Here's what rhymes with problemei.
my nigh mai muy nai mei lanai by high why die lie thy y buy guy tie vi hi shy sigh bi bye chi dye fi hy pi pie thai thigh vie dei ly psi quae rye ty wir awry hai lye wry cy fy kai lai luy sy tai thei untie wai phi amebae apply dry try cry fly sky deny occupy rely spy fry ply sly alibi amplify pry ratify tri trie lullaby pri pupae terrify amoebae sty aquae bonsai deify stye drachmai slier supply reply imply nearby comply modify alkali defy verify certify glorify gratify purify underlie nullify pacify unify belie decry termini typify edify mollify overlie ramify ossify preoccupy retry spry stratify triply ultrahigh blowfly horrify petrify turfy barfly mummify prettify shanghai vitrify beatify ripply banzais overbuy yuppify thereby justify satisfy stimuli whereby clarify hereby nuclei qualify specify classify simplify testify butterfly goodbye notify alveoli magnify rectify samurai beautify falsify codify crucify descry dignify liquefy resupply vilify dragonfly electrify firefly stultify calcify reunify stupefy liquify overfly scarify scurfy versify gentrify speechify dandify identify multiply signify diversify fortify standby solidify mortify personify acidify detoxify mystify vivify emulsify misapply cumuli dissatisfy declassify hyperbolae refortify syllabify exemplify intensify quantify disqualify indemnify objectify oversupply demystify reclassify revivify transmogrify solemnify oversimplify misidentify