A computational complexity of decision procedure for the intuitionistic logic without weakening rule

Non-classical logics have been studied to realize some logics we use in our everyday lives, and have something to do with the resource problem in Computer Science. In this paper we discuss such non-classical logics from viewpoints of decidability and computational complexity. We deal with a system FLec in Gentzen-type sequent calculus (LJ) without the weakening rule, which is also an intutionistic relevant logic without distributive law. We proved in our previous paper that the propositional logic FLec is decidable in a non-constructive way. In the present paper we give an upper bound for the decision procedure by using McAloon’s ideas