source("boot.R")
box_use(./b4)

#' @export
free_reduce <- function(w) b4$braid_reduce(w)

#' @export
yang_baxter_normalize <- function(w) {
  w <- unclass(b4$braid_reduce(w))
  changed <- TRUE
  while (changed) {
    changed <- FALSE
    i <- 1
    while (i <= length(w) - 2) {
      a <- w[i]; b <- w[i + 1]; c <- w[i + 2]
      ia <- abs(a); ib <- abs(b); ic <- abs(c)
      if (ia == ic && abs(ia - ib) == 1 && sign(a) == sign(b) && sign(b) == sign(c)) {
        if (ia > ib) {
          w[i] <- b; w[i + 1] <- a; w[i + 2] <- b; changed <- TRUE
        }
      }
      i <- i + 1
    }
  }
  b4$braid_word(w)
}

#' @export
far_commute_sort <- function(w) {
  w <- unclass(b4$braid_reduce(w))
  changed <- TRUE
  while (changed) {
    changed <- FALSE
    i <- 1
    while (i <= length(w) - 1) {
      a <- w[i]; b <- w[i + 1]
      if (abs(a) > abs(b) + 1 || abs(a) + 1 < abs(b)) {
        if (abs(a) > abs(b) || (abs(a) == abs(b) && a > b)) {
          w[i] <- b; w[i + 1] <- a; changed <- TRUE
        }
      }
      i <- i + 1
    }
  }
  b4$braid_word(w)
}

#' @export
rewrite_normalize <- function(w) {
  prev <- NULL
  w <- b4$braid_reduce(w)
  while (!identical(prev, unclass(w))) {
    prev <- unclass(w)
    w <- yang_baxter_normalize(w)
    w <- far_commute_sort(w)
    w <- b4$braid_reduce(w)
  }
  w
}