Learn English – Usage of “but” as preposition

Here is a long article that goes over a great deal of the use of gerunds vs infinitives and Wikipedia has some information as well. In short, it is not a simple answer, but there are rules to follow, and many instances where both work fine, but the meaning can change depending on which you use. In reference to the list you supplied, verbs of communication (acknowledge, admit, accuse, advise) tend to take the gerund (but not always - advise for example - advised against entering vs advised not to enter). Some just take an infinitive for no real reason other than there had to be a rule to govern them (arrange, afford, appear, agree). Some verbs can take either (love, prefer, like) but the meaning changes drastically (I love boxing vs I love to box).

There are quite a lot of verb + preposition combinations able to take an -ing form, and rely on is certainly a commonly used example. Though it might be argued that the actual -ing form used should be called a gerund, it would be less contentious to simply call it an -ing form (somewhere along the verb - noun cline). Thus We can rely on him going / We can rely on his going are both acceptable, as are we must gamble on their finishing the bridge / we must gamble on rapidly finishing the bridge.

However, now you've told us you've replaced the original word 'emulation', it becomes clear that this (verb + preposition + -ing form) isn't the construction involved. The original 'emulation' was correct - it's being used as a noun-modifier (ie adjectivally) here.