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?