There are , 5, different equivalence classes

For the equivalence class of patterns,

    {{[1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]}}

the member , {[1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]},

    has a scheme of depth , 2

                                  here it is:

{[[], {}, {}], [[1, 2], {[1, 0, 0], [0, 1, 0]}, {1}], [[1], {[1, 1]}, {}],

    [[2, 1], {[0, 1, 0], [0, 0, 1]}, {1}]}

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,

    2, 2, 2, 2, 2]

                      the sequence seems to be polynomial

                                       2

For the equivalence class of patterns, {

    {[3, 2, 1], [1, 2, 3], [1, 3, 2], [2, 1, 3]},

    {[3, 2, 1], [1, 2, 3], [2, 3, 1], [3, 1, 2]}}

the member , {[3, 2, 1], [1, 2, 3], [1, 3, 2], [2, 1, 3]},

    has a scheme of depth , 2

                                  here it is:

{[[], {}, {}], [[1], {[0, 2], [3, 0]}, {}],

    [[2, 1], {[1, 0, 0], [0, 0, 1], [0, 2, 0]}, {1}],

    [[1, 2], {[0, 1, 0], [0, 0, 1], [3, 0, 0]}, {1}]}

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

    0, 0, 0, 0, 0]

                             the sequence is finite

For the equivalence class of patterns, {

    {[3, 2, 1], [1, 2, 3], [1, 3, 2], [2, 3, 1]},

    {[3, 2, 1], [1, 2, 3], [1, 3, 2], [3, 1, 2]},

    {[3, 2, 1], [1, 2, 3], [2, 1, 3], [2, 3, 1]},

    {[3, 2, 1], [1, 2, 3], [2, 1, 3], [3, 1, 2]}}

the member , {[3, 2, 1], [1, 2, 3], [1, 3, 2], [2, 3, 1]},

    has a scheme of depth , 2

                                  here it is:

{[[], {}, {}], [[1, 2], {[1, 0, 0], [0, 1, 0], [0, 0, 1]}, {1}],

    [[2, 1], {[1, 0, 0], [0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1}],

    [[1], {[2, 1], [0, 2], [3, 0]}, {}]}

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

    0, 0, 0, 0, 0]

                             the sequence is finite

For the equivalence class of patterns, {

    {[3, 2, 1], [1, 3, 2], [2, 1, 3], [2, 3, 1]},

    {[3, 2, 1], [1, 3, 2], [2, 1, 3], [3, 1, 2]},

    {[1, 2, 3], [1, 3, 2], [2, 3, 1], [3, 1, 2]},

    {[1, 2, 3], [2, 1, 3], [2, 3, 1], [3, 1, 2]}}

the member , {[3, 2, 1], [1, 3, 2], [2, 1, 3], [2, 3, 1]},

    has a scheme of depth , 2

                                  here it is:

{[[], {}, {}], [[1, 2], {[1, 0, 0], [0, 1, 0]}, {1}], [[1], {[1, 1]}, {}],

    [[2, 1], {[1, 0, 0], [0, 0, 1]}, {1}]}

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,

    2, 2, 2, 2, 2]

                      the sequence seems to be polynomial

                                       2

For the equivalence class of patterns, {

    {[3, 2, 1], [1, 3, 2], [2, 3, 1], [3, 1, 2]},

    {[3, 2, 1], [2, 1, 3], [2, 3, 1], [3, 1, 2]},

    {[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1]},

    {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 1, 2]}}

the member , {[3, 2, 1], [1, 3, 2], [2, 3, 1], [3, 1, 2]},

    has a scheme of depth , 2

                                  here it is:

{[[], {}, {}], [[1, 2], {[1, 0, 0], [0, 1, 0]}, {1}],

    [[2, 1], {[1, 0, 0], [0, 1, 0]}, {1}], [[1], {[2, 0]}, {}]}

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,

    2, 2, 2, 2, 2]

                      the sequence seems to be polynomial

                                       2

                         Out of a total of , 5, cases

                      5, were successful and , 0, failed

                               Success Rate: , 1.

                             Here are the failures

                                       {}

                                       {}

                     It took, 0.404, seconds of CPU time .