# Q = 128
# 548 successful iterations

INCREASE Q INCREASE Q INCREASE Q INCREASE Q # 4^3 = 64
 
#CLEAR S # s <= (x > 0) assume empty
#CLEAR L assume empty
#CLEAR M assume empty
INCREASE M
REPEAT X TIMES (
    REPEAT M TIMES ( REPEAT L TIMES ( CLEAR M INCREASE S ) INCREASE L )
)

PRINT X
REPEAT Q TIMES (
    REPEAT S TIMES ( # skips iterations a lot faster if there are a lot to skip
        REPEAT Q TIMES (
            REPEAT S TIMES (
                REPEAT Q TIMES ( # repeat 4 times 4 times 4 times: 64 times
                    # if x > 1
                    REPEAT S TIMES (
                    
                        # o: store x / 8
                        CLEAR O
                
                        # ea: % 8 == 0
                        # eb: % 8 == 1
                        # ec: % 8 == 2
                        # ed: % 8 == 3
                        
                        # fa: % 8 == 4
                        # fb: % 8 == 5
                        # fc: % 8 == 6
                        # fd: % 8 == 7
                        INCREASE A

                        # e-f flip-flop
                        INCREASE E
                        
                        REPEAT X TIMES (
                            REPEAT D TIMES ( CLEAR D INCREASE T
                                REPEAT F TIMES ( CLEAR F INCREASE H INCREASE O )

                                REPEAT E TIMES ( CLEAR E INCREASE F )
                                REPEAT H TIMES ( CLEAR H INCREASE E )
                            )
                            REPEAT C TIMES ( CLEAR C INCREASE D )
                            REPEAT B TIMES ( CLEAR B INCREASE C )
                            REPEAT A TIMES ( CLEAR A INCREASE B )
                            REPEAT T TIMES ( CLEAR T INCREASE A )
                        )
                        
                        REPEAT E TIMES (
                            CLEAR E

                            # % 8 == 0
                            REPEAT A TIMES (
                                CLEAR A

                                # o > 0
                                CLEAR X
                                CLEAR Y
                                REPEAT O TIMES ( INCREASE O INCREASE O INCREASE O INCREASE Y INCREASE Y INCREASE X )
                                
                                PRINT O # 4o
                                
                                PRINT Y # 2o
                                
                                PRINT X # o
                            )

                            # % 8 == 1
                            REPEAT B TIMES (
                                CLEAR B

                                # TODO: maybe unneeded check?
                                CLEAR S # o > 0?
                                REPEAT O TIMES ( CLEAR S INCREASE S )

                                REPEAT S TIMES (
                                    # X = 8n + 1; X = 24n + 4 (3x+1); X = 0; X = 6n + 1; X = 9n + 2
                                    # Y = 12n + 2; Y = 18n + 4

                                    REPEAT X TIMES ( INCREASE X INCREASE X )
                                    INCREASE X 
                                    PRINT X # 3x + 1

                                    CLEAR X # X = 0; X <= 6n + 1
                                    CLEAR Y # Y = 12n + 2
                                    REPEAT O TIMES (
                                        INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                        INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                        INCREASE Y INCREASE Y INCREASE Y INCREASE Y  
                                        INCREASE X INCREASE X INCREASE X 
                                        INCREASE X INCREASE X INCREASE X 
                                    )
                                    INCREASE Y INCREASE Y
                                    PRINT Y # 12n + 2

                                    INCREASE X
                                    PRINT X # 6n + 1

                                    REPEAT O TIMES (
                                        INCREASE Y INCREASE Y INCREASE Y 
                                        INCREASE Y INCREASE Y INCREASE Y 
                                        INCREASE X INCREASE X INCREASE X
                                    )
                                    INCREASE Y INCREASE Y 
                                    PRINT Y # Y = 18n + 4

                                    INCREASE X
                                    PRINT X # X = 9n + 2
                                )
                            )
                            
                            # % 8 == 2
                            REPEAT C TIMES (
                                CLEAR C

                                CLEAR S # o > 0?
                                REPEAT O TIMES ( CLEAR S INCREASE S )

                                INCREASE T # o == 0?
                                REPEAT S TIMES ( CLEAR T )

                                REPEAT T TIMES (
                                    # (2) 1

                                    PRINT T # 1
                                )

                                REPEAT S TIMES (
                                    # x <= 12n + 4
                                    CLEAR Y # 4n + 1
                                    REPEAT O TIMES (
                                        INCREASE Y INCREASE Y INCREASE Y INCREASE Y
                                        INCREASE X INCREASE X INCREASE X INCREASE X
                                    )
                                    INCREASE Y
                                    PRINT Y # 4n + 1

                                    INCREASE X INCREASE X
                                    PRINT X # 12n + 4

                                    # Y <= 6n + 2
                                    CLEAR X # <= 3n + 1
                                    REPEAT O TIMES (
                                        INCREASE Y INCREASE Y
                                        INCREASE X INCREASE X INCREASE X
                                    )
                                    INCREASE Y
                                    PRINT Y # 6n + 2

                                    INCREASE X
                                    PRINT X # 3n + 1
                                )
                            )
                            
                            # % 8 == 3
                            REPEAT D TIMES (
                                CLEAR D

                                # x = 24n + 10
                                REPEAT X TIMES ( INCREASE X INCREASE X )
                                INCREASE X
                                PRINT X # 24n + 10 (3x + 1)

                                # Y = 12n + 5
                                CLEAR Y
                                REPEAT O TIMES (
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y
                                )
                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y
                                PRINT Y # 12n + 5

                                # x <= 24n+10 + 12n+5 = 36n + 15
                                REPEAT Y TIMES ( INCREASE X )
                                INCREASE X 
                                PRINT X # 36n + 16

                                CLEAR X # x <= 9n + 4
                                # y = 12n+5 + 6n + 3
                                REPEAT O TIMES (
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y
                                    INCREASE X INCREASE X INCREASE X INCREASE X INCREASE X
                                    INCREASE X INCREASE X INCREASE X INCREASE X
                                )
                                INCREASE Y INCREASE Y INCREASE Y
                                PRINT Y # 18n + 8

                                INCREASE X INCREASE X INCREASE X INCREASE X
                                PRINT X # 9n + 4
                            )
                        )

                        REPEAT F TIMES (
                            CLEAR F

                            # % 8 == 4
                            REPEAT A TIMES (
                                CLEAR A
                                
                                CLEAR S # o > 0?
                                REPEAT O TIMES ( CLEAR S INCREASE S )

                                INCREASE T # o == 0?
                                REPEAT S TIMES ( CLEAR T )

                                REPEAT T TIMES (
                                    # (4) 2 1

                                    CLEAR Z
                                    INCREASE Z INCREASE Z
                                    PRINT Z # 2

                                    PRINT T # 1
                                )

                                REPEAT S TIMES (
                                    CLEAR X # X <= 2n + 1; X <= 3n + 2
                                    CLEAR Y # Y <= 4n + 2; Y <= 6n + 4

                                    REPEAT O TIMES (
                                        INCREASE X INCREASE X
                                        INCREASE Y INCREASE Y INCREASE Y INCREASE Y
                                    )
                                    INCREASE Y INCREASE Y
                                    PRINT Y # 4n + 2

                                    INCREASE X 
                                    PRINT X # 2n + 1

                                    REPEAT O TIMES (
                                        INCREASE X
                                        INCREASE Y INCREASE Y
                                    )
                                    INCREASE Y INCREASE Y
                                    PRINT Y # 6n + 4

                                    INCREASE X
                                    PRINT X # 3n + 2
                                )
                            )

                            # % 8 == 5
                            REPEAT B TIMES (
                                CLEAR B

                                # X <= 24n + 16 (3x + 1)
                                REPEAT X TIMES ( INCREASE X INCREASE X )
                                INCREASE X
                                PRINT X # 24n + 16
                            
                                CLEAR Y # 12n + 8
                                # O <= 6n + 4
                                CLEAR X # 3n + 2
                                REPEAT O TIMES (
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                    INCREASE O INCREASE O INCREASE O INCREASE O INCREASE O
                                    INCREASE X INCREASE X INCREASE X
                                )
                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                PRINT Y # 12n + 8

                                INCREASE O INCREASE O INCREASE O INCREASE O 
                                PRINT O # 6n + 4

                                INCREASE X INCREASE X
                                PRINT X # 3n + 2
                            )
                            
                            # % 8 == 6
                            REPEAT C TIMES (
                                CLEAR C

                                CLEAR Y
                                CLEAR Z
                                # X = 9n + 8
                                # Y = 4n + 3; Y = 6n + 5
                                # Z = 12n + 10; Z = 18n + 16
                                REPEAT O TIMES (
                                    INCREASE X
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                    INCREASE Z INCREASE Z INCREASE Z INCREASE Z 
                                    INCREASE Z INCREASE Z INCREASE Z INCREASE Z 
                                    INCREASE Z INCREASE Z INCREASE Z INCREASE Z 
                                )
                                INCREASE Y INCREASE Y INCREASE Y 
                                PRINT Y # 4n + 3

                                INCREASE Z INCREASE Z INCREASE Z INCREASE Z INCREASE Z 
                                INCREASE Z INCREASE Z INCREASE Z INCREASE Z INCREASE Z 
                                PRINT Z # 12n + 10

                                REPEAT O TIMES (
                                    INCREASE Y INCREASE Y
                                    INCREASE Z INCREASE Z INCREASE Z
                                    INCREASE Z INCREASE Z INCREASE Z 
                                )
                                INCREASE Y INCREASE Y
                                PRINT Y # 6n + 5

                                INCREASE Z INCREASE Z INCREASE Z
                                INCREASE Z INCREASE Z INCREASE Z
                                PRINT Z # 18n + 16 

                                INCREASE X INCREASE X
                                PRINT X # 9n + 8
                            )
                            
                            # % 8 == 7
                            REPEAT D TIMES (
                                CLEAR D

                                # Y = 24n + 22 (3x + 1); Y = 36n + 34; Y = 54n + 52;
                                # X = 8n + 7; X = 12n + 11; X = 18n + 17; X = 27n + 26
                                CLEAR Y # 3x + 1
                                REPEAT X TIMES (
                                    INCREASE Y INCREASE Y INCREASE Y
                                )
                                INCREASE Y
                                PRINT Y # 24n + 22

                                REPEAT O TIMES (
                                    INCREASE X INCREASE X INCREASE X INCREASE X 
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                )
                                INCREASE X INCREASE X INCREASE X INCREASE X 
                                PRINT X # 12n + 11

                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y
                                PRINT Y # 36n + 34
                                
                                REPEAT O TIMES (
                                    INCREASE X INCREASE X INCREASE X 
                                    INCREASE X INCREASE X INCREASE X 
                                    
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                    INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                    INCREASE Y INCREASE Y 
                                )
                                INCREASE X INCREASE X INCREASE X 
                                INCREASE X INCREASE X INCREASE X 
                                PRINT X # 18n + 17

                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                INCREASE Y INCREASE Y INCREASE Y INCREASE Y 
                                INCREASE Y INCREASE Y
                                PRINT Y # 54n + 52

                                REPEAT O TIMES (
                                    INCREASE X INCREASE X INCREASE X 
                                    INCREASE X INCREASE X INCREASE X 
                                    INCREASE X INCREASE X INCREASE X 
                                )
                                INCREASE X INCREASE X INCREASE X 
                                INCREASE X INCREASE X INCREASE X 
                                INCREASE X INCREASE X INCREASE X 
                                PRINT X # 27n + 26
                            )
                        )

                    )
                ) 
            )
        )
    ) 
)