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

YES