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We prove that a group has word problem that is a growing contextsensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and Shapiro in ). We generalise results of  to find many examples of groups not admitting non-deterministic Cannon's algorithms. This adds to the examples of Kambites and Otto in  of groups separating context-sensitive and growing contextsensitive word problems,doi:10.1142/s0218196708004834 pmid:19997524 pmcid:PMC2789434 fatcat:epgfqrvulfexfbtua4fldbkp5i