MAYBE

Problem:
 app(app(app(fold(),f),nil()),x) -> x
 app(app(app(fold(),f),app(app(cons(),h),t)),x) -> app(app(app(fold(),f),t),app(app(f,x),h))
 app(sum(),l) -> app(app(app(fold(),add()),l),0())
 app(app(app(fold(),mul()),l),1()) -> app(prod(),l)

Proof:
 DP Processor:
  DPs:
   app#(app(app(fold(),f),app(app(cons(),h),t)),x) -> app#(f,x)
   app#(app(app(fold(),f),app(app(cons(),h),t)),x) -> app#(app(f,x),h)
   app#(app(app(fold(),f),app(app(cons(),h),t)),x) -> app#(app(fold(),f),t)
   app#(app(app(fold(),f),app(app(cons(),h),t)),x) -> app#(app(app(fold(),f),t),app(app(f,x),h))
   app#(sum(),l) -> app#(fold(),add())
   app#(sum(),l) -> app#(app(fold(),add()),l)
   app#(sum(),l) -> app#(app(app(fold(),add()),l),0())
   app#(app(app(fold(),mul()),l),1()) -> app#(prod(),l)
  TRS:
   app(app(app(fold(),f),nil()),x) -> x
   app(app(app(fold(),f),app(app(cons(),h),t)),x) -> app(app(app(fold(),f),t),app(app(f,x),h))
   app(sum(),l) -> app(app(app(fold(),add()),l),0())
   app(app(app(fold(),mul()),l),1()) -> app(prod(),l)
  Open