YES
Input TRS:
      1: app(app(map_1(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map_1(),f),t))
      2: app(app(app(map_2(),f),c),app(app(cons(),h),t)) -> app(app(cons(),app(app(f,h),c)),app(app(app(map_2(),f),c),t))
      3: app(app(app(app(map_3(),f),g()),c),app(app(cons(),h),t)) -> app(app(cons(),app(app(app(f,g()),h),c)),app(app(app(app(map_3(),f),g()),c),t))
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying app
      1: app^2_map_1(f,app^2_cons(h,t)) -> app^2_cons(app(f,h),app^2_map_1(f,t))
      2: app^3_map_2(f,c,app^2_cons(h,t)) -> app^2_cons(app(app(f,h),c),app^3_map_2(f,c,t))
      3: app^4_map_3(f,g(),c,app^2_cons(h,t)) -> app^2_cons(app(app(app(f,g()),h),c),app^4_map_3(f,g(),c,t))
      4: app(map_2(),_1) ->= app^1_map_2(_1)
      5: app(app^1_map_2(_1),_2) ->= app^2_map_2(_1,_2)
      6: app(app^2_map_2(_1,_2),_3) ->= app^3_map_2(_1,_2,_3)
      7: app(cons(),_1) ->= app^1_cons(_1)
      8: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
      9: app(map_3(),_1) ->= app^1_map_3(_1)
      10: app(app^1_map_3(_1),_2) ->= app^2_map_3(_1,_2)
      11: app(app^2_map_3(_1,_2),_3) ->= app^3_map_3(_1,_2,_3)
      12: app(app^3_map_3(_1,_2,_3),_4) ->= app^4_map_3(_1,_2,_3,_4)
      13: app(map_1(),_1) ->= app^1_map_1(_1)
      14: app(app^1_map_1(_1),_2) ->= app^2_map_1(_1,_2)
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #app^3_map_2(f,c,app^2_cons(h,t)) -> #app(app(f,h),c)
     #2: #app^3_map_2(f,c,app^2_cons(h,t)) -> #app(f,h)
     #3: #app^3_map_2(f,c,app^2_cons(h,t)) -> #app^3_map_2(f,c,t)
     #4: #app(app^2_map_2(_1,_2),_3) ->? #app^3_map_2(_1,_2,_3)
     #5: #app(app^3_map_3(_1,_2,_3),_4) ->? #app^4_map_3(_1,_2,_3,_4)
     #6: #app(app^1_map_1(_1),_2) ->? #app^2_map_1(_1,_2)
     #7: #app^4_map_3(f,g(),c,app^2_cons(h,t)) -> #app(app(app(f,g()),h),c)
     #8: #app^4_map_3(f,g(),c,app^2_cons(h,t)) -> #app(app(f,g()),h)
     #9: #app^4_map_3(f,g(),c,app^2_cons(h,t)) -> #app(f,g())
     #10: #app^4_map_3(f,g(),c,app^2_cons(h,t)) -> #app^4_map_3(f,g(),c,t)
     #11: #app^2_map_1(f,app^2_cons(h,t)) -> #app(f,h)
     #12: #app^2_map_1(f,app^2_cons(h,t)) -> #app^2_map_1(f,t)
Number of SCCs: 1, DPs: 12
  SCC { #1..12 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      map_2	w: 26584
      app^1_map_1	w: max(x1 + 8862, 0)
      app^1_cons	w: max(x1 + 44304, 0)
      app^1_map_2	w: max(x1 + 17723, 0)
      #app^3_map_2	w: max(x1 + x2 + x3 - 8862, 0)
      app^1_map_3	w: max(x1 + 29021, 0)
      map_1	w: 17723
      app^3_map_2	w: max(x1 + x2 + x3 + 1, 0)
      app^3_map_3	w: max(x1 + x2 + x3 + 8862, 0)
      app^2_map_2	w: max(x1 + x2 + 8862, 0)
      #app	w: max(x1 + x2 - 2, 0)
      app^2_map_1	w: max(x1 + x2 + 1, 0)
      map_3	w: 37882
      #app^2_map_1	w: max(x1 + x2 - 3, 0)
      cons	w: 53165
      app^4_map_3	w: max(x1 + x3 + x4 + 1, 0)
      #app^4_map_3	w: max(x1 + x3 + x4 + 1, 0)
      app^2_map_3	w: max(x1 + x2 + 17723, 0)
      g 	w: 1
      app^2_cons	w: max(x1 + 35443, x2 + 8859, 0)
      app	w: max(x1 + x2 - 8861, 0)
    USABLE RULES: { 1..14 }
    Removed DPs: #1..12
Number of SCCs: 0, DPs: 0