(define (process-list-of-x lox)
  (cond
    ;; trivial case
    [(empty? lox) ...]
    [(cons? lox)
     ; combine the solutions
     (...
      ; solve the first sub-problem
      (process-x (first lox))
      ...
      ; solve the second sub-problem
      (process-lox (rest lox))
      ...)]))