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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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#############################################################################
##
#W  testmanual.g               automata package                Dmytro Savchuk
#W                                                             Yevgen Muntyan
##  automgrp v 1.3
##
#Y  Copyright (C) 2003 - 2016 Dmytro Savchuk, Yevgen Muntyan
##

UnitTest("Examples from manual", function()
  local L, T, a, b, t;

# from selfs.gd

  T := AutomatonGroup("t=(1,t)(1,2)");
  L := AutomatonGroup("a=(a,b)(1,2), b=(a,b)");

  AssertEqual( OrbitOfVertex([1,1,1], T.1), [[1,1,1],[2,1,1],[1,2,1],[2,2,1],[1,1,2],[2,1,2],[1,2,2],[2,2,2]]);

  AssertEqual(NumberOfVertex([1,2,1,2], 2), 6);
  AssertEqual(NumberOfVertex("333", 3), 27);

  AssertEqual(VertexNumber(1,3,2), [1, 1, 1]);
  AssertEqual(VertexNumber(4,4,3), [ 1, 1, 2, 1 ]);

  AssertEqual(PermActionOnLevel((1,4,2,3), 2, 1, 2), (1,2) );
  AssertEqual(PermActionOnLevel((1,13,5,9,3,15,7,11)(2,14,6,10,4,16,8,12), 4, 2, 2), (1,4,2,3) );

  AssertEqual(PermOnLevelAsMatrix(L.1*L.2, 2), [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]);

  AssertEqual(MarkovOperator(AutomatonGroup("p=(p,q)(1,2), q=(p,q)"), 3),
[ [ 0, 0, 1/4, 1/4, 0, 1/4, 0, 1/4 ], [ 0, 0, 1/4, 1/4, 1/4, 0, 1/4, 0 ], [ 1/4, 1/4, 0, 0, 1/4, 0, 1/4, 0 ], [ 1/4, 1/4, 0, 0, 0, 1/4, 0, 1/4 ],
  [ 0, 1/4, 1/4, 0, 0, 1/2, 0, 0 ], [ 1/4, 0, 0, 1/4, 1/2, 0, 0, 0 ], [ 0, 1/4, 1/4, 0, 0, 0, 1/2, 0 ], [ 1/4, 0, 0, 1/4, 0, 0, 0, 1/2 ] ]);

  AssertEqual(MarkovOperator(AutomatonSemigroup("c=(c,d)[1,1],d=(c,c)(1,2)"),3,[1/3,2/3]),
[ [ 1/3, 0, 0, 0, 2/3, 0, 0, 0 ], [ 1/3, 0, 0, 0, 2/3, 0, 0, 0 ], [ 0, 1/3, 0, 0, 0, 2/3, 0, 0 ], [ 1/3, 0, 0, 0, 2/3, 0, 0, 0 ],
[ 2/3, 0, 1/3, 0, 0, 0, 0, 0 ], [ 2/3, 0, 1/3, 0, 0, 0, 0, 0 ], [ 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ]);

end);