Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that rigid reachability, the non-symmetric form of rigid E-unification, is undecidable already in the case of a single constraint. From this  infer the undecidability of a new rather restricted kind of second-order unification.  also show that certain decidable subclasses of the problem which are ρ-complete in the equational case become EXPTIME-complete when symmetry is absent. By applying automata-theoretic methods, simultaneous monadic rigid reachability with ground rules is shown to be in EXPTIME.
['Harald Ganzinger', 'Florent Jacquemard', 'Margus Veanes']
I am writing a research paper on a idea Rigid Reachability
[{"from": "human", "value": "I am writing a research paper on a idea Rigid Reachability"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that rigid reachability, the non-symmetric form of rigid E-unification, is undecidable already in the case of a single constraint. From this  infer the undecidability of a new rather restricted kind of second-order unification.  also show that certain decidable subclasses of the problem which are \u03c1-complete in the equational case become EXPTIME-complete when symmetry is absent. By applying automata-theoretic methods, simultaneous monadic rigid reachability with ground rules is shown to be in EXPTIME."}]