YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. eval1(A,B,C) -> eval2(A,B,C)           [A >= 1 + B && C = A]                          (?,1)
          1. eval2(A,B,C) -> eval2(-1 + A,B,-1 + C) [A + -1*C >= 0 && -1*A + C >= 0 && A >= 1 + B] (?,1)
          2. eval2(A,B,C) -> eval1(A,B,C)           [A + -1*C >= 0 && -1*A + C >= 0 && B >= A]     (?,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:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(2,0)]
* Step 2: Looptree YES
    + Considered Problem:
        Rules:
          0. eval1(A,B,C) -> eval2(A,B,C)           [A >= 1 + B && C = A]                          (?,1)
          1. eval2(A,B,C) -> eval2(-1 + A,B,-1 + C) [A + -1*C >= 0 && -1*A + C >= 0 && A >= 1 + B] (?,1)
          2. eval2(A,B,C) -> eval1(A,B,C)           [A + -1*C >= 0 && -1*A + C >= 0 && B >= A]     (?,1)
          3. start(A,B,C) -> eval1(A,B,C)           True                                           (1,1)
        Signature:
          {(eval1,3);(eval2,3);(start,3)}
        Flow Graph:
          [0->{1},1->{1,2},2->{},3->{0}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1]

YES