y))))
      12: app(app(min(),x),nil()) -> x
      13: app(app(min(),x),app(app(cons(),y),z)) -> app(app(app(if(),app(app(le(),x),y)),app(app(min(),x),z)),app(app(min(),y),z))
      14: app(app(del(),x),nil()) -> nil()
      15: app(app(del(),x),app(app(cons(),y),z)) -> app(app(app(if(),app(app(eq(),x),y)),z),app(app(cons(),y),app(app(del(),x),z)))
      16: app(app(map(),f),nil()) -> nil()
      17: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
      18: app(app(filter(),f),nil()) -> nil()
      19: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
      20: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
      21: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 21
Direct POLO(bPol) ... failed.
Uncurrying app
      1: app^2_le(0(),y) -> true()
      2: app^2_le(app^1_s(x),0()) -> false()
      3: app^2_le(app^1_s(x),app^1_s(y)) -> app^2_le(x,y)
      4: app^2_eq(0(),0()) -> true()
      5: app^2_eq(0(),app^1_s(y)) -> false()
      6: app^2_eq(app^1_s(x),0()) -> false()
      7: app^2_eq(app^1_s(x),app^1_s(y)) -> app^2_eq(x,y)
      8: app^3_if(true(),x,y) -> x
      9: app^3_if(false(),x,y) -> y
      10: app^1_minsort(nil()) -> nil()
      11: app^1_minsort(app^2_cons(x,y)) -> app^2_cons(app^2_min(x,y),app^1_minsort(app^2_del(app^2_min(x,y),app^2_cons(x,y))))
      12: app^2_min(x,nil()) -> x
      13: app^2_min(x,app^2_cons(y,z)) -> app^3_if(app^2_le(x,y),app^2_min(x,z),app^2_min(y,z))
      14: app^2_del(x,nil()) -> nil()
      15: app^2_del(x,app^2_cons(y,z)) -> app^3_if(app^2_eq(x,y),z,app^2_cons(y,app^2_del(x,z)))
      16: app^2_map(f,nil()) -> nil()
      17: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
      18: app^2_filter(f,nil()) -> nil()
      19: app^2_filter(f,app^2_cons(x,xs)) -> app^4_filter2(app(f,x),f,x,xs)
      20: app^4_filter2(true(),f,x,xs) -> app^2_cons(x,app^2_filter(f,xs))
      21: app^4_filter2(false(),f,x,xs) -> app^2_filter(f,xs)
      22: app(eq(),_1) ->= app^1_eq(_1)
      23: app(app^1_eq(_1),_2) ->= app^2_eq(_1,_2)
      24: app(min(),_1) ->= app^1_min(_1)
      25: app(app^1_min(_1),_2) ->= app^2_min(_1,_2)
      26: app(le(),_1) ->= app^1_le(_1)
      27: app(app^1_le(_1),_2) ->= app^2_le(_1,_2)
      28: app(if(),_1) ->= app^1_if(_1)
      29: app(app^1_if(_1),_2) ->= app^2_if(_1,_2)
      30: app(app^2_if(_1,_2),_3) ->= app^3_if(_1,_2,_3)
      31: app(cons(),_1) ->= app^1_cons(_1)
      32: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
      33: app(del(),_1) ->= app^1_del(_1)
      34: app(app^1_del(_1),_2) ->= app^2_del(_1,_2)
      35: app(s(),_1) ->= app^1_s(_1)
      36: app(filter(),_1) ->= app^1_filter(_1)
      37: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2)
      38: app(minsort(),_1) ->= app^1_minsort(_1)
      39: app(map(),_1) ->= app^1_map(_1)
      40: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
      41: app(filter2(),_1) ->= app^1_filter2(_1)
      42: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2)
      43: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3)
      44: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4)
Number of strict rules: 21
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2)
     #2: #app(minsort(),_1) ->? #app^1_minsort(_1)
     #3: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
     #4: #app^2_min(x,app^2_cons(y,z)) -> #app^3_if(app^2_le(x,y),app^2_min(x,z),app^2_min(y,z))
     #5: #app^2_min(x,app^2_cons(y,z)) -> #app^2_le(x,y)
     #6: #app^2_min(x,app^2_cons(y,z)) -> #app^2_min(x,z)
     #7: #app^2_min(x,app^2_cons(y,z)) -> #app^2_min(y,z)
     #8: #app^1_minsort(app^2_cons(x,y)) -> #app^2_min(x,y)
     #9: #app^1_minsort(app^2_cons(x,y)) -> #app^1_minsort(app^2_del(app^2_min(x,y),app^2_cons(x,y)))
     #10: #app^1_minsort(app^2_cons(x,y)) -> #app^2_del(app^2_min(x,y),app^2_cons(x,y))
     #11: #app^1_minsort(app^2_cons(x,y)) -> #app^2_min(x,y)
     #12: #app(app^1_eq(_1),_2) ->? #app^2_eq(_1,_2)
     #13: #app(app^2_if(_1,_2),_3) ->? #app^3_if(_1,_2,_3)
     #14: #app(app^1_min(_1),_2) ->? #app^2_min(_1,_2)
     #15: #app^4_filter2(true(),f,x,xs) -> #app^2_filter(f,xs)
     #16: #app^2_eq(app^1_s(x),app^1_s(y)) -> #app^2_eq(x,y)
     #17: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4)
     #18: #app(app^1_del(_1),_2) ->? #app^2_del(_1,_2)
     #19: #app(app^1_le(_1),_2) ->? #app^2_le(_1,_2)
     #20: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
     #21: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
     #22: #app^2_filter(f,app^2_cons(x,xs)) -> #app^4_filter2(app(f,x),f,x,xs)
     #23: #app^2_filter(f,app^2_cons(x,xs)) -> #app(f,x)
     #24: #app^4_filter2(false(),f,x,xs) -> #app^2_filter(f,xs)
     #25: #app^2_le(app^1_s(x),app^1_s(y)) -> #app^2_le(x,y)
     #26: #app^2_del(x,app^2_cons(y,z)) -> #app^3_if(app^2_eq(x,y),z,app^2_cons(y,app^2_del(x,z)))
     #27: #app^2_del(x,app^2_cons(y,z)) -> #app^2_eq(x,y)
     #28: #app^2_del(x,app^2_cons(y,z)) -> #app^2_del(x,z)
Number of SCCs: 6, DPs: 15
  SCC { #28 }
POLO(Sum)... succeeded.
      #app^3_if	w: 0
      le	w: 0
      app^1_minsort	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^1_min	w: 0
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      eq	w: 0
      false	w: 0
      app^2_min	w: 0
      #app^2_le	w: 0
      app^1_del	w: 0
      app^1_le	w: 0
      app^1_filter2	w: 0
      true	w: 0
      filter2	w: 0
      #app^2_del	w: x2
      0 	w: 0
      if	w: 0
      del	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      app^2_le	w: 0
      #app	w: 0
      app^2_del	w: 0
      #app^2_min	w: 0
      map	w: 0
      app^1_filter	w: 0
      #app^2_eq	w: 0
      min	w: 0
      #app^1_minsort	w: 0
      cons	w: 0
      app^2_if	w: 0
      app^3_if	w: 0
      app^2_eq	w: 0
      filter	w: 0
      minsort	w: 0
      app^3_filter2	w: 0
      app^2_filter	w: 0
      app^1_map	w: 0
      app^2_cons	w: x2 + 1
      app^1_eq	w: 0
      app^1_if	w: 0
      app^1_s	w: 0
      app^2_map	w: 0
      #app^2_filter	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #28
Number of SCCs: 5, DPs: 14
  SCC { #16 }
POLO(Sum)... succeeded.
      #app^3_if	w: 0
      le	w: 0
      app^1_minsort	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^1_min	w: 0
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      eq	w: 0
      false	w: 0
      app^2_min	w: 0
      #app^2_le	w: 0
      app^1_del	w: 0
      app^1_le	w: 0
      app^1_filter2	w: 0
      true	w: 0
      filter2	w: 0
      #app^2_del	w: 0
      0 	w: 0
      if	w: 0
      del	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      app^2_le	w: 0
      #app	w: 0
      app^2_del	w: 0
      #app^2_min	w: 0
      map	w: 0
      app^1_filter	w: 0
      #app^2_eq	w: x2
      min	w: 0
      #app^1_minsort	w: 0
      cons	w: 0
      app^2_if	w: 0
      app^3_if	w: 0
      app^2_eq	w: 0
      filter	w: 0
      minsort	w: 0
      app^3_filter2	w: 0
      app^2_filter	w: 0
      app^1_map	w: 0
      app^2_cons	w: 1
      app^1_eq	w: 0
      app^1_if	w: 0
      app^1_s	w: x1 + 1
      app^2_map	w: 0
      #app^2_filter	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #16
Number of SCCs: 4, DPs: 13
  SCC { #25 }
POLO(Sum)... succeeded.
      #app^3_if	w: 0
      le	w: 0
      app^1_minsort	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^1_min	w: 0
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      eq	w: 0
      false	w: 0
      app^2_min	w: 0
      #app^2_le	w: x2
      app^1_del	w: 0
      app^1_le	w: 0
      app^1_filter2	w: 0
      true	w: 0
      filter2	w: 0
      #app^2_del	w: 0
      0 	w: 0
      if	w: 0
      del	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      app^2_le	w: 0
      #app	w: 0
      app^2_del	w: 0
      #app^2_min	w: 0
      map	w: 0
      app^1_filter	w: 0
      #app^2_eq	w: 0
      min	w: 0
      #app^1_minsort	w: 0
      cons	w: 0
      app^2_if	w: 0
      app^3_if	w: 0
      app^2_eq	w: 0
      filter	w: 0
      minsort	w: 0
      app^3_filter2	w: 0
      app^2_filter	w: 0
      app^1_map	w: 0
      app^2_cons	w: 1
      app^1_eq	w: 0
      app^1_if	w: 0
      app^1_s	w: x1 + 1
      app^2_map	w: 0
      #app^2_filter	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #25
Number of SCCs: 3, DPs: 12
  SCC { #9 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.