Converting my recursive function to top down dynamic programming

Question

I have been struggling with this problem all week. The problem is as follows, given such a string, S, of n uppercase letters, describe an efficient way of breaking it into a sequence of valid English words. You may assume the valid(s) function runs in O(1) time. Example of how it should work is like this. Lets say you are given CABIN as input. [A, BIN, IN, CAB, CABIN] are valid words. Function should return [[CAB, IN], [CABIN]].

I managed to get a recursive function working but can't seem to figure out how to create a dynamic solution.

Recursive Implementation (JS)

var test = 'ABORTTHEPLANMEETATTHEDARKCABIN';
var words = {
    ABORT: true,
    THE: true,
    PLAN: true,
    MEET: true,
    AT: true,
    DARK: true,
    CABIN: true
};
var valid = function(word) {
    if (words[word]) return true;
    return false;
};
String.prototype.suffix = function(i) {
    return this.substring(this.length - i);
};

String.prototype.prefix = function(i) {
    return this.substring(0, i);
};


var breakCode = function(S) {
    var T = [];

    for (var i = 1; i <= S.length; i++) {
        var str = S.suffix(i);
        if (valid(str)) {
            if (i < S.length) {
                var prefix = S.prefix(S.length - i);
                var P = breakCode(prefix);
                P.forEach(function(p) {
                    p.push(str);
                    T.push(p);
                });
            } else {
                T.push([str]);
            }
        }
    }
    return T;
}

Non Working Attempt at DP Solution

var breakCodeDP = function(S) {
    var T=[];

    for (var i = 1; i <= S.length; i++) {
        for (var j = 1; j <= i; j++) {
            var str = S.suffix(j);
            if (valid(str)) {
                if (j < i) {
                    var P = T[i - j];
                    // console.log(T);
                    // P = typeof P === 'undefined'?[]:P;
                    // P.forEach(function(p) {
                    //   if (!Array.isArray(T[i])) T[i] = [];
                    //     T[i].push([p, str]);
                    // });
                } else {
                    T[i] = [str];
                }
            }
        }
    }
}