MAYBE

Problem:
 app(app(map_1(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map_1(),f),t))
 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))
 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))

Proof:
 DP Processor:
  DPs:
   app#(app(map_1(),f),app(app(cons(),h),t)) -> app#(app(map_1(),f),t)
   app#(app(map_1(),f),app(app(cons(),h),t)) -> app#(f,h)
   app#(app(map_1(),f),app(app(cons(),h),t)) -> app#(cons(),app(f,h))
   app#(app(map_1(),f),app(app(cons(),h),t)) -> app#(app(cons(),app(f,h)),app(app(map_1(),f),t))
   app#(app(app(map_2(),f),c),app(app(cons(),h),t)) -> app#(app(app(map_2(),f),c),t)
   app#(app(app(map_2(),f),c),app(app(cons(),h),t)) -> app#(f,h)
   app#(app(app(map_2(),f),c),app(app(cons(),h),t)) -> app#(app(f,h),c)
   app#(app(app(map_2(),f),c),app(app(cons(),h),t)) -> app#(cons(),app(app(f,h),c))
   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))
   app#(app(app(app(map_3(),f),g()),c),app(app(cons(),h),t)) ->
   app#(app(app(app(map_3(),f),g()),c),t)
   app#(app(app(app(map_3(),f),g()),c),app(app(cons(),h),t)) -> app#(f,g())
   app#(app(app(app(map_3(),f),g()),c),app(app(cons(),h),t)) -> app#(app(f,g()),h)
   app#(app(app(app(map_3(),f),g()),c),app(app(cons(),h),t)) -> app#(app(app(f,g()),h),c)
   app#(app(app(app(map_3(),f),g()),c),app(app(cons(),h),t)) ->
   app#(cons(),app(app(app(f,g()),h),c))
   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))
  TRS:
   app(app(map_1(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map_1(),f),t))
   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))
   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))
  Open