#This file does not begin to find all of the equivalence classes of sets of 1 pattern of length 4 and 3 patterns of length 5. An attempt has not been made to use SipurF([4,5,5,5],4,2,10,20,n,N,x,3,2). Though as a reference point, [4,4,5,5] was not able to list all of its equivalence classes.
#Begin samples of attempting to find enumeration schemes for random sets of patterns (1 length four and 3 length five).
#At line 27, begin attempts with updated VatterR4S5 (lists failures and ensures K different attempts).

>VatterR4S5(1,3,100,3,2);
VatterR4S5(1,3,100,4,2);


      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 3, PATTERNS OF LENGTH 5



             The computation took, 34.232, seconds.



      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 3, PATTERNS OF LENGTH 5



            The computation took, 589.323, seconds.

########################################################################################################
#After updating VatterR4S5 to list the failures:
>VatterR4S5(1,3,100,3,2);


      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 3, PATTERNS OF LENGTH 5



            The computation took , 34.523, seconds.
       SchemeFast failed for the following , 100,  sets:
{{[1, 2, 3, 4], [1, 4, 5, 3, 2], [2, 4, 1, 3, 5], [2, 4, 5, 1, 3]

  }, {[1, 2, 3, 4], [1, 5, 3, 4, 2], [3, 1, 4, 2, 5], 

  [4, 5, 2, 1, 3]}, {[1, 2, 3, 4], [3, 1, 5, 2, 4], 

  [3, 5, 2, 4, 1], [4, 1, 3, 5, 2]}, {[1, 2, 3, 4], 

  [3, 5, 2, 4, 1], [4, 2, 3, 5, 1], [4, 5, 3, 2, 1]}, {

  [1, 2, 4, 3], [2, 1, 3, 4, 5], [3, 4, 2, 5, 1], [4, 5, 3, 1, 2]

  }, {[1, 2, 4, 3], [4, 1, 5, 3, 2], [4, 2, 1, 5, 3], 

  [5, 1, 4, 2, 3]}, {[1, 3, 2, 4], [1, 2, 3, 5, 4], 

  [1, 5, 2, 3, 4], [4, 2, 1, 3, 5]}, {[1, 3, 2, 4], 

  [1, 2, 4, 5, 3], [2, 5, 1, 4, 3], [5, 3, 4, 2, 1]}, {

  [1, 3, 2, 4], [2, 1, 3, 4, 5], [5, 1, 2, 4, 3], [5, 4, 2, 3, 1]

  }, {[1, 3, 2, 4], [2, 3, 5, 1, 4], [3, 1, 5, 4, 2], 

  [5, 2, 1, 3, 4]}, {[1, 3, 4, 2], [1, 2, 3, 4, 5], 

  [2, 3, 1, 5, 4], [3, 2, 5, 4, 1]}, {[1, 3, 4, 2], 

  [2, 3, 4, 1, 5], [4, 3, 5, 2, 1], [4, 5, 1, 3, 2]}, {

  [1, 3, 4, 2], [2, 3, 5, 1, 4], [3, 4, 5, 1, 2], [4, 5, 1, 2, 3]

  }, {[1, 3, 4, 2], [2, 4, 1, 3, 5], [4, 3, 1, 5, 2], 

  [5, 3, 4, 1, 2]}, {[1, 3, 4, 2], [3, 2, 4, 5, 1], 

  [3, 2, 5, 4, 1], [5, 3, 4, 2, 1]}, {[1, 4, 2, 3], 

  [2, 1, 3, 4, 5], [4, 1, 3, 2, 5], [4, 3, 5, 1, 2]}, {

  [1, 4, 2, 3], [3, 1, 2, 4, 5], [3, 4, 1, 2, 5], [4, 3, 1, 2, 5]

  }, {[1, 4, 2, 3], [3, 1, 4, 5, 2], [5, 3, 1, 4, 2], 

  [5, 3, 2, 1, 4]}, {[1, 4, 2, 3], [3, 5, 2, 1, 4], 

  [5, 2, 4, 1, 3], [5, 3, 1, 2, 4]}, {[1, 4, 2, 3], 

  [4, 1, 2, 5, 3], [4, 3, 1, 2, 5], [5, 3, 2, 4, 1]}, {

  [1, 4, 3, 2], [1, 2, 4, 3, 5], [5, 1, 4, 2, 3], [5, 4, 3, 2, 1]

  }, {[1, 4, 3, 2], [1, 2, 5, 3, 4], [4, 1, 3, 2, 5], 

  [4, 3, 1, 5, 2]}, {[1, 4, 3, 2], [1, 4, 2, 3, 5], 

  [5, 4, 3, 1, 2], [5, 4, 3, 2, 1]}, {[1, 4, 3, 2], 

  [2, 1, 3, 4, 5], [3, 2, 4, 1, 5], [5, 2, 3, 1, 4]}, {

  [1, 4, 3, 2], [3, 5, 1, 4, 2], [4, 1, 2, 3, 5], [5, 2, 1, 4, 3]

  }, {[2, 1, 3, 4], [1, 2, 3, 5, 4], [1, 3, 5, 4, 2], 

  [2, 4, 1, 5, 3]}, {[2, 1, 3, 4], [1, 3, 2, 5, 4], 

  [3, 2, 1, 5, 4], [3, 4, 1, 2, 5]}, {[2, 1, 3, 4], 

  [1, 4, 2, 3, 5], [3, 2, 5, 4, 1], [5, 2, 4, 3, 1]}, {

  [2, 1, 3, 4], [1, 5, 2, 4, 3], [2, 5, 1, 4, 3], [3, 5, 1, 2, 4]

  }, {[2, 1, 3, 4], [3, 2, 5, 1, 4], [4, 3, 2, 1, 5], 

  [5, 3, 1, 4, 2]}, {[2, 1, 3, 4], [3, 2, 5, 1, 4], 

  [5, 2, 1, 4, 3], [5, 2, 3, 4, 1]}, {[2, 1, 4, 3], 

  [2, 3, 1, 4, 5], [4, 1, 2, 3, 5], [5, 2, 1, 3, 4]}, {

  [2, 1, 4, 3], [4, 2, 3, 1, 5], [5, 2, 4, 1, 3], [5, 3, 2, 1, 4]

  }, {[2, 3, 1, 4], [1, 2, 5, 4, 3], [1, 5, 2, 3, 4], 

  [2, 1, 4, 3, 5]}, {[2, 3, 1, 4], [2, 1, 3, 4, 5], 

  [2, 3, 4, 5, 1], [5, 3, 2, 4, 1]}, {[2, 3, 1, 4], 

  [2, 4, 5, 1, 3], [3, 5, 1, 2, 4], [4, 1, 5, 3, 2]}, {

  [2, 3, 1, 4], [2, 5, 1, 4, 3], [4, 2, 5, 3, 1], [5, 3, 1, 2, 4]

  }, {[2, 3, 1, 4], [3, 4, 5, 2, 1], [4, 3, 1, 2, 5], 

  [5, 2, 3, 4, 1]}, {[2, 3, 4, 1], [2, 5, 1, 3, 4], 

  [4, 2, 3, 1, 5], [5, 3, 1, 2, 4]}, {[2, 3, 4, 1], 

  [2, 5, 3, 1, 4], [4, 5, 2, 3, 1], [5, 4, 2, 1, 3]}, {

  [2, 3, 4, 1], [3, 2, 5, 1, 4], [5, 3, 1, 2, 4], [5, 4, 2, 3, 1]

  }, {[2, 4, 1, 3], [1, 2, 5, 4, 3], [2, 4, 5, 3, 1], 

  [4, 3, 5, 1, 2]}, {[2, 4, 1, 3], [1, 4, 5, 3, 2], 

  [1, 5, 2, 4, 3], [5, 2, 1, 4, 3]}, {[2, 4, 1, 3], 

  [1, 5, 4, 2, 3], [4, 3, 2, 5, 1], [5, 4, 3, 1, 2]}, {

  [2, 4, 1, 3], [3, 2, 1, 5, 4], [4, 3, 5, 1, 2], [4, 5, 3, 1, 2]

  }, {[2, 4, 3, 1], [1, 2, 4, 5, 3], [2, 1, 4, 3, 5], 

  [4, 5, 1, 3, 2]}, {[2, 4, 3, 1], [4, 1, 5, 2, 3], 

  [4, 5, 1, 3, 2], [5, 2, 4, 1, 3]}, {[3, 1, 2, 4], 

  [1, 3, 2, 4, 5], [1, 4, 5, 2, 3], [4, 5, 3, 2, 1]}, {

  [3, 1, 2, 4], [1, 3, 4, 2, 5], [3, 4, 2, 5, 1], [4, 2, 1, 5, 3]

  }, {[3, 1, 2, 4], [1, 4, 2, 5, 3], [2, 3, 4, 1, 5], 

  [4, 3, 2, 5, 1]}, {[3, 1, 2, 4], [1, 5, 3, 4, 2], 

  [4, 2, 5, 3, 1], [4, 3, 5, 2, 1]}, {[3, 1, 2, 4], 

  [1, 5, 4, 2, 3], [3, 4, 5, 2, 1], [4, 2, 5, 3, 1]}, {

  [3, 1, 2, 4], [2, 1, 4, 3, 5], [3, 4, 5, 1, 2], [5, 1, 2, 4, 3]

  }, {[3, 1, 4, 2], [1, 2, 5, 4, 3], [2, 1, 5, 4, 3], 

  [4, 3, 5, 2, 1]}, {[3, 1, 4, 2], [1, 2, 5, 4, 3], 

  [3, 5, 2, 4, 1], [4, 5, 2, 1, 3]}, {[3, 1, 4, 2], 

  [1, 3, 5, 2, 4], [2, 1, 4, 5, 3], [2, 3, 4, 1, 5]}, {

  [3, 1, 4, 2], [1, 3, 5, 4, 2], [3, 5, 2, 1, 4], [5, 4, 3, 2, 1]

  }, {[3, 1, 4, 2], [2, 1, 5, 3, 4], [4, 5, 2, 1, 3], 

  [5, 2, 3, 1, 4]}, {[3, 1, 4, 2], [2, 5, 3, 1, 4], 

  [3, 1, 2, 5, 4], [5, 2, 1, 4, 3]}, {[3, 2, 1, 4], 

  [1, 3, 2, 5, 4], [2, 4, 3, 5, 1], [5, 3, 4, 2, 1]}, {

  [3, 2, 1, 4], [1, 4, 5, 2, 3], [4, 2, 5, 3, 1], [4, 5, 3, 2, 1]

  }, {[3, 2, 1, 4], [1, 4, 5, 3, 2], [2, 1, 3, 5, 4], 

  [5, 2, 1, 3, 4]}, {[3, 2, 4, 1], [1, 4, 5, 2, 3], 

  [2, 5, 4, 3, 1], [5, 4, 1, 3, 2]}, {[3, 4, 1, 2], 

  [1, 4, 2, 3, 5], [5, 4, 2, 1, 3], [5, 4, 3, 2, 1]}, {

  [3, 4, 1, 2], [3, 2, 5, 4, 1], [5, 3, 2, 4, 1], [5, 4, 2, 1, 3]

  }, {[3, 4, 2, 1], [1, 2, 4, 5, 3], [1, 3, 5, 2, 4], 

  [2, 3, 5, 1, 4]}, {[3, 4, 2, 1], [1, 3, 4, 2, 5], 

  [1, 5, 2, 3, 4], [2, 1, 5, 4, 3]}, {[3, 4, 2, 1], 

  [1, 4, 2, 3, 5], [3, 5, 1, 2, 4], [4, 3, 2, 5, 1]}, {

  [3, 4, 2, 1], [1, 4, 3, 5, 2], [4, 3, 2, 1, 5], [5, 4, 2, 1, 3]

  }, {[3, 4, 2, 1], [2, 1, 5, 4, 3], [3, 2, 4, 5, 1], 

  [5, 1, 2, 4, 3]}, {[3, 4, 2, 1], [2, 5, 1, 3, 4], 

  [4, 2, 1, 5, 3], [5, 3, 2, 1, 4]}, {[3, 4, 2, 1], 

  [4, 2, 1, 5, 3], [4, 3, 1, 5, 2], [5, 4, 3, 1, 2]}, {

  [4, 1, 2, 3], [1, 4, 3, 2, 5], [3, 1, 5, 4, 2], [4, 3, 1, 5, 2]

  }, {[4, 1, 2, 3], [2, 4, 5, 1, 3], [4, 3, 1, 5, 2], 

  [4, 5, 3, 2, 1]}, {[4, 1, 2, 3], [3, 2, 1, 4, 5], 

  [3, 4, 5, 2, 1], [4, 3, 2, 1, 5]}, {[4, 1, 3, 2], 

  [1, 2, 3, 5, 4], [1, 3, 5, 4, 2], [4, 5, 3, 2, 1]}, {

  [4, 1, 3, 2], [1, 2, 5, 4, 3], [3, 4, 1, 2, 5], [3, 4, 2, 1, 5]

  }, {[4, 1, 3, 2], [1, 3, 5, 4, 2], [2, 3, 5, 4, 1], 

  [3, 4, 5, 1, 2]}, {[4, 1, 3, 2], [1, 5, 3, 2, 4], 

  [3, 4, 1, 5, 2], [4, 2, 3, 1, 5]}, {[4, 1, 3, 2], 

  [1, 5, 4, 2, 3], [2, 1, 3, 5, 4], [4, 3, 5, 2, 1]}, {

  [4, 1, 3, 2], [2, 1, 4, 3, 5], [3, 1, 4, 2, 5], [3, 4, 2, 1, 5]

  }, {[4, 1, 3, 2], [2, 1, 5, 3, 4], [3, 5, 4, 1, 2], 

  [4, 3, 1, 5, 2]}, {[4, 1, 3, 2], [2, 4, 3, 1, 5], 

  [3, 2, 4, 5, 1], [5, 4, 2, 1, 3]}, {[4, 2, 1, 3], 

  [1, 2, 3, 4, 5], [3, 5, 4, 2, 1], [5, 4, 2, 3, 1]}, {

  [4, 2, 1, 3], [1, 3, 5, 4, 2], [2, 3, 5, 1, 4], [3, 2, 1, 5, 4]

  }, {[4, 2, 1, 3], [1, 5, 2, 3, 4], [2, 4, 1, 5, 3], 

  [2, 5, 3, 4, 1]}, {[4, 2, 1, 3], [2, 3, 5, 1, 4], 

  [2, 5, 4, 3, 1], [3, 5, 4, 2, 1]}, {[4, 2, 3, 1], 

  [1, 2, 3, 5, 4], [2, 3, 4, 1, 5], [2, 4, 1, 5, 3]}, {

  [4, 2, 3, 1], [1, 2, 5, 3, 4], [1, 4, 5, 2, 3], [2, 5, 1, 4, 3]

  }, {[4, 2, 3, 1], [1, 2, 5, 4, 3], [1, 4, 3, 2, 5], 

  [5, 1, 2, 4, 3]}, {[4, 2, 3, 1], [1, 3, 5, 2, 4], 

  [2, 3, 4, 5, 1], [3, 4, 5, 1, 2]}, {[4, 2, 3, 1], 

  [1, 4, 2, 5, 3], [1, 4, 3, 5, 2], [5, 1, 3, 2, 4]}, {

  [4, 2, 3, 1], [3, 2, 5, 1, 4], [3, 4, 2, 5, 1], [4, 2, 5, 1, 3]

  }, {[4, 3, 1, 2], [1, 3, 4, 5, 2], [2, 1, 4, 5, 3], 

  [5, 3, 2, 4, 1]}, {[4, 3, 1, 2], [1, 5, 2, 3, 4], 

  [1, 5, 2, 4, 3], [2, 3, 1, 4, 5]}, {[4, 3, 1, 2], 

  [2, 1, 3, 4, 5], [2, 4, 1, 3, 5], [4, 5, 2, 3, 1]}, {

  [4, 3, 1, 2], [2, 4, 1, 5, 3], [2, 5, 4, 3, 1], [3, 5, 1, 2, 4]

  }, {[4, 3, 2, 1], [2, 4, 1, 3, 5], [3, 1, 4, 5, 2], 

  [3, 2, 1, 5, 4]}, {[4, 3, 2, 1], [2, 4, 5, 3, 1], 

  [3, 2, 4, 1, 5], [4, 3, 1, 5, 2]}, {[4, 3, 2, 1], 

  [3, 1, 2, 4, 5], [3, 4, 5, 2, 1], [4, 5, 1, 2, 3]}}