YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. start(A,B) -> eval(A,B) True         (1,1)
          1. eval(A,B)  -> eval(B,A) [A >= 1 + B] (?,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{1},1->{1}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(1,1)]
* Step 2: Looptree YES
    + Considered Problem:
        Rules:
          0. start(A,B) -> eval(A,B) True         (1,1)
          1. eval(A,B)  -> eval(B,A) [A >= 1 + B] (?,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{1},1->{}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1]

YES