# regular languages – Simplify \$R:=0^*+0^*1left(1+000^*1right)^*0^*\$

I’m trying to simplify the following REGEX:

$$R:=0^*+0^*1left(1+000^*1right)^*0^*$$

$$R$$ is the result of transforming a GNFA that recognizes $$L:= {w in {0,1}^* | left(forall i in left(1,|w|-2right)cap mathbb{N}right) w_iw_{i+1}w_{i+2} neq 101}$$

I already know that there exists $$R’:=0^*left(1+000^*1right)^*0^*$$ such that $$L(R)=L(R’)=L$$

Any hints?