* Step 1: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z)
            e2(x,x,y,z,z,a()) -> e6(x,y,z)
            e2(i(),x,y,z,i(),a()) -> e6(x,y,z)
            e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z)
            e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)
            e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x)
            e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z)
            e5(i(),x,y,z) -> e6(x,y,z)
            f1(x,a()) -> g2(x,x)
            f1(a(),x) -> g1(x,x)
            f2(x,a()) -> g2(x,x)
            f2(a(),x) -> g1(x,x)
            g1(x,a()) -> h2(x)
            g1(a(),x) -> h1(x)
            g2(x,a()) -> h2(x)
            g2(a(),x) -> h1(x)
            h1(a()) -> i()
            h2(a()) -> i()
        - Signature:
            {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1} / {a/0,e6/3,i/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {e1,e2,e3,e4,e5,f1,f2,g1,g2,h1,h2} and constructors {a,e6
            ,i}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
          e2#(x,x,y,z,z,a()) -> c_2()
          e2#(i(),x,y,z,i(),a()) -> c_3()
          e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_4()
          e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_5(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
          e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_6()
          e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_7(e5#(x1,x,y,z))
          e5#(i(),x,y,z) -> c_8()
          f1#(x,a()) -> c_9(g2#(x,x))
          f1#(a(),x) -> c_10(g1#(x,x))
          f2#(x,a()) -> c_11(g2#(x,x))
          f2#(a(),x) -> c_12(g1#(x,x))
          g1#(x,a()) -> c_13(h2#(x))
          g1#(a(),x) -> c_14(h1#(x))
          g2#(x,a()) -> c_15(h2#(x))
          g2#(a(),x) -> c_16(h1#(x))
          h1#(a()) -> c_17()
          h2#(a()) -> c_18()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
            e2#(x,x,y,z,z,a()) -> c_2()
            e2#(i(),x,y,z,i(),a()) -> c_3()
            e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_4()
            e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_5(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
            e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_6()
            e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_7(e5#(x1,x,y,z))
            e5#(i(),x,y,z) -> c_8()
            f1#(x,a()) -> c_9(g2#(x,x))
            f1#(a(),x) -> c_10(g1#(x,x))
            f2#(x,a()) -> c_11(g2#(x,x))
            f2#(a(),x) -> c_12(g1#(x,x))
            g1#(x,a()) -> c_13(h2#(x))
            g1#(a(),x) -> c_14(h1#(x))
            g2#(x,a()) -> c_15(h2#(x))
            g2#(a(),x) -> c_16(h1#(x))
            h1#(a()) -> c_17()
            h2#(a()) -> c_18()
        - Weak TRS:
            e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z)
            e2(x,x,y,z,z,a()) -> e6(x,y,z)
            e2(i(),x,y,z,i(),a()) -> e6(x,y,z)
            e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z)
            e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)
            e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x)
            e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z)
            e5(i(),x,y,z) -> e6(x,y,z)
            f1(x,a()) -> g2(x,x)
            f1(a(),x) -> g1(x,x)
            f2(x,a()) -> g2(x,x)
            f2(a(),x) -> g1(x,x)
            g1(x,a()) -> h2(x)
            g1(a(),x) -> h1(x)
            g2(x,a()) -> h2(x)
            g2(a(),x) -> h1(x)
            h1(a()) -> i()
            h2(a()) -> i()
        - Signature:
            {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2
            ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/0,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/1
            ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/0,c_18/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1#
            ,h2#} and constructors {a,e6,i}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
          e2#(x,x,y,z,z,a()) -> c_2()
          e2#(i(),x,y,z,i(),a()) -> c_3()
          e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_4()
          e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_5(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
          e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_6()
          e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_7(e5#(x1,x,y,z))
          e5#(i(),x,y,z) -> c_8()
          f1#(x,a()) -> c_9(g2#(x,x))
          f1#(a(),x) -> c_10(g1#(x,x))
          f2#(x,a()) -> c_11(g2#(x,x))
          f2#(a(),x) -> c_12(g1#(x,x))
          g1#(x,a()) -> c_13(h2#(x))
          g1#(a(),x) -> c_14(h1#(x))
          g2#(x,a()) -> c_15(h2#(x))
          g2#(a(),x) -> c_16(h1#(x))
          h1#(a()) -> c_17()
          h2#(a()) -> c_18()
* Step 3: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
            e2#(x,x,y,z,z,a()) -> c_2()
            e2#(i(),x,y,z,i(),a()) -> c_3()
            e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_4()
            e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_5(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
            e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_6()
            e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_7(e5#(x1,x,y,z))
            e5#(i(),x,y,z) -> c_8()
            f1#(x,a()) -> c_9(g2#(x,x))
            f1#(a(),x) -> c_10(g1#(x,x))
            f2#(x,a()) -> c_11(g2#(x,x))
            f2#(a(),x) -> c_12(g1#(x,x))
            g1#(x,a()) -> c_13(h2#(x))
            g1#(a(),x) -> c_14(h1#(x))
            g2#(x,a()) -> c_15(h2#(x))
            g2#(a(),x) -> c_16(h1#(x))
            h1#(a()) -> c_17()
            h2#(a()) -> c_18()
        - Signature:
            {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2
            ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/0,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/1
            ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/0,c_18/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1#
            ,h2#} and constructors {a,e6,i}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
             -->_1 e5#(i(),x,y,z) -> c_8():8
          
          2:S:e2#(x,x,y,z,z,a()) -> c_2()
             
          
          3:S:e2#(i(),x,y,z,i(),a()) -> c_3()
             
          
          4:S:e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_4()
             
          
          5:S:e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_5(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
             -->_1 e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_7(e5#(x1,x,y,z)):7
             -->_1 e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_6():6
          
          6:S:e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_6()
             
          
          7:S:e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_7(e5#(x1,x,y,z))
             -->_1 e5#(i(),x,y,z) -> c_8():8
          
          8:S:e5#(i(),x,y,z) -> c_8()
             
          
          9:S:f1#(x,a()) -> c_9(g2#(x,x))
             -->_1 g2#(a(),x) -> c_16(h1#(x)):16
             -->_1 g2#(x,a()) -> c_15(h2#(x)):15
          
          10:S:f1#(a(),x) -> c_10(g1#(x,x))
             -->_1 g1#(a(),x) -> c_14(h1#(x)):14
             -->_1 g1#(x,a()) -> c_13(h2#(x)):13
          
          11:S:f2#(x,a()) -> c_11(g2#(x,x))
             -->_1 g2#(a(),x) -> c_16(h1#(x)):16
             -->_1 g2#(x,a()) -> c_15(h2#(x)):15
          
          12:S:f2#(a(),x) -> c_12(g1#(x,x))
             -->_1 g1#(a(),x) -> c_14(h1#(x)):14
             -->_1 g1#(x,a()) -> c_13(h2#(x)):13
          
          13:S:g1#(x,a()) -> c_13(h2#(x))
             -->_1 h2#(a()) -> c_18():18
          
          14:S:g1#(a(),x) -> c_14(h1#(x))
             -->_1 h1#(a()) -> c_17():17
          
          15:S:g2#(x,a()) -> c_15(h2#(x))
             -->_1 h2#(a()) -> c_18():18
          
          16:S:g2#(a(),x) -> c_16(h1#(x))
             -->_1 h1#(a()) -> c_17():17
          
          17:S:h1#(a()) -> c_17()
             
          
          18:S:h2#(a()) -> c_18()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2
            ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/0,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/1
            ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/0,c_18/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1#
            ,h2#} and constructors {a,e6,i}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))