YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. start(A,B) -> eval(A,B)      True               (1,1)
          1. eval(A,B)  -> eval(A,-1 + B) [B >= 1 && 0 >= A] (?,1)
          2. eval(A,B)  -> eval(-1 + A,B) [B >= 1 && A >= 1] (?,1)
          3. eval(A,B)  -> eval(-1 + A,B) [A >= 1]           (?,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{1,2,3}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(1,2),(1,3)]
* Step 2: Looptree YES
    + Considered Problem:
        Rules:
          0. start(A,B) -> eval(A,B)      True               (1,1)
          1. eval(A,B)  -> eval(A,-1 + B) [B >= 1 && 0 >= A] (?,1)
          2. eval(A,B)  -> eval(-1 + A,B) [B >= 1 && A >= 1] (?,1)
          3. eval(A,B)  -> eval(-1 + A,B) [A >= 1]           (?,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{1,2,3},1->{1},2->{1,2,3},3->{1,2,3}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          +- p:[2,3] c: [3]
          |  |
          |  `- p:[2] c: [2]
          |
          `- p:[1] c: [1]

YES