YES
* Step 1: FromIts YES
    + Considered Problem:
        Rules:
          0. eval1(A,B,C) -> eval2(A,B,C)      [A >= 1 + B]                                     (?,1)
          1. eval2(A,B,C) -> eval2(A,B,-1 + C) [-1 + A + -1*B >= 0 && A >= 1 + B && C >= 1 + B] (?,1)
          2. eval2(A,B,C) -> eval1(-1 + A,B,C) [-1 + A + -1*B >= 0 && A >= 1 + B && B >= C]     (?,1)
          3. start(A,B,C) -> eval1(A,B,C)      True                                             (1,1)
        Signature:
          {(eval1,3);(eval2,3);(start,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{0},3->{0}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 2: Decompose YES
    + Considered Problem:
        Rules:
          eval1(A,B,C) -> eval2(A,B,C)       [A >= 1 + B]
          eval2(A,B,C) -> eval2(A,B,-1 + C)  [-1 + A + -1*B >= 0 && A >= 1 + B && C >= 1 + B]
          eval2(A,B,C) -> eval1(-1 + A,B,C)  [-1 + A + -1*B >= 0 && A >= 1 + B && B >= C]
          start(A,B,C) -> eval1(A,B,C)       True
        Signature:
          {(eval1,3);(eval2,3);(start,3)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{0},3->{0}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[0,2,1] c: [0,2]
             |
             `- p:[1] c: [1]
* Step 3: CloseWith YES
    + Considered Problem:
        (Rules:
          eval1(A,B,C) -> eval2(A,B,C)       [A >= 1 + B]
          eval2(A,B,C) -> eval2(A,B,-1 + C)  [-1 + A + -1*B >= 0 && A >= 1 + B && C >= 1 + B]
          eval2(A,B,C) -> eval1(-1 + A,B,C)  [-1 + A + -1*B >= 0 && A >= 1 + B && B >= C]
          start(A,B,C) -> eval1(A,B,C)       True
        Signature:
          {(eval1,3);(eval2,3);(start,3)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{0},3->{0}]
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[0,2,1] c: [0,2]
             |
             `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES