Here's what rhymes with brainmechanism.
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mizzen commission mission rhythm arisen risen given addition condition vision edition listen permission prison admission ambition cognition collision emission omission fission audition riven position driven physician petition coalition incision submission clinician forgiven ignition remission attrition derision magician apposition contrition envision imprison stiffen glisten decision definition division opposition tradition provision recognition transition acquisition algorithm suspicion abolition ammunition exhibition intuition nutrition partition revision excision musician supposition tuition admonition apparition circumcision erudition fruition sedition technician volition dentition intermission logarithm patrician rendition striven cataclysm logician manumission academician dietitian ebullition munition readmission rescission tactician competition composition television transmission expedition precision repetition supervision deposition exposition inhibition politician prohibition imposition demolition mathematician requisition indecision inquisition paroxysm precondition premonition rhetorician theoretician imprecision prevision disposition proposition decomposition superstition subdivision preposition extradition interposition presupposition redefinition disquisition electrician juxtaposition malnutrition predisposition transposition indisposition superposition obstetrician pediatrician statistician diagnostician superimposition wisdom serum theorem cecum gingham system kingdom victim dictum gypsum fearsome winsome symptom pilgrim ecosystem