#Make Example Data

df_a<-data.frame(A = c(1:9,11),    B = letters[1:10],                   C = sample(1:4,10,replace = T))
df_b<-data.frame(A = c(1:10,1:10), B = letters[c(1:5,10,9,8,7,5,6:15)], C = sample(1:4,20,replace = T))

order_of_importance<-c("A"="A","B"="B")

#Define Recursive Join Function

recursive_join<-function(left_df,right_df,variable_order){
  #work out which rows don't match with this many cols
  new_left_df<-anti_join(left_df,right_df,by=variable_order)
  #new list of cols minus the last one
  new_variable_order<-head(variable_order, -1)
  last_variable<-tail(variable_order,1)
  print(last_variable)
  #joined df on the rows that matched with this many cols
  intermediate<-inner_join(left_df,right_df,by=variable_order,suffix = c("", ".y"))
  #rename the joined df to be the same as later levels
  #names(intermediate)[which(names(intermediate)==names(variable_order))]<-paste0(names(variable_order),".x")
  #rename the antijoined df to be the same as later levels
  names(new_left_df)[which(names(new_left_df)==names(last_variable))]<-paste0(names(last_variable),".x")
  #write the join order
  if(nrow(intermediate)!=0){
  intermediate$cols_matched<-length(variable_order)
  }
  #condition for recursive call
  if ( is_empty(new_variable_order) ){
    if(nrow(new_left_df)!=0){
    new_left_df[,last_variable]<-NA
    new_left_df$cols_matched<-0
    }
    return(bind_rows(intermediate,
                     new_left_df))
  } else if ( nrow(new_left_df)==0 ){

    return(intermediate)
  } else {
    #define output
    return(bind_rows(intermediate,
                          recursive_join(new_left_df,right_df,new_variable_order)))
  }
}

#apply recursive join and look at output

joined_output<-recursive_join(df_a,df_b,order_of_importance)