WORST_CASE(?,O(1))
* Step 1: Sum.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            F(k(a()),k(b()),z0) -> c6(F(z0,z0,z0))
            G(z0) -> c1(U(h(z0),h(z0),z0),H(z0))
            G(z0) -> c2(U(h(z0),h(z0),z0),H(z0))
            H(d()) -> c4()
            H(d()) -> c5()
            U(d(),c(z0),z1) -> c3()
        - Weak TRS:
            f(k(a()),k(b()),z0) -> f(z0,z0,z0)
            g(z0) -> u(h(z0),h(z0),z0)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(z0),z1) -> k(z0)
        - Signature:
            {F/3,G/1,H/1,U/3,f/3,g/1,h/1,u/3} / {a/0,b/0,c/1,c1/2,c2/2,c3/0,c4/0,c5/0,c6/1,d/0,k/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F,G,H,U,f,g,h,u} and constructors {a,b,c,c1,c2,c3,c4,c5
            ,c6,d,k}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  MAYBE
    + Considered Problem:
        - Strict TRS:
            F(k(a()),k(b()),z0) -> c6(F(z0,z0,z0))
            G(z0) -> c1(U(h(z0),h(z0),z0),H(z0))
            G(z0) -> c2(U(h(z0),h(z0),z0),H(z0))
            H(d()) -> c4()
            H(d()) -> c5()
            U(d(),c(z0),z1) -> c3()
        - Weak TRS:
            f(k(a()),k(b()),z0) -> f(z0,z0,z0)
            g(z0) -> u(h(z0),h(z0),z0)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(z0),z1) -> k(z0)
        - Signature:
            {F/3,G/1,H/1,U/3,f/3,g/1,h/1,u/3} / {a/0,b/0,c/1,c1/2,c2/2,c3/0,c4/0,c5/0,c6/1,d/0,k/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F,G,H,U,f,g,h,u} and constructors {a,b,c,c1,c2,c3,c4,c5
            ,c6,d,k}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            F(k(a()),k(b()),z0) -> c6(F(z0,z0,z0))
            G(z0) -> c1(U(h(z0),h(z0),z0),H(z0))
            G(z0) -> c2(U(h(z0),h(z0),z0),H(z0))
            H(d()) -> c4()
            H(d()) -> c5()
            U(d(),c(z0),z1) -> c3()
        - Weak TRS:
            f(k(a()),k(b()),z0) -> f(z0,z0,z0)
            g(z0) -> u(h(z0),h(z0),z0)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(z0),z1) -> k(z0)
        - Signature:
            {F/3,G/1,H/1,U/3,f/3,g/1,h/1,u/3} / {a/0,b/0,c/1,c1/2,c2/2,c3/0,c4/0,c5/0,c6/1,d/0,k/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F,G,H,U,f,g,h,u} and constructors {a,b,c,c1,c2,c3,c4,c5
            ,c6,d,k}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "F") :: ["A"(0, 1, 0) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "G") :: ["A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "H") :: ["A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "U") :: ["A"(1, 1, 1) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "a") :: [] -(0)-> "A"(1, 1, 0)
          F (TrsFun "a") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "b") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "c") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "c1") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "c2") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "c3") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "c4") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "c5") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "c6") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "d") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "d") :: [] -(0)-> "A"(1, 1, 1)
          F (TrsFun "f") :: ["A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "g") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "h") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "k") :: ["A"(1, 1, 0)] -(0)-> "A"(0, 1, 0)
          F (TrsFun "k") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "main") :: ["A"(1, 1, 1) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "u") :: ["A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          F(k(a()),k(b()),z0) -> c6(F(z0,z0,z0))
          G(z0) -> c1(U(h(z0),h(z0),z0),H(z0))
          G(z0) -> c2(U(h(z0),h(z0),z0),H(z0))
          H(d()) -> c4()
          H(d()) -> c5()
          U(d(),c(z0),z1) -> c3()
          main(x1,x2,x3) -> U(x1,x2,x3)
        2. Weak:
          
        

** Step 1.b:1: DependencyPairs.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            F(k(a()),k(b()),z0) -> c6(F(z0,z0,z0))
            G(z0) -> c1(U(h(z0),h(z0),z0),H(z0))
            G(z0) -> c2(U(h(z0),h(z0),z0),H(z0))
            H(d()) -> c4()
            H(d()) -> c5()
            U(d(),c(z0),z1) -> c3()
        - Weak TRS:
            f(k(a()),k(b()),z0) -> f(z0,z0,z0)
            g(z0) -> u(h(z0),h(z0),z0)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(z0),z1) -> k(z0)
        - Signature:
            {F/3,G/1,H/1,U/3,f/3,g/1,h/1,u/3} / {a/0,b/0,c/1,c1/2,c2/2,c3/0,c4/0,c5/0,c6/1,d/0,k/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F,G,H,U,f,g,h,u} and constructors {a,b,c,c1,c2,c3,c4,c5
            ,c6,d,k}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          F#(k(a()),k(b()),z0) -> c_1(F#(z0,z0,z0))
          G#(z0) -> c_2(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
          G#(z0) -> c_3(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
          H#(d()) -> c_4()
          H#(d()) -> c_5()
          U#(d(),c(z0),z1) -> c_6()
        Weak DPs
          f#(k(a()),k(b()),z0) -> c_7(f#(z0,z0,z0))
          g#(z0) -> c_8(u#(h(z0),h(z0),z0),h#(z0),h#(z0))
          h#(d()) -> c_9()
          h#(d()) -> c_10()
          u#(d(),c(z0),z1) -> c_11()
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            F#(k(a()),k(b()),z0) -> c_1(F#(z0,z0,z0))
            G#(z0) -> c_2(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
            G#(z0) -> c_3(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
            H#(d()) -> c_4()
            H#(d()) -> c_5()
            U#(d(),c(z0),z1) -> c_6()
        - Weak DPs:
            f#(k(a()),k(b()),z0) -> c_7(f#(z0,z0,z0))
            g#(z0) -> c_8(u#(h(z0),h(z0),z0),h#(z0),h#(z0))
            h#(d()) -> c_9()
            h#(d()) -> c_10()
            u#(d(),c(z0),z1) -> c_11()
        - Weak TRS:
            F(k(a()),k(b()),z0) -> c6(F(z0,z0,z0))
            G(z0) -> c1(U(h(z0),h(z0),z0),H(z0))
            G(z0) -> c2(U(h(z0),h(z0),z0),H(z0))
            H(d()) -> c4()
            H(d()) -> c5()
            U(d(),c(z0),z1) -> c3()
            f(k(a()),k(b()),z0) -> f(z0,z0,z0)
            g(z0) -> u(h(z0),h(z0),z0)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(z0),z1) -> k(z0)
        - Signature:
            {F/3,G/1,H/1,U/3,f/3,g/1,h/1,u/3,F#/3,G#/1,H#/1,U#/3,f#/3,g#/1,h#/1,u#/3} / {a/0,b/0,c/1,c1/2,c2/2,c3/0,c4/0
            ,c5/0,c6/1,d/0,k/1,c_1/1,c_2/4,c_3/4,c_4/0,c_5/0,c_6/0,c_7/1,c_8/3,c_9/0,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F#,G#,H#,U#,f#,g#,h#,u#} and constructors {a,b,c,c1,c2,c3
            ,c4,c5,c6,d,k}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,5,6}
        by application of
          Pre({1,4,5,6}) = {2,3}.
        Here rules are labelled as follows:
          1: F#(k(a()),k(b()),z0) -> c_1(F#(z0,z0,z0))
          2: G#(z0) -> c_2(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
          3: G#(z0) -> c_3(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
          4: H#(d()) -> c_4()
          5: H#(d()) -> c_5()
          6: U#(d(),c(z0),z1) -> c_6()
          7: f#(k(a()),k(b()),z0) -> c_7(f#(z0,z0,z0))
          8: g#(z0) -> c_8(u#(h(z0),h(z0),z0),h#(z0),h#(z0))
          9: h#(d()) -> c_9()
          10: h#(d()) -> c_10()
          11: u#(d(),c(z0),z1) -> c_11()
** Step 1.b:3: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            G#(z0) -> c_2(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
            G#(z0) -> c_3(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
        - Weak DPs:
            F#(k(a()),k(b()),z0) -> c_1(F#(z0,z0,z0))
            H#(d()) -> c_4()
            H#(d()) -> c_5()
            U#(d(),c(z0),z1) -> c_6()
            f#(k(a()),k(b()),z0) -> c_7(f#(z0,z0,z0))
            g#(z0) -> c_8(u#(h(z0),h(z0),z0),h#(z0),h#(z0))
            h#(d()) -> c_9()
            h#(d()) -> c_10()
            u#(d(),c(z0),z1) -> c_11()
        - Weak TRS:
            F(k(a()),k(b()),z0) -> c6(F(z0,z0,z0))
            G(z0) -> c1(U(h(z0),h(z0),z0),H(z0))
            G(z0) -> c2(U(h(z0),h(z0),z0),H(z0))
            H(d()) -> c4()
            H(d()) -> c5()
            U(d(),c(z0),z1) -> c3()
            f(k(a()),k(b()),z0) -> f(z0,z0,z0)
            g(z0) -> u(h(z0),h(z0),z0)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(z0),z1) -> k(z0)
        - Signature:
            {F/3,G/1,H/1,U/3,f/3,g/1,h/1,u/3,F#/3,G#/1,H#/1,U#/3,f#/3,g#/1,h#/1,u#/3} / {a/0,b/0,c/1,c1/2,c2/2,c3/0,c4/0
            ,c5/0,c6/1,d/0,k/1,c_1/1,c_2/4,c_3/4,c_4/0,c_5/0,c_6/0,c_7/1,c_8/3,c_9/0,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F#,G#,H#,U#,f#,g#,h#,u#} and constructors {a,b,c,c1,c2,c3
            ,c4,c5,c6,d,k}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2}
        by application of
          Pre({1,2}) = {}.
        Here rules are labelled as follows:
          1: G#(z0) -> c_2(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
          2: G#(z0) -> c_3(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
          3: F#(k(a()),k(b()),z0) -> c_1(F#(z0,z0,z0))
          4: H#(d()) -> c_4()
          5: H#(d()) -> c_5()
          6: U#(d(),c(z0),z1) -> c_6()
          7: f#(k(a()),k(b()),z0) -> c_7(f#(z0,z0,z0))
          8: g#(z0) -> c_8(u#(h(z0),h(z0),z0),h#(z0),h#(z0))
          9: h#(d()) -> c_9()
          10: h#(d()) -> c_10()
          11: u#(d(),c(z0),z1) -> c_11()
** Step 1.b:4: RemoveWeakSuffixes.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            F#(k(a()),k(b()),z0) -> c_1(F#(z0,z0,z0))
            G#(z0) -> c_2(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
            G#(z0) -> c_3(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
            H#(d()) -> c_4()
            H#(d()) -> c_5()
            U#(d(),c(z0),z1) -> c_6()
            f#(k(a()),k(b()),z0) -> c_7(f#(z0,z0,z0))
            g#(z0) -> c_8(u#(h(z0),h(z0),z0),h#(z0),h#(z0))
            h#(d()) -> c_9()
            h#(d()) -> c_10()
            u#(d(),c(z0),z1) -> c_11()
        - Weak TRS:
            F(k(a()),k(b()),z0) -> c6(F(z0,z0,z0))
            G(z0) -> c1(U(h(z0),h(z0),z0),H(z0))
            G(z0) -> c2(U(h(z0),h(z0),z0),H(z0))
            H(d()) -> c4()
            H(d()) -> c5()
            U(d(),c(z0),z1) -> c3()
            f(k(a()),k(b()),z0) -> f(z0,z0,z0)
            g(z0) -> u(h(z0),h(z0),z0)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(z0),z1) -> k(z0)
        - Signature:
            {F/3,G/1,H/1,U/3,f/3,g/1,h/1,u/3,F#/3,G#/1,H#/1,U#/3,f#/3,g#/1,h#/1,u#/3} / {a/0,b/0,c/1,c1/2,c2/2,c3/0,c4/0
            ,c5/0,c6/1,d/0,k/1,c_1/1,c_2/4,c_3/4,c_4/0,c_5/0,c_6/0,c_7/1,c_8/3,c_9/0,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F#,G#,H#,U#,f#,g#,h#,u#} and constructors {a,b,c,c1,c2,c3
            ,c4,c5,c6,d,k}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:F#(k(a()),k(b()),z0) -> c_1(F#(z0,z0,z0))
             
          
          2:W:G#(z0) -> c_2(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
             -->_3 h#(d()) -> c_10():10
             -->_2 h#(d()) -> c_10():10
             -->_3 h#(d()) -> c_9():9
             -->_2 h#(d()) -> c_9():9
             -->_1 U#(d(),c(z0),z1) -> c_6():6
             -->_4 H#(d()) -> c_5():5
             -->_4 H#(d()) -> c_4():4
          
          3:W:G#(z0) -> c_3(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
             -->_3 h#(d()) -> c_10():10
             -->_2 h#(d()) -> c_10():10
             -->_3 h#(d()) -> c_9():9
             -->_2 h#(d()) -> c_9():9
             -->_1 U#(d(),c(z0),z1) -> c_6():6
             -->_4 H#(d()) -> c_5():5
             -->_4 H#(d()) -> c_4():4
          
          4:W:H#(d()) -> c_4()
             
          
          5:W:H#(d()) -> c_5()
             
          
          6:W:U#(d(),c(z0),z1) -> c_6()
             
          
          7:W:f#(k(a()),k(b()),z0) -> c_7(f#(z0,z0,z0))
             
          
          8:W:g#(z0) -> c_8(u#(h(z0),h(z0),z0),h#(z0),h#(z0))
             -->_1 u#(d(),c(z0),z1) -> c_11():11
             -->_3 h#(d()) -> c_10():10
             -->_2 h#(d()) -> c_10():10
             -->_3 h#(d()) -> c_9():9
             -->_2 h#(d()) -> c_9():9
          
          9:W:h#(d()) -> c_9()
             
          
          10:W:h#(d()) -> c_10()
             
          
          11:W:u#(d(),c(z0),z1) -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: g#(z0) -> c_8(u#(h(z0),h(z0),z0),h#(z0),h#(z0))
          11: u#(d(),c(z0),z1) -> c_11()
          7: f#(k(a()),k(b()),z0) -> c_7(f#(z0,z0,z0))
          3: G#(z0) -> c_3(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
          2: G#(z0) -> c_2(U#(h(z0),h(z0),z0),h#(z0),h#(z0),H#(z0))
          4: H#(d()) -> c_4()
          5: H#(d()) -> c_5()
          6: U#(d(),c(z0),z1) -> c_6()
          9: h#(d()) -> c_9()
          10: h#(d()) -> c_10()
          1: F#(k(a()),k(b()),z0) -> c_1(F#(z0,z0,z0))
** Step 1.b:5: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            F(k(a()),k(b()),z0) -> c6(F(z0,z0,z0))
            G(z0) -> c1(U(h(z0),h(z0),z0),H(z0))
            G(z0) -> c2(U(h(z0),h(z0),z0),H(z0))
            H(d()) -> c4()
            H(d()) -> c5()
            U(d(),c(z0),z1) -> c3()
            f(k(a()),k(b()),z0) -> f(z0,z0,z0)
            g(z0) -> u(h(z0),h(z0),z0)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(z0),z1) -> k(z0)
        - Signature:
            {F/3,G/1,H/1,U/3,f/3,g/1,h/1,u/3,F#/3,G#/1,H#/1,U#/3,f#/3,g#/1,h#/1,u#/3} / {a/0,b/0,c/1,c1/2,c2/2,c3/0,c4/0
            ,c5/0,c6/1,d/0,k/1,c_1/1,c_2/4,c_3/4,c_4/0,c_5/0,c_6/0,c_7/1,c_8/3,c_9/0,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F#,G#,H#,U#,f#,g#,h#,u#} and constructors {a,b,c,c1,c2,c3
            ,c4,c5,c6,d,k}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))