WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B,C,D,E)  -> eval(A,1 + B,C,D,1 + E) [A >= 1 + B && C >= 1 + D] (?,1)
          1. eval(A,B,C,D,E)  -> eval(A,B,C,1 + D,1 + E) [A >= 1 + B && C >= 1 + D] (?,1)
          2. eval(A,B,C,D,E)  -> eval(A,B,C,1 + D,1 + E) [B >= A && C >= 1 + D]     (?,1)
          3. eval(A,B,C,D,E)  -> eval(A,1 + B,C,D,1 + E) [A >= 1 + B && D >= C]     (?,1)
          4. start(A,B,C,D,E) -> eval(A,B,C,D,E)         True                       (1,1)
        Signature:
          {(eval,5);(start,5)}
        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:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [E] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1)
          1. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1)
          2. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D]     (?,1)
          3. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C]     (?,1)
          4. start(A,B,C,D) -> eval(A,B,C,D)     True                       (1,1)
        Signature:
          {(eval,4);(start,4)}
        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:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, A, .= 0) (<0,0,B>, 1 + B, .+ 1) (<0,0,C>, C, .= 0) (<0,0,D>,     D, .= 0) 
          (<1,0,A>, A, .= 0) (<1,0,B>,     B, .= 0) (<1,0,C>, C, .= 0) (<1,0,D>, 1 + D, .+ 1) 
          (<2,0,A>, A, .= 0) (<2,0,B>,     B, .= 0) (<2,0,C>, C, .= 0) (<2,0,D>, 1 + D, .+ 1) 
          (<3,0,A>, A, .= 0) (<3,0,B>, 1 + B, .+ 1) (<3,0,C>, C, .= 0) (<3,0,D>,     D, .= 0) 
          (<4,0,A>, A, .= 0) (<4,0,B>,     B, .= 0) (<4,0,C>, C, .= 0) (<4,0,D>,     D, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1)
          1. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1)
          2. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D]     (?,1)
          3. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C]     (?,1)
          4. start(A,B,C,D) -> eval(A,B,C,D)     True                       (1,1)
        Signature:
          {(eval,4);(start,4)}
        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}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<0,0,D>, ?) 
          (<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?) (<1,0,D>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, ?) 
          (<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, A) (<0,0,B>,     A) (<0,0,C>, C) (<0,0,D>,     C) 
          (<1,0,A>, A) (<1,0,B>,     A) (<1,0,C>, C) (<1,0,D>,     C) 
          (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>,     C) 
          (<3,0,A>, A) (<3,0,B>,     A) (<3,0,C>, C) (<3,0,D>, C + D) 
          (<4,0,A>, A) (<4,0,B>,     B) (<4,0,C>, C) (<4,0,D>,     D) 
* Step 4: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1)
          1. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1)
          2. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D]     (?,1)
          3. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C]     (?,1)
          4. start(A,B,C,D) -> eval(A,B,C,D)     True                       (1,1)
        Signature:
          {(eval,4);(start,4)}
        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}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     A) (<0,0,C>, C) (<0,0,D>,     C) 
          (<1,0,A>, A) (<1,0,B>,     A) (<1,0,C>, C) (<1,0,D>,     C) 
          (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>,     C) 
          (<3,0,A>, A) (<3,0,B>,     A) (<3,0,C>, C) (<3,0,D>, C + D) 
          (<4,0,A>, A) (<4,0,B>,     B) (<4,0,C>, C) (<4,0,D>,     D) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,3),(1,2),(2,0),(2,1),(2,3),(3,0),(3,1),(3,2)]
* Step 5: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1)
          1. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1)
          2. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D]     (?,1)
          3. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C]     (?,1)
          4. start(A,B,C,D) -> eval(A,B,C,D)     True                       (1,1)
        Signature:
          {(eval,4);(start,4)}
        Flow Graph:
          [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     A) (<0,0,C>, C) (<0,0,D>,     C) 
          (<1,0,A>, A) (<1,0,B>,     A) (<1,0,C>, C) (<1,0,D>,     C) 
          (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>,     C) 
          (<3,0,A>, A) (<3,0,B>,     A) (<3,0,C>, C) (<3,0,D>, C + D) 
          (<4,0,A>, A) (<4,0,B>,     B) (<4,0,C>, C) (<4,0,D>,     D) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(eval) = x1 + -1*x2
          p(start) = x1 + -1*x2
        
        The following rules are strictly oriented:
        [A >= 1 + B && D >= C] ==>                  
                 eval(A,B,C,D)   = A + -1*B         
                                 > -1 + A + -1*B    
                                 = eval(A,1 + B,C,D)
        
        
        The following rules are weakly oriented:
        [A >= 1 + B && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = A + -1*B         
                                    >= -1 + A + -1*B    
                                     = eval(A,1 + B,C,D)
        
        [A >= 1 + B && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = A + -1*B         
                                    >= A + -1*B         
                                     = eval(A,B,C,1 + D)
        
            [B >= A && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = A + -1*B         
                                    >= A + -1*B         
                                     = eval(A,B,C,1 + D)
        
                              True ==>                  
                    start(A,B,C,D)   = A + -1*B         
                                    >= A + -1*B         
                                     = eval(A,B,C,D)    
        
        
* Step 6: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1)    
          1. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1)    
          2. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D]     (?,1)    
          3. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C]     (A + B,1)
          4. start(A,B,C,D) -> eval(A,B,C,D)     True                       (1,1)    
        Signature:
          {(eval,4);(start,4)}
        Flow Graph:
          [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     A) (<0,0,C>, C) (<0,0,D>,     C) 
          (<1,0,A>, A) (<1,0,B>,     A) (<1,0,C>, C) (<1,0,D>,     C) 
          (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>,     C) 
          (<3,0,A>, A) (<3,0,B>,     A) (<3,0,C>, C) (<3,0,D>, C + D) 
          (<4,0,A>, A) (<4,0,B>,     B) (<4,0,C>, C) (<4,0,D>,     D) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(eval) = x3 + -1*x4
          p(start) = x3 + -1*x4
        
        The following rules are strictly oriented:
        [B >= A && C >= 1 + D] ==>                  
                 eval(A,B,C,D)   = C + -1*D         
                                 > -1 + C + -1*D    
                                 = eval(A,B,C,1 + D)
        
        
        The following rules are weakly oriented:
        [A >= 1 + B && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = C + -1*D         
                                    >= C + -1*D         
                                     = eval(A,1 + B,C,D)
        
        [A >= 1 + B && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = C + -1*D         
                                    >= -1 + C + -1*D    
                                     = eval(A,B,C,1 + D)
        
            [A >= 1 + B && D >= C] ==>                  
                     eval(A,B,C,D)   = C + -1*D         
                                    >= C + -1*D         
                                     = eval(A,1 + B,C,D)
        
                              True ==>                  
                    start(A,B,C,D)   = C + -1*D         
                                    >= C + -1*D         
                                     = eval(A,B,C,D)    
        
        
* Step 7: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1)    
          1. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1)    
          2. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D]     (C + D,1)
          3. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C]     (A + B,1)
          4. start(A,B,C,D) -> eval(A,B,C,D)     True                       (1,1)    
        Signature:
          {(eval,4);(start,4)}
        Flow Graph:
          [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     A) (<0,0,C>, C) (<0,0,D>,     C) 
          (<1,0,A>, A) (<1,0,B>,     A) (<1,0,C>, C) (<1,0,D>,     C) 
          (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>,     C) 
          (<3,0,A>, A) (<3,0,B>,     A) (<3,0,C>, C) (<3,0,D>, C + D) 
          (<4,0,A>, A) (<4,0,B>,     B) (<4,0,C>, C) (<4,0,D>,     D) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(eval) = x3 + -1*x4
          p(start) = x3 + -1*x4
        
        The following rules are strictly oriented:
        [A >= 1 + B && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = C + -1*D         
                                     > -1 + C + -1*D    
                                     = eval(A,B,C,1 + D)
        
            [B >= A && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = C + -1*D         
                                     > -1 + C + -1*D    
                                     = eval(A,B,C,1 + D)
        
        
        The following rules are weakly oriented:
        [A >= 1 + B && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = C + -1*D         
                                    >= C + -1*D         
                                     = eval(A,1 + B,C,D)
        
            [A >= 1 + B && D >= C] ==>                  
                     eval(A,B,C,D)   = C + -1*D         
                                    >= C + -1*D         
                                     = eval(A,1 + B,C,D)
        
                              True ==>                  
                    start(A,B,C,D)   = C + -1*D         
                                    >= C + -1*D         
                                     = eval(A,B,C,D)    
        
        
* Step 8: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1)    
          1. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (C + D,1)
          2. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D]     (C + D,1)
          3. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C]     (A + B,1)
          4. start(A,B,C,D) -> eval(A,B,C,D)     True                       (1,1)    
        Signature:
          {(eval,4);(start,4)}
        Flow Graph:
          [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     A) (<0,0,C>, C) (<0,0,D>,     C) 
          (<1,0,A>, A) (<1,0,B>,     A) (<1,0,C>, C) (<1,0,D>,     C) 
          (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>,     C) 
          (<3,0,A>, A) (<3,0,B>,     A) (<3,0,C>, C) (<3,0,D>, C + D) 
          (<4,0,A>, A) (<4,0,B>,     B) (<4,0,C>, C) (<4,0,D>,     D) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(eval) = x1 + -1*x2
          p(start) = x1 + -1*x2
        
        The following rules are strictly oriented:
        [A >= 1 + B && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = A + -1*B         
                                     > -1 + A + -1*B    
                                     = eval(A,1 + B,C,D)
        
            [A >= 1 + B && D >= C] ==>                  
                     eval(A,B,C,D)   = A + -1*B         
                                     > -1 + A + -1*B    
                                     = eval(A,1 + B,C,D)
        
        
        The following rules are weakly oriented:
        [A >= 1 + B && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = A + -1*B         
                                    >= A + -1*B         
                                     = eval(A,B,C,1 + D)
        
            [B >= A && C >= 1 + D] ==>                  
                     eval(A,B,C,D)   = A + -1*B         
                                    >= A + -1*B         
                                     = eval(A,B,C,1 + D)
        
                              True ==>                  
                    start(A,B,C,D)   = A + -1*B         
                                    >= A + -1*B         
                                     = eval(A,B,C,D)    
        
        
* Step 9: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (A + B,1)
          1. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (C + D,1)
          2. eval(A,B,C,D)  -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D]     (C + D,1)
          3. eval(A,B,C,D)  -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C]     (A + B,1)
          4. start(A,B,C,D) -> eval(A,B,C,D)     True                       (1,1)    
        Signature:
          {(eval,4);(start,4)}
        Flow Graph:
          [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     A) (<0,0,C>, C) (<0,0,D>,     C) 
          (<1,0,A>, A) (<1,0,B>,     A) (<1,0,C>, C) (<1,0,D>,     C) 
          (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>,     C) 
          (<3,0,A>, A) (<3,0,B>,     A) (<3,0,C>, C) (<3,0,D>, C + D) 
          (<4,0,A>, A) (<4,0,B>,     B) (<4,0,C>, C) (<4,0,D>,     D) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))