WORST_CASE(?,O(n^1))
* Step 1: UnreachableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. zip3(A,B,C)   -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1)
          1. group3(A,B,C) -> group3(-3 + A,B,C)         [A >= 4]                     (?,1)
          2. start(A,B,C)  -> zip3(A,B,C)                True                         (1,1)
        Signature:
          {(group3,3);(start,3);(zip3,3)}
        Flow Graph:
          [0->{0},1->{1},2->{0}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        The following transitions are not reachable from the starting states and are removed: [1]
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. zip3(A,B,C)  -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1)
          2. start(A,B,C) -> zip3(A,B,C)                True                         (1,1)
        Signature:
          {(group3,3);(start,3);(zip3,3)}
        Flow Graph:
          [0->{0},2->{0}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, 1 + A, .+ 1) (<0,0,B>, 1 + B, .+ 1) (<0,0,C>, 1 + C, .+ 1) 
          (<2,0,A>,     A, .= 0) (<2,0,B>,     B, .= 0) (<2,0,C>,     C, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. zip3(A,B,C)  -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1)
          2. start(A,B,C) -> zip3(A,B,C)                True                         (1,1)
        Signature:
          {(group3,3);(start,3);(zip3,3)}
        Flow Graph:
          [0->{0},2->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) 
          (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) 
* Step 4: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. zip3(A,B,C)  -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1)
          2. start(A,B,C) -> zip3(A,B,C)                True                         (1,1)
        Signature:
          {(group3,3);(start,3);(zip3,3)}
        Flow Graph:
          [0->{0},2->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) 
          (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(start) = x1
           p(zip3) = x1
        
        The following rules are strictly oriented:
        [A >= 1 && B >= 1 && C >= 1] ==>                           
                         zip3(A,B,C)   = A                         
                                       > -1 + A                    
                                       = zip3(-1 + A,-1 + B,-1 + C)
        
        
        The following rules are weakly oriented:
                  True ==>            
          start(A,B,C)   = A          
                        >= A          
                         = zip3(A,B,C)
        
        
* Step 5: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. zip3(A,B,C)  -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (A,1)
          2. start(A,B,C) -> zip3(A,B,C)                True                         (1,1)
        Signature:
          {(group3,3);(start,3);(zip3,3)}
        Flow Graph:
          [0->{0},2->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) 
          (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))