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This will determine whether or not u=v= R-related to 1.ISis NOTYour word u Your word v The words u and v are EQUAL in M. Stack: Remaining= State=:Step You will see the attempt to read u in SC(1) step-by-step.Enter the word u which you wish to try to read in SC(1). Next (or num of steps): but not all of u. Therefore, u is not R-related to 1. letters of u can be read in SC(1), The first u is equivalent to 1 under Green's R-relation.Therefore, u is NOT >= 1. However, this does mean . attained is not the accept state, All of u can be read inside SC(1), but the final state SC(1) accepts u. Therefore, u = 1.Your monoid is M=graph of 1: the language of geodesic words in the Schutzenberger The following is the cone type automaton. It recognizes Welcome to 'spar'. This program computes the PDA associated with the Schutzenberger complex of 1 for inverse monoids of the form M=Inv, where w is a sparse word, and allows you to test whether words are accepted by this PDA. (Note: When this program asks for input, you may respond with ? or 'help' to get more information on what kind of response is required. Also, you may run this program by giving operands and commands on the command line and in files; type 'spar help' at the command line for more information.) Enter your relator w: If you wish to stop this program, enter quit .at least 2. Please enter a sparse relator of length , has length Your relator, relator.Please enter a cyclically reduced and sparse , is not cyclically reduced. overlaps itself., is not sparse because the pointed piece overlap. and , is not sparse because the pointed pieces Please enter a sparse relator..M=Inv, w= I have computed the Schutzenberger complex of 1 for What next (1:list,2:u>=1,3:u=v,4:geo,8:newrel,9:quit)? 981234--helpCommands for spar operands/commandsUsage: |sparconf.spar)Too few arguments (Bad command: Bad argument: Final operand list:-list-showitempos2 > len2n > max_size ()pos > length ()pos > lenlen - n1 > max_size () - n2out of memoryInput a word, such as abABcdCD. Use upper-/lowercase letters for the inverses of their lower-/uppercase counterparts (a^-1=A, A^-1=a, etc.). You may enter 1, eps, epsilon, or nothing to specify the empty word.Enter an integer number of steps to perform (letters to read) before I stop and ask you again. The