Cyclic logic encryption is a newly proposed circuit obfuscation technique in hardware security. It was claimed to be SAT-unresolvable because feedback cycles were intentionally inserted under keys into the encryption. We show in the paper that even though feedback cycles introduce extra difficulty for an attacker, they can still be overcome with SAT- based techniques. Specifically, we propose CycSAT Algorithms based on SAT with different acyclic conditions that can efficiently decrypt cyclic encryptions. Experimental results have shown that our CycSAT is efficient and effective to decrypt cyclic encryptions, and we need to develop new encryptions with better security properties.