YES
* Step 1: UnsatRules YES
    + Considered Problem:
        Rules:
          0. eval(A,B)  -> eval(-1 + A,B) [A + B >= 1 && A >= 1 + B]           (?,1)
          1. eval(A,B)  -> eval(-1 + A,B) [2*A >= 1 && B = A]                  (?,1)
          2. eval(A,B)  -> eval(A,-1 + B) [A + B >= 1 && B >= A && B >= 1 + A] (?,1)
          3. eval(A,B)  -> eval(A,-1 + B) [A + B >= 1 && B >= A && A >= 1 + B] (?,1)
          4. start(A,B) -> eval(A,B)      True                                 (1,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{0,1,2,3},4->{0,1,2,3}]
        
    + Applied Processor:
        UnsatRules
    + Details:
        Following transitions have unsatisfiable constraints and are removed:  [3]
* Step 2: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. eval(A,B)  -> eval(-1 + A,B) [A + B >= 1 && A >= 1 + B]           (?,1)
          1. eval(A,B)  -> eval(-1 + A,B) [2*A >= 1 && B = A]                  (?,1)
          2. eval(A,B)  -> eval(A,-1 + B) [A + B >= 1 && B >= A && B >= 1 + A] (?,1)
          4. start(A,B) -> eval(A,B)      True                                 (1,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{0,1,2},1->{0,1,2},2->{0,1,2},4->{0,1,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(1,0),(1,1),(2,0)]
* Step 3: FromIts YES
    + Considered Problem:
        Rules:
          0. eval(A,B)  -> eval(-1 + A,B) [A + B >= 1 && A >= 1 + B]           (?,1)
          1. eval(A,B)  -> eval(-1 + A,B) [2*A >= 1 && B = A]                  (?,1)
          2. eval(A,B)  -> eval(A,-1 + B) [A + B >= 1 && B >= A && B >= 1 + A] (?,1)
          4. start(A,B) -> eval(A,B)      True                                 (1,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{0,1},1->{2},2->{1,2},4->{0,1,2}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 4: Decompose YES
    + Considered Problem:
        Rules:
          eval(A,B)  -> eval(-1 + A,B)  [A + B >= 1 && A >= 1 + B]
          eval(A,B)  -> eval(-1 + A,B)  [2*A >= 1 && B = A]
          eval(A,B)  -> eval(A,-1 + B)  [A + B >= 1 && B >= A && B >= 1 + A]
          start(A,B) -> eval(A,B)       True
        Signature:
          {(eval,2);(start,2)}
        Rule Graph:
          [0->{0,1},1->{2},2->{1,2},4->{0,1,2}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,4]
          |
          +- p:[0] c: [0]
          |
          `- p:[1,2] c: [1,2]
* Step 5: CloseWith YES
    + Considered Problem:
        (Rules:
          eval(A,B)  -> eval(-1 + A,B)  [A + B >= 1 && A >= 1 + B]
          eval(A,B)  -> eval(-1 + A,B)  [2*A >= 1 && B = A]
          eval(A,B)  -> eval(A,-1 + B)  [A + B >= 1 && B >= A && B >= 1 + A]
          start(A,B) -> eval(A,B)       True
        Signature:
          {(eval,2);(start,2)}
        Rule Graph:
          [0->{0,1},1->{2},2->{1,2},4->{0,1,2}]
        ,We construct a looptree:
          P: [0,1,2,4]
          |
          +- p:[0] c: [0]
          |
          `- p:[1,2] c: [1,2])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES