YES(?,O(n^1))
* Step 1: UnsatRules WORST_CASE(?,O(n^1))
    + 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: PolyRank WORST_CASE(?,O(n^1))
    + 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:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(eval) = x2
          p(start) = x2
        
        Following rules are strictly oriented:
        [B >= 1 + A && A >= 1 && B >= 1 && B >= A] ==>                 
                                         eval(A,B)   = B               
                                                     > -1*A + B        
                                                     = eval(A,-1*A + B)
        
        
        Following rules are weakly oriented:
        [A >= 1 + B && A >= 1 && B >= 1] ==>                 
                               eval(A,B)   = B               
                                          >= B               
                                           = eval(A + -1*B,B)
        
                                    True ==>                 
                              start(A,B)   = B               
                                          >= B               
                                           = eval(A,B)       
        
        
* Step 3: PolyRank WORST_CASE(?,O(n^1))
    + 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] (B,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:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(eval) = x1
          p(start) = x1
        
        Following rules are strictly oriented:
        [A >= 1 + B && A >= 1 && B >= 1] ==>                 
                               eval(A,B)   = A               
                                           > A + -1*B        
                                           = eval(A + -1*B,B)
        
        
        Following rules are weakly oriented:
        [B >= 1 + A && A >= 1 && B >= 1 && B >= A] ==>                 
                                         eval(A,B)   = A               
                                                    >= A               
                                                     = eval(A,-1*A + B)
        
                                              True ==>                 
                                        start(A,B)   = A               
                                                    >= A               
                                                     = eval(A,B)       
        
        
* Step 4: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B)  -> eval(A + -1*B,B) [A >= 1 + B && A >= 1 && B >= 1]           (A,1)
          3. eval(A,B)  -> eval(A,-1*A + B) [B >= 1 + A && A >= 1 && B >= 1 && B >= A] (B,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:
        KnowledgePropagation
    + Details:
        The problem is already solved.

YES(?,O(n^1))