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:
 Open