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

WORST_CASE(?,O(1))