First, generally on interpretation of association rules.
0.3 0.7 18x0 -> trt1
Assuming that 0.3 is support and 0.7 confidence, then the rule is to be read as variable 18x with value 0 (i.e. item 18x0) is with 70% probability associated with item trt1. In other words, 70% of transactions containing item 18x0 also contain item trt1. The support says that 30% of all transactions in the data match both sides of this rule.
Note that there are no requirements on the values of other variables (presence of other items) apart from item 18x0 for this rule to be applied to an instance (a new transaction).
Now to the core of your question.
Considering a pure implementation of the apriori algorithm , what does it mean that there is no rule as follows on the output?
18x0 17x0 -> trt1
In my opinion this should be indeed interpreted so that this rule is not supported by your data observing parameters that you had to specify: the minimum confidence threshold and minimum support threshold. The apriori algorithm generates all rules meeting these criteria.
The absence of such rule can mean that there is not any transaction containing 18x0, 17x0 and trt1. But there can also be such transaction in the data, or even multiple of them, but the corresponding rule does not meet the thresholds. For example, the number of transactions matching the rule can be lower than required by the minimum support threshold.
 Agrawal, Rakesh, and Ramakrishnan Srikant. "Fast algorithms for mining association rules." Proc. 20th int. conf. very large data bases, VLDB. Vol. 1215. 1994.