"Search" has been the name for the A* space. So it makes absolute sense.
"Planning" means in the symbolic AI space often something quite in the direction of PDDL/STRIPS/ICAPS planning.
T1* and T2* are common terms in magnetic nuclear resonance imaging, suggesting Tn* for any integer n should be free of bullshit IP protection. May I thus suggest T10*, following the pattern of a11y and i18n?