4trus

4trus is a very new method for 4x4 invented by Owen Smith. This method is intended to be used by petrus solvers, so that they can achieve some of the advantages of yau whilst using petrus but also not having to use redux. The steps are fairly simple, more simple than that of 4x4 ZZ methods but not as simple as Yau.
Just like many recent methods, nobody uses this method. The creator himself does not use petrus, so he does not even use this method.
Contents
Steps
 F2C. If you are color neutral, then these do not have to be the white and yellow centers.
 Place 2 cross edges and the edge that has the same colors as those edges. This will be explained further.
 L4C just like Yau
 Place your final edge into the d layer. This can be another cross edge or one edge that has at least one color relative to your first two cross edges. This will be explained further.
 Finish pairing edges. Any edge pairing method can be used, although I recommend 323.
 Assemble your 2x2x2 with the pieces in the bottom and then expand to 2x2x3 with the other lone piece in the bottom.
 Petrus style EO Plus fixing parity
 Finish F2L
 COLL
 EPLL+Parity
The Yau stage
The Yau stage needs to have these edges in it:
 2 cross edges that are adjacent colors (make sure these are placed correctly next to each other)
 1 non cross edge that has the same colors as our 2 cross edges we created last step.
 Make sure to put d layer cross edges or l layer cross edges. It depends on how you hold the first two centers when creating your first 3 edges.
Final Yau edge
Your final Yau edge will need to be placed once you have finished L4C. This can be:
 another d layer edge or:
 a non d layer edge (cannot be a top layer edge though) that has at least one color that is the same as your first two d edges.
This is fairly simple. You just see which one is easier to make and put it in.
Building your blocks
For this step you will need to take your non D colored edge that is the same color as your first two D layer edges out of the bottom. If possible, you can find the corresponding corner and try to make the pair easier to make while it’s in the d layer. Once the pair is made in any way, insert it into your two cross edges. Than take your other edge that was placed in step 4 and expand to 2x2x3 with that edge.
EO+Parity
This is the same as petrus EO except for if you get parity. I will explain anyway though. Make sure you’re 2x2x3 is in back.
 If an edge that has your left or right colors is in top or bottom, it is bad.
 If an edge has a front or back color on the front or back, it is good.
 If a front or back colored edge is on top, it is good UNLESS there is a top or bottom color on the other sticker.
 If a top color edge is in the e slice or the top layer, (make sure the top or bottom sticker is actually on the top or bottom) it is good.
To solve EO look at the twist the edges section.
If you have an odd number of bad edges, than this is an impossible case so you have parity. Joseph Tudor has a parity algorithm that will not preserve F2L on the right side. It is a shorter algorithm so you can hold the 2x2x3 on the left. Also make sure the parity edge is on the FR position: Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw'.
Finishing F2L
You do this the same as petrus so if you don’t know how to do it, then look at the Finish two layers section.
Last Layer
For last layer there are a few options:
The reason why I don’t recommend using ZBLL is because if you have PLL parity than the ZBLL can be really confusing.
Now we will either have a PLL or a EPLL depending on what you used for OLL. There is a chance you will get PLL parity. The way you can tell is if it’s not a normal PLL or EPLL. If it’s not, then you can use this algorithm: r2 U2 r2 Uw2 r2 Uw2. Then you will have a normal PLL or EPLL.
Walkthrough solves
Scramble: U2 B' D F2 U' F2 U' L2 U2 R2 U2 L' D F U2 F2 D U Rw2 Fw2 R Uw2 D R' Fw2 D R2 Fw2 R2 U2 Fw L2 B' L2 F Rw' Uw R2 Uw B Rw' L
Uw L' Dw x' Uw' Lw U2 Lw' U' y' Lw' U2 Lw // F2C
B' R U' F' Uw2 D L F D' L' Uw2 F // 3 Yau edges
z L' x' U2 Rw U' Rw' L2 D Rw2 L2 U2 Rw2 x' L' U Rw U' Rw' U Lw L' U2 Lw' // L4C
z' y' L' U2 L Uw' L' U L Uw U2 L2 // final Yau edge
Uw U2 L' U L U R U' R' y R U' R' Uw' y L' U L Uw' U' y L' U L Uw U' F' L F L' y' Uw' R U R' F R' F' R Uw // 323 edge pairing
R B2 R2 y' R U2 R' y' U L2 U L U' L U2 y' R' U R // 2x2x2 to 2x2x3
F' R' F R L' U' L F2 R U R' U2 R U' R' L' U L U' L' U L // EO Plus F2L
U2 R U R' U R U2 R' F R U' R' U' R U R' F' R U R' U' R' F R F' U2 R U R' U' 2R2 U2 2R2 Uw2 2R2 Uw2 U' R U' R' U' // last layer
More coming soon.