YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. eval0(A,B,C) -> eval1(A,B,C)        [A >= 1]                             (1,1)
          1. eval1(A,B,C) -> eval1(A,A + B,C)    [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
          2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
        Signature:
          {(eval0,3);(eval1,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,1),(2,2)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. eval0(A,B,C) -> eval1(A,B,C)        [A >= 1]                             (1,1)
          1. eval1(A,B,C) -> eval1(A,A + B,C)    [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
          2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
        Signature:
          {(eval0,3);(eval1,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          eval0(A,B,C) -> eval1(A,B,C)         [A >= 1]
          eval1(A,B,C) -> eval1(A,A + B,C)     [A >= 1 + B && C >= 1 + A && A >= 1]
          eval1(A,B,C) -> eval1(A,B,-1*A + B)  [A >= 1 + B && C >= 1 + A && A >= 1]
        Signature:
          {(eval0,3);(eval1,3)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2]
          |
          `- p:[1] c: [1]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          eval0(A,B,C) -> eval1(A,B,C)         [A >= 1]
          eval1(A,B,C) -> eval1(A,A + B,C)     [A >= 1 + B && C >= 1 + A && A >= 1]
          eval1(A,B,C) -> eval1(A,B,-1*A + B)  [A >= 1 + B && C >= 1 + A && A >= 1]
        Signature:
          {(eval0,3);(eval1,3)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{}]
        ,We construct a looptree:
          P: [0,1,2]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES