WORST_CASE(?,O(n^1))
* Step 1: UnreachableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eq(A,B,C,D)      -> eq(-1 + A,-1 + B,C,D)                 [A >= 1 && B >= 1]     (?,1)
          1. nub0(A,B,C,D)    -> remove(A,-1 + B,C,D)                  True                   (?,1)
          2. nub1(A,B,C,D)    -> nub(C,D,C,D)                          True                   (?,1)
          3. nub(A,B,C,D)     -> c2(nub0(F,A,E,B),nub1(F,A,E,B))       [A >= 1 && A >= 1 + E] (?,1)
          4. remove0(A,B,C,D) -> eq(A,B,C,D)                           True                   (?,1)
          5. remove1(A,B,C,D) -> remove(A,-1 + D,C,B)                  True                   (?,1)
          6. remove(A,B,C,D)  -> c2(remove0(A,D,C,B),remove1(A,D,C,B)) [B >= 1]               (?,1)
          7. remove(A,B,C,D)  -> remove(A,-1 + B,C,D)                  [B >= 1]               (?,1)
          8. start(A,B,C,D)   -> eq(A,B,C,D)                           True                   (1,1)
        Signature:
          {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)}
        Flow Graph:
          [0->{0},1->{6,7},2->{3},3->{1,2},4->{0},5->{6,7},6->{4,5},7->{6,7},8->{0}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        The following transitions are not reachable from the starting states and are removed: [1,2,3,4,5,6,7]
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eq(A,B,C,D)    -> eq(-1 + A,-1 + B,C,D) [A >= 1 && B >= 1] (?,1)
          8. start(A,B,C,D) -> eq(A,B,C,D)           True               (1,1)
        Signature:
          {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)}
        Flow Graph:
          [0->{0},8->{0}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, 1 + A, .+ 1) (<0,0,B>, 1 + B, .+ 1) (<0,0,C>, C, .= 0) (<0,0,D>, D, .= 0) 
          (<8,0,A>,     A, .= 0) (<8,0,B>,     B, .= 0) (<8,0,C>, C, .= 0) (<8,0,D>, D, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eq(A,B,C,D)    -> eq(-1 + A,-1 + B,C,D) [A >= 1 && B >= 1] (?,1)
          8. start(A,B,C,D) -> eq(A,B,C,D)           True               (1,1)
        Signature:
          {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)}
        Flow Graph:
          [0->{0},8->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<0,0,D>, ?) 
          (<8,0,A>, ?) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, C) (<0,0,D>, D) 
          (<8,0,A>, A) (<8,0,B>, B) (<8,0,C>, C) (<8,0,D>, D) 
* Step 4: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eq(A,B,C,D)    -> eq(-1 + A,-1 + B,C,D) [A >= 1 && B >= 1] (?,1)
          8. start(A,B,C,D) -> eq(A,B,C,D)           True               (1,1)
        Signature:
          {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)}
        Flow Graph:
          [0->{0},8->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, C) (<0,0,D>, D) 
          (<8,0,A>, A) (<8,0,B>, B) (<8,0,C>, C) (<8,0,D>, D) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
             p(eq) = x2
          p(start) = x2
        
        The following rules are strictly oriented:
        [A >= 1 && B >= 1] ==>                      
               eq(A,B,C,D)   = B                    
                             > -1 + B               
                             = eq(-1 + A,-1 + B,C,D)
        
        
        The following rules are weakly oriented:
                    True ==>            
          start(A,B,C,D)   = B          
                          >= B          
                           = eq(A,B,C,D)
        
        
* Step 5: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eq(A,B,C,D)    -> eq(-1 + A,-1 + B,C,D) [A >= 1 && B >= 1] (B,1)
          8. start(A,B,C,D) -> eq(A,B,C,D)           True               (1,1)
        Signature:
          {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)}
        Flow Graph:
          [0->{0},8->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, C) (<0,0,D>, D) 
          (<8,0,A>, A) (<8,0,B>, B) (<8,0,C>, C) (<8,0,D>, D) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))