Let
bbab + ba - 1 = r
bbaa + bbb + a = s

Then 
-ba + ab = -7baabrbabbab + 7baabbbarbab - 3brbabbaabb - 3brbabbaaba + 3bbbarbaabb + 3bbbarbaaba + 4barbababab + barbababaa - 4babbarabab - babbarabaa - 4babarbabab - babarbabaa + 4bababbarab + bababbaraa - 3brbabbbbb - 3brbabbbba - brbabbaab - 4brbabbaaa + 3bbbarbbbb + 3bbbarbbba + bbbarbaab + 4bbbarbaaa + 4barbababb + 3barbababa + 4babrbaaab + babrbaaaa - 4babbbasab - babbbasaa - 4babbarabb - 3babbaraba - 4babarbabb - 3babarbaba + 4bababbarb + 3bababbara + 7baarabbab - 7baabrbaba - 7baabrabab + 7baabbbara + 3abrbabbab - abrbabbaa - 3abbbarbab + abbbarbaa + 4rbabbaab + rbabbaaa - 4rbaaabab - rbaaabaa + 3rabbaabb + 3rabbaaba - brbabbbb - 4brbabbba + 3brbabbaa + 4brbabaab + brbabaaa + 7brbaabab - 3brabaabb - 3brabaaba + 2bbrbabab + 7bbrbabaa + 3bbrbaabb + 3bbrbaaba - bbbrbabb - 3bbbbrbab - 3bbbbrbaa + 3bbbbbbas + 3bbbbbbar + bbbbbarb - 3bbbbasbb - 3bbbbasba - 2bbbbarab - 7bbbbaraa - 7bbbasbab + bbbarbbb + 4bbbarbba - 2bbbarbab - 10bbbarbaa - 4bbbaraab - bbbaraaa + 7bbbabbas + 2bbbabbar + 4bbasabab + bbasabaa - 4bbarbaab - bbarbaaa + 11barbabab + 4barbaaab + barbaaaa + 4baraabab + baraabaa + 4babrbbab + babrbbaa + 9babrbaab + 3babrbaaa - 5babbrbaa + 5babbbbas - 9babbbasb - 3babbbasa - 4babbasab - babbasaa - 11babbarab - 11babarbab - 4babaraab - babaraaa + 11bababbar - abrbabbb + abbbarbb - 4rbbabab - rbbabaa + 2rbabbaa - rbababb + 3rbababa + 2rbabaab + 5rbabaaa - 4rbaaabb - 3rbaaaba + 4rbaaaab + rbaaaaa + 3rabbbbb + 3rabbbba + rabbaab + 4rabbaaa + 7brbbbab + 3brbabbb - 4brbabab + 8brbabaa - 4brbaabb + 2brbaaab + 5brbaaaa - 3brabbbb - 3brabbba - brabaab - 4brabaaa + 3bbrbbbb + 3bbrbbba + 10bbrbabb + bbrbaab + 4bbrbaaa + 6bbbrbab + 5bbbrbaa - 3bbbbrbb - 5bbbbbas - 6bbbbbar - bbbbasb - 4bbbbasa - 10bbbbarb + 4bbbasbb - 2bbbasab - 5bbbasaa - 10bbbarbb + 4bbbarab - 8bbbaraa + 4bbasabb + 3bbasaba - 4bbasaab - bbasaaa - 2bbarbaa + bbarabb - 3bbaraba - 2bbaraab - 5bbaraaa + 4barbbab + barbbaa + barbabb - 3barbaba + 2barbaab - 2barbaaa + 4baraabb + 3baraaba - 4baraaab - baraaaa + 9babrbbb + 3babrbba + 7babrbab + 10babrbaa - 5babbrbb - 10babbbas - 7babbbar - 2babbasb + 2babbasa - babbarb + 3babbara - 4babarab - 3babaraa + 7baasbab - 7baarbab + 7baaraba + 7baabrab - 7baabraa - 7baabaar - 3arabbab + arabbaa + 3abrbabb + 6abrbaba + 3abrabab - abrabaa - 3abbbarb - 6abbbara + 3sbaabb + 3sbaaba - 4rbbabb - 3rbbaba + 4rbbaab + rbbaaa - 2rbabbb + 13rbabba - 5rbabab + 10rbabaa - 3rbaabb - 3rbaaba - 2rbaaab + 3rbaaaa + rabbbb + 4rabbba - 3rabbaa - 7raabab - 4brbbbb + 2brbbab + 5brbbaa + 4brbabb + 20brbaba - 9brbaab + 14brbaaa - brabbb - 4brabba + 3brabaa + 4braaab + braaaa + bbrbbb + 4bbrbba + bbrbab + 8bbrbaa + bbrabb + 2bbraab + 7bbraaa + 5bbbrbb + 2bbbrab + 3bbbraa - 3bbbbra - 8bbbbas - bbbbar + 9bbbasb - 14bbbasa - 4bbbarb - 22bbbara + 2bbasab - 3bbasaa + 2bbarbb - 13bbarba + 5bbarab - 10bbaraa - 4basbab - basbaa + 2barbbb - 2barbba + 5barbab + barbaa + 2baraab - 3baraaa + 4babsab + babsaa + 10babrbb + 5babraa - 2babbas - 9babbar - 11babara - 3baasbb - 3baasba - 7baabbr + arabbb + abrbab + 3abrbaa - abrabb - 3abbbas - abbbar + 3sbbbb + 3sbbba + sbaab + 4sbaaa - 4sabab - sabaa - 3rbbbb - 3rbbba - 9rbbab + 3rbbaa + 7rbabb + 3rbaba - 3rbaab + 7rbaaa - 3rabbb + 4rabab - 6rabaa + 3raabb + 3raaba + 7bsbab - 9brbbb + 14brbba + 4brbab + brbaa - 4braab + 8braaa + 8bbrbb + 4bbrab - 5bbraa + 3bbbrb + 6bbbra - 3bbbbs - 8bbbas - 4bbbar + 2bbasb - 11bbasa - 7bbarb - 3bbara - 4basbb - 3basba + 8basab + 2basaa - 7barbb - 3barba - 2barab - 12baraa + 9babsb + 3babsa + 5babrb + 7babra - 5babbs - 8baasb + 3baasa - 7baara + 7baabs + 7baaar - 3asbab + asbaa + 3arbab - arbaa - 3arabb - 6araba + 3abrbb + 7abraa - abaas + 3abaar + sbbb + 4sbba + 7sbab - 3sbaa - 4sabb - 3saba + rbbb + 7rbba - 10rbab - 7rbaa - 6rabb - 7raba + 4raab - 4raaa - 2bsbb + 3bsba - 4bsab - 3bsaa + 8brbb + 2brba + 7brab + 12braa - 4bbsb - 10bbsa - 6bbrb + bbra + 5bbbs - 9bbbr + 5bbas + 8bbar - 4basa - 6barb + 12bara + 4babs - 4babr + 3baas + 4asbb + 3asba - arbb - arab - 3araa + abrb + abra - abbs + 3abbr - 3sbb - 3sba + 2sab - 5saa + 7rbb - 14rba - 5rab + 7raa - 8bsb + 15bsa - 4brb + 7bra + 13bbs - 3bbr + 8bas + 14bar + asb - 3asa + 6ara - 3abs - 3abr + aas - 3aar - 7sb + 11sa - 5rb - 6ra + 6bs + 5br - as - 6s