Which alcohol produces more alkenes through E1 mechanism?

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[tex]\alpha[/tex]-terpineol produces four different alkene products (including imonene) when it is dehydrated via E1 mechanism.
On the other hand, 2-methylcyclohexanol produces two different alkenes through E1 mechanism.

Which of these product do you think would be formed in the greatest amount? I personally think 2-methylcyclohexanol will be formed in larger amount. Here's my explanation:2-methylcyclohexanol has more product since alpha-terpineol might have more side reactions during dehydrations. (carbocation+alcohol --> ether / carbocation+alkene --> plymeric alkene)

I am not completely sure. What do you think? Alpha-terpineol or 2-methylcyclohexanol?
 

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Am I misunderstanding the question or are you: it sounds like it's asking, "Which of the alkene products of the dehydration of 2-methylcyclohexanol would be formed in the largest proportion?"

Carbocation + alcohol -(acid)-> ether? possible..

carbocation + alkene -(acid)-> polymeric alkene? maybe...

I don't think either of those two proposed reactions are relevant here. If I were you, I'd consider the thermodynamic stabilities of all the alkene products to determine which one is formed in greatest quantity.
 
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Carbocation + alcohol -(acid)-> ether?

carbocation + alkene -(acid)-> polymeric alkene?
They wre just an example of the side reactions that could occur. Those reactions might disturb the yield. Thank you for your advice. :)