YES
* Step 1: UnsatRules YES
    + Considered Problem:
        Rules:
          0. eval(A,B)  -> eval(A + -1*B,B) [A >= 1 + B && A >= 1 && B >= 1]               (?,1)
          1. eval(A,B)  -> eval(A + -1*B,B) [B >= 1 + A && A >= 1 && B >= 1 && A >= 1 + B] (?,1)
          2. eval(A,B)  -> eval(A,-1*A + B) [A >= 1 + B && A >= 1 && B >= 1 && B >= A]     (?,1)
          3. eval(A,B)  -> eval(A,-1*A + B) [B >= 1 + A && A >= 1 && B >= 1 && B >= A]     (?,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:  [1,2]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. eval(A,B)  -> eval(A + -1*B,B) [A >= 1 + B && A >= 1 && B >= 1]           (?,1)
          3. eval(A,B)  -> eval(A,-1*A + B) [B >= 1 + A && A >= 1 && B >= 1 && B >= A] (?,1)
          4. start(A,B) -> eval(A,B)        True                                       (1,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{0,3},3->{0,3},4->{0,3}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          eval(A,B)  -> eval(A + -1*B,B)  [A >= 1 + B && A >= 1 && B >= 1]
          eval(A,B)  -> eval(A,-1*A + B)  [B >= 1 + A && A >= 1 && B >= 1 && B >= A]
          start(A,B) -> eval(A,B)         True
        Signature:
          {(eval,2);(start,2)}
        Rule Graph:
          [0->{0,3},3->{0,3},4->{0,3}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,3,4]
          |
          `- p:[0,3] c: [3]
             |
             `- p:[0] c: [0]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          eval(A,B)  -> eval(A + -1*B,B)  [A >= 1 + B && A >= 1 && B >= 1]
          eval(A,B)  -> eval(A,-1*A + B)  [B >= 1 + A && A >= 1 && B >= 1 && B >= A]
          start(A,B) -> eval(A,B)         True
        Signature:
          {(eval,2);(start,2)}
        Rule Graph:
          [0->{0,3},3->{0,3},4->{0,3}]
        ,We construct a looptree:
          P: [0,3,4]
          |
          `- p:[0,3] c: [3]
             |
             `- p:[0] c: [0])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES