WORST_CASE(?,O(n^1))
* Step 1: DependencyPairs WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a(C(x1,x2),y) -> C(a(x1,y),a(x2,C(x1,x2)))
            a(Z(),y) -> Z()
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            first(C(x1,x2)) -> x1
            second(C(x1,x2)) -> x2
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1} / {C/2,False/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,and,eqZList,first,second} and constructors {C,False
            ,True,Z}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak innermost dependency pairs:
        
        Strict DPs
          a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
          a#(Z(),y) -> c_2()
          eqZList#(C(x1,x2),C(y1,y2)) -> c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
          eqZList#(C(x1,x2),Z()) -> c_4()
          eqZList#(Z(),C(y1,y2)) -> c_5()
          eqZList#(Z(),Z()) -> c_6()
          first#(C(x1,x2)) -> c_7()
          second#(C(x1,x2)) -> c_8()
        Weak DPs
          and#(False(),False()) -> c_9()
          and#(False(),True()) -> c_10()
          and#(True(),False()) -> c_11()
          and#(True(),True()) -> c_12()
        
        and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
            a#(Z(),y) -> c_2()
            eqZList#(C(x1,x2),C(y1,y2)) -> c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
            eqZList#(C(x1,x2),Z()) -> c_4()
            eqZList#(Z(),C(y1,y2)) -> c_5()
            eqZList#(Z(),Z()) -> c_6()
            first#(C(x1,x2)) -> c_7()
            second#(C(x1,x2)) -> c_8()
        - Strict TRS:
            a(C(x1,x2),y) -> C(a(x1,y),a(x2,C(x1,x2)))
            a(Z(),y) -> Z()
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            first(C(x1,x2)) -> x1
            second(C(x1,x2)) -> x2
        - Weak DPs:
            and#(False(),False()) -> c_9()
            and#(False(),True()) -> c_10()
            and#(True(),False()) -> c_11()
            and#(True(),True()) -> c_12()
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          and(False(),False()) -> False()
          and(False(),True()) -> False()
          and(True(),False()) -> False()
          and(True(),True()) -> True()
          eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
          eqZList(C(x1,x2),Z()) -> False()
          eqZList(Z(),C(y1,y2)) -> False()
          eqZList(Z(),Z()) -> True()
          a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
          a#(Z(),y) -> c_2()
          and#(False(),False()) -> c_9()
          and#(False(),True()) -> c_10()
          and#(True(),False()) -> c_11()
          and#(True(),True()) -> c_12()
          eqZList#(C(x1,x2),C(y1,y2)) -> c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
          eqZList#(C(x1,x2),Z()) -> c_4()
          eqZList#(Z(),C(y1,y2)) -> c_5()
          eqZList#(Z(),Z()) -> c_6()
          first#(C(x1,x2)) -> c_7()
          second#(C(x1,x2)) -> c_8()
* Step 3: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
            a#(Z(),y) -> c_2()
            eqZList#(C(x1,x2),C(y1,y2)) -> c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
            eqZList#(C(x1,x2),Z()) -> c_4()
            eqZList#(Z(),C(y1,y2)) -> c_5()
            eqZList#(Z(),Z()) -> c_6()
            first#(C(x1,x2)) -> c_7()
            second#(C(x1,x2)) -> c_8()
        - Strict TRS:
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
        - Weak DPs:
            and#(False(),False()) -> c_9()
            and#(False(),True()) -> c_10()
            and#(True(),False()) -> c_11()
            and#(True(),True()) -> c_12()
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnTrs}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(and) = {1,2},
            uargs(and#) = {1,2},
            uargs(c_1) = {1,2},
            uargs(c_3) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                   p(C) = [1] x1 + [1] x2 + [2]
               p(False) = [0]                  
                p(True) = [0]                  
                   p(Z) = [0]                  
                   p(a) = [0]                  
                 p(and) = [1] x1 + [1] x2 + [0]
             p(eqZList) = [1] x1 + [1] x2 + [3]
               p(first) = [0]                  
              p(second) = [0]                  
                  p(a#) = [1] x1 + [6]         
                p(and#) = [1] x1 + [1] x2 + [0]
            p(eqZList#) = [1] x1 + [1] x2 + [2]
              p(first#) = [0]                  
             p(second#) = [0]                  
                 p(c_1) = [1] x1 + [1] x2 + [0]
                 p(c_2) = [0]                  
                 p(c_3) = [1] x1 + [0]         
                 p(c_4) = [0]                  
                 p(c_5) = [0]                  
                 p(c_6) = [0]                  
                 p(c_7) = [0]                  
                 p(c_8) = [0]                  
                 p(c_9) = [0]                  
                p(c_10) = [0]                  
                p(c_11) = [0]                  
                p(c_12) = [0]                  
          
          Following rules are strictly oriented:
                           a#(Z(),y) = [6]                                    
                                     > [0]                                    
                                     = c_2()                                  
          
              eqZList#(C(x1,x2),Z()) = [1] x1 + [1] x2 + [4]                  
                                     > [0]                                    
                                     = c_4()                                  
          
              eqZList#(Z(),C(y1,y2)) = [1] y1 + [1] y2 + [4]                  
                                     > [0]                                    
                                     = c_5()                                  
          
                   eqZList#(Z(),Z()) = [2]                                    
                                     > [0]                                    
                                     = c_6()                                  
          
          eqZList(C(x1,x2),C(y1,y2)) = [1] x1 + [1] x2 + [1] y1 + [1] y2 + [7]
                                     > [1] x1 + [1] x2 + [1] y1 + [1] y2 + [6]
                                     = and(eqZList(x1,y1),eqZList(x2,y2))     
          
               eqZList(C(x1,x2),Z()) = [1] x1 + [1] x2 + [5]                  
                                     > [0]                                    
                                     = False()                                
          
               eqZList(Z(),C(y1,y2)) = [1] y1 + [1] y2 + [5]                  
                                     > [0]                                    
                                     = False()                                
          
                    eqZList(Z(),Z()) = [3]                                    
                                     > [0]                                    
                                     = True()                                 
          
          
          Following rules are (at-least) weakly oriented:
                       a#(C(x1,x2),y) =  [1] x1 + [1] x2 + [8]                   
                                      >= [1] x1 + [1] x2 + [12]                  
                                      =  c_1(a#(x1,y),a#(x2,C(x1,x2)))           
          
                and#(False(),False()) =  [0]                                     
                                      >= [0]                                     
                                      =  c_9()                                   
          
                 and#(False(),True()) =  [0]                                     
                                      >= [0]                                     
                                      =  c_10()                                  
          
                 and#(True(),False()) =  [0]                                     
                                      >= [0]                                     
                                      =  c_11()                                  
          
                  and#(True(),True()) =  [0]                                     
                                      >= [0]                                     
                                      =  c_12()                                  
          
          eqZList#(C(x1,x2),C(y1,y2)) =  [1] x1 + [1] x2 + [1] y1 + [1] y2 + [6] 
                                      >= [1] x1 + [1] x2 + [1] y1 + [1] y2 + [6] 
                                      =  c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
          
                     first#(C(x1,x2)) =  [0]                                     
                                      >= [0]                                     
                                      =  c_7()                                   
          
                    second#(C(x1,x2)) =  [0]                                     
                                      >= [0]                                     
                                      =  c_8()                                   
          
                 and(False(),False()) =  [0]                                     
                                      >= [0]                                     
                                      =  False()                                 
          
                  and(False(),True()) =  [0]                                     
                                      >= [0]                                     
                                      =  False()                                 
          
                  and(True(),False()) =  [0]                                     
                                      >= [0]                                     
                                      =  False()                                 
          
                   and(True(),True()) =  [0]                                     
                                      >= [0]                                     
                                      =  True()                                  
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 4: PredecessorEstimation WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
            eqZList#(C(x1,x2),C(y1,y2)) -> c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
            first#(C(x1,x2)) -> c_7()
            second#(C(x1,x2)) -> c_8()
        - Weak DPs:
            a#(Z(),y) -> c_2()
            and#(False(),False()) -> c_9()
            and#(False(),True()) -> c_10()
            and#(True(),False()) -> c_11()
            and#(True(),True()) -> c_12()
            eqZList#(C(x1,x2),Z()) -> c_4()
            eqZList#(Z(),C(y1,y2)) -> c_5()
            eqZList#(Z(),Z()) -> c_6()
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,3,4}
        by application of
          Pre({2,3,4}) = {}.
        Here rules are labelled as follows:
          1: a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
          2: eqZList#(C(x1,x2),C(y1,y2)) -> c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
          3: first#(C(x1,x2)) -> c_7()
          4: second#(C(x1,x2)) -> c_8()
          5: a#(Z(),y) -> c_2()
          6: and#(False(),False()) -> c_9()
          7: and#(False(),True()) -> c_10()
          8: and#(True(),False()) -> c_11()
          9: and#(True(),True()) -> c_12()
          10: eqZList#(C(x1,x2),Z()) -> c_4()
          11: eqZList#(Z(),C(y1,y2)) -> c_5()
          12: eqZList#(Z(),Z()) -> c_6()
* Step 5: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
        - Weak DPs:
            a#(Z(),y) -> c_2()
            and#(False(),False()) -> c_9()
            and#(False(),True()) -> c_10()
            and#(True(),False()) -> c_11()
            and#(True(),True()) -> c_12()
            eqZList#(C(x1,x2),C(y1,y2)) -> c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
            eqZList#(C(x1,x2),Z()) -> c_4()
            eqZList#(Z(),C(y1,y2)) -> c_5()
            eqZList#(Z(),Z()) -> c_6()
            first#(C(x1,x2)) -> c_7()
            second#(C(x1,x2)) -> c_8()
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
             -->_2 a#(Z(),y) -> c_2():2
             -->_1 a#(Z(),y) -> c_2():2
             -->_2 a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2))):1
             -->_1 a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2))):1
          
          2:W:a#(Z(),y) -> c_2()
             
          
          3:W:and#(False(),False()) -> c_9()
             
          
          4:W:and#(False(),True()) -> c_10()
             
          
          5:W:and#(True(),False()) -> c_11()
             
          
          6:W:and#(True(),True()) -> c_12()
             
          
          7:W:eqZList#(C(x1,x2),C(y1,y2)) -> c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
             -->_1 and#(True(),True()) -> c_12():6
             -->_1 and#(True(),False()) -> c_11():5
             -->_1 and#(False(),True()) -> c_10():4
             -->_1 and#(False(),False()) -> c_9():3
          
          8:W:eqZList#(C(x1,x2),Z()) -> c_4()
             
          
          9:W:eqZList#(Z(),C(y1,y2)) -> c_5()
             
          
          10:W:eqZList#(Z(),Z()) -> c_6()
             
          
          11:W:first#(C(x1,x2)) -> c_7()
             
          
          12:W:second#(C(x1,x2)) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          12: second#(C(x1,x2)) -> c_8()
          11: first#(C(x1,x2)) -> c_7()
          10: eqZList#(Z(),Z()) -> c_6()
          9: eqZList#(Z(),C(y1,y2)) -> c_5()
          8: eqZList#(C(x1,x2),Z()) -> c_4()
          7: eqZList#(C(x1,x2),C(y1,y2)) -> c_3(and#(eqZList(x1,y1),eqZList(x2,y2)))
          6: and#(True(),True()) -> c_12()
          5: and#(True(),False()) -> c_11()
          4: and#(False(),True()) -> c_10()
          3: and#(False(),False()) -> c_9()
          2: a#(Z(),y) -> c_2()
* Step 6: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
* Step 7: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
          
        The strictly oriented rules are moved into the weak component.
** Step 7.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1,2}
        
        Following symbols are considered usable:
          {a#,and#,eqZList#,first#,second#}
        TcT has computed the following interpretation:
                 p(C) = [1] x1 + [1] x2 + [2]
             p(False) = [1]                  
              p(True) = [8]                  
                 p(Z) = [8]                  
                 p(a) = [1] x1 + [1] x2 + [1]
               p(and) = [1] x1 + [1] x2 + [2]
           p(eqZList) = [0]                  
             p(first) = [8] x1 + [0]         
            p(second) = [2] x1 + [1]         
                p(a#) = [8] x1 + [0]         
              p(and#) = [1] x1 + [4] x2 + [2]
          p(eqZList#) = [2] x1 + [1]         
            p(first#) = [0]                  
           p(second#) = [1] x1 + [0]         
               p(c_1) = [1] x1 + [1] x2 + [8]
               p(c_2) = [0]                  
               p(c_3) = [1] x1 + [1]         
               p(c_4) = [1]                  
               p(c_5) = [1]                  
               p(c_6) = [0]                  
               p(c_7) = [0]                  
               p(c_8) = [1]                  
               p(c_9) = [4]                  
              p(c_10) = [1]                  
              p(c_11) = [4]                  
              p(c_12) = [0]                  
        
        Following rules are strictly oriented:
        a#(C(x1,x2),y) = [8] x1 + [8] x2 + [16]       
                       > [8] x1 + [8] x2 + [8]        
                       = c_1(a#(x1,y),a#(x2,C(x1,x2)))
        
        
        Following rules are (at-least) weakly oriented:
        
** Step 7.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

** Step 7.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
             -->_2 a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2))):1
             -->_1 a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2))):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: a#(C(x1,x2),y) -> c_1(a#(x1,y),a#(x2,C(x1,x2)))
** Step 7.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {a/2,and/2,eqZList/2,first/1,second/1,a#/2,and#/2,eqZList#/2,first#/1,second#/1} / {C/2,False/0,True/0,Z/0
            ,c_1/2,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,and#,eqZList#,first#,second#} and constructors {C
            ,False,True,Z}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))