YES
* Step 1: Looptree YES
    + Considered Problem:
        Rules:
          0. start(A) -> eval(A)        True                      (1,1)
          1. eval(A)  -> eval(-2 + 2*B) [2*B >= 0 && A = 1 + 2*B] (?,1)
        Signature:
          {(eval,1);(start,1)}
        Flow Graph:
          [0->{1},1->{1}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1]
          |
          `- p:[1] c: [1]

YES