WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            F_0(z0) -> c()
            F_1(z0) -> c1(G_1(z0,z0))
            F_2(z0) -> c4(G_2(z0,z0))
            F_3(z0) -> c7(G_3(z0,z0))
            F_4(z0) -> c10(G_4(z0,z0))
            F_5(z0) -> c13(G_5(z0,z0))
            G_1(s(z0),z1) -> c2(F_0(z1))
            G_1(s(z0),z1) -> c3(G_1(z0,z1))
            G_2(s(z0),z1) -> c5(F_1(z1))
            G_2(s(z0),z1) -> c6(G_2(z0,z1))
            G_3(s(z0),z1) -> c8(F_2(z1))
            G_3(s(z0),z1) -> c9(G_3(z0,z1))
            G_4(s(z0),z1) -> c11(F_3(z1))
            G_4(s(z0),z1) -> c12(G_4(z0,z1))
            G_5(s(z0),z1) -> c14(F_4(z1))
            G_5(s(z0),z1) -> c15(G_5(z0,z1))
        - Weak TRS:
            f_0(z0) -> a()
            f_1(z0) -> g_1(z0,z0)
            f_2(z0) -> g_2(z0,z0)
            f_3(z0) -> g_3(z0,z0)
            f_4(z0) -> g_4(z0,z0)
            f_5(z0) -> g_5(z0,z0)
            g_1(s(z0),z1) -> b(f_0(z1),g_1(z0,z1))
            g_2(s(z0),z1) -> b(f_1(z1),g_2(z0,z1))
            g_3(s(z0),z1) -> b(f_2(z1),g_3(z0,z1))
            g_4(s(z0),z1) -> b(f_3(z1),g_4(z0,z1))
            g_5(s(z0),z1) -> b(f_4(z1),g_5(z0,z1))
        - Signature:
            {F_0/1,F_1/1,F_2/1,F_3/1,F_4/1,F_5/1,G_1/2,G_2/2,G_3/2,G_4/2,G_5/2,f_0/1,f_1/1,f_2/1,f_3/1,f_4/1,f_5/1,g_1/2
            ,g_2/2,g_3/2,g_4/2,g_5/2} / {a/0,b/2,c/0,c1/1,c10/1,c11/1,c12/1,c13/1,c14/1,c15/1,c2/1,c3/1,c4/1,c5/1,c6/1
            ,c7/1,c8/1,c9/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F_0,F_1,F_2,F_3,F_4,F_5,G_1,G_2,G_3,G_4,G_5,f_0,f_1,f_2
            ,f_3,f_4,f_5,g_1,g_2,g_3,g_4,g_5} and constructors {a,b,c,c1,c10,c11,c12,c13,c14,c15,c2,c3,c4,c5,c6,c7,c8,c9
            ,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            F_0(z0) -> c()
            F_1(z0) -> c1(G_1(z0,z0))
            F_2(z0) -> c4(G_2(z0,z0))
            F_3(z0) -> c7(G_3(z0,z0))
            F_4(z0) -> c10(G_4(z0,z0))
            F_5(z0) -> c13(G_5(z0,z0))
            G_1(s(z0),z1) -> c2(F_0(z1))
            G_1(s(z0),z1) -> c3(G_1(z0,z1))
            G_2(s(z0),z1) -> c5(F_1(z1))
            G_2(s(z0),z1) -> c6(G_2(z0,z1))
            G_3(s(z0),z1) -> c8(F_2(z1))
            G_3(s(z0),z1) -> c9(G_3(z0,z1))
            G_4(s(z0),z1) -> c11(F_3(z1))
            G_4(s(z0),z1) -> c12(G_4(z0,z1))
            G_5(s(z0),z1) -> c14(F_4(z1))
            G_5(s(z0),z1) -> c15(G_5(z0,z1))
        - Weak TRS:
            f_0(z0) -> a()
            f_1(z0) -> g_1(z0,z0)
            f_2(z0) -> g_2(z0,z0)
            f_3(z0) -> g_3(z0,z0)
            f_4(z0) -> g_4(z0,z0)
            f_5(z0) -> g_5(z0,z0)
            g_1(s(z0),z1) -> b(f_0(z1),g_1(z0,z1))
            g_2(s(z0),z1) -> b(f_1(z1),g_2(z0,z1))
            g_3(s(z0),z1) -> b(f_2(z1),g_3(z0,z1))
            g_4(s(z0),z1) -> b(f_3(z1),g_4(z0,z1))
            g_5(s(z0),z1) -> b(f_4(z1),g_5(z0,z1))
        - Signature:
            {F_0/1,F_1/1,F_2/1,F_3/1,F_4/1,F_5/1,G_1/2,G_2/2,G_3/2,G_4/2,G_5/2,f_0/1,f_1/1,f_2/1,f_3/1,f_4/1,f_5/1,g_1/2
            ,g_2/2,g_3/2,g_4/2,g_5/2} / {a/0,b/2,c/0,c1/1,c10/1,c11/1,c12/1,c13/1,c14/1,c15/1,c2/1,c3/1,c4/1,c5/1,c6/1
            ,c7/1,c8/1,c9/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F_0,F_1,F_2,F_3,F_4,F_5,G_1,G_2,G_3,G_4,G_5,f_0,f_1,f_2
            ,f_3,f_4,f_5,g_1,g_2,g_3,g_4,g_5} and constructors {a,b,c,c1,c10,c11,c12,c13,c14,c15,c2,c3,c4,c5,c6,c7,c8,c9
            ,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            F_0(z0) -> c()
            F_1(z0) -> c1(G_1(z0,z0))
            F_2(z0) -> c4(G_2(z0,z0))
            F_3(z0) -> c7(G_3(z0,z0))
            F_4(z0) -> c10(G_4(z0,z0))
            F_5(z0) -> c13(G_5(z0,z0))
            G_1(s(z0),z1) -> c2(F_0(z1))
            G_1(s(z0),z1) -> c3(G_1(z0,z1))
            G_2(s(z0),z1) -> c5(F_1(z1))
            G_2(s(z0),z1) -> c6(G_2(z0,z1))
            G_3(s(z0),z1) -> c8(F_2(z1))
            G_3(s(z0),z1) -> c9(G_3(z0,z1))
            G_4(s(z0),z1) -> c11(F_3(z1))
            G_4(s(z0),z1) -> c12(G_4(z0,z1))
            G_5(s(z0),z1) -> c14(F_4(z1))
            G_5(s(z0),z1) -> c15(G_5(z0,z1))
        - Weak TRS:
            f_0(z0) -> a()
            f_1(z0) -> g_1(z0,z0)
            f_2(z0) -> g_2(z0,z0)
            f_3(z0) -> g_3(z0,z0)
            f_4(z0) -> g_4(z0,z0)
            f_5(z0) -> g_5(z0,z0)
            g_1(s(z0),z1) -> b(f_0(z1),g_1(z0,z1))
            g_2(s(z0),z1) -> b(f_1(z1),g_2(z0,z1))
            g_3(s(z0),z1) -> b(f_2(z1),g_3(z0,z1))
            g_4(s(z0),z1) -> b(f_3(z1),g_4(z0,z1))
            g_5(s(z0),z1) -> b(f_4(z1),g_5(z0,z1))
        - Signature:
            {F_0/1,F_1/1,F_2/1,F_3/1,F_4/1,F_5/1,G_1/2,G_2/2,G_3/2,G_4/2,G_5/2,f_0/1,f_1/1,f_2/1,f_3/1,f_4/1,f_5/1,g_1/2
            ,g_2/2,g_3/2,g_4/2,g_5/2} / {a/0,b/2,c/0,c1/1,c10/1,c11/1,c12/1,c13/1,c14/1,c15/1,c2/1,c3/1,c4/1,c5/1,c6/1
            ,c7/1,c8/1,c9/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F_0,F_1,F_2,F_3,F_4,F_5,G_1,G_2,G_3,G_4,G_5,f_0,f_1,f_2
            ,f_3,f_4,f_5,g_1,g_2,g_3,g_4,g_5} and constructors {a,b,c,c1,c10,c11,c12,c13,c14,c15,c2,c3,c4,c5,c6,c7,c8,c9
            ,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          G_1(x,y){x -> s(x)} =
            G_1(s(x),y) ->^+ c3(G_1(x,y))
              = C[G_1(x,y) = G_1(x,y){}]

** Step 1.b:1: Ara.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            F_0(z0) -> c()
            F_1(z0) -> c1(G_1(z0,z0))
            F_2(z0) -> c4(G_2(z0,z0))
            F_3(z0) -> c7(G_3(z0,z0))
            F_4(z0) -> c10(G_4(z0,z0))
            F_5(z0) -> c13(G_5(z0,z0))
            G_1(s(z0),z1) -> c2(F_0(z1))
            G_1(s(z0),z1) -> c3(G_1(z0,z1))
            G_2(s(z0),z1) -> c5(F_1(z1))
            G_2(s(z0),z1) -> c6(G_2(z0,z1))
            G_3(s(z0),z1) -> c8(F_2(z1))
            G_3(s(z0),z1) -> c9(G_3(z0,z1))
            G_4(s(z0),z1) -> c11(F_3(z1))
            G_4(s(z0),z1) -> c12(G_4(z0,z1))
            G_5(s(z0),z1) -> c14(F_4(z1))
            G_5(s(z0),z1) -> c15(G_5(z0,z1))
        - Weak TRS:
            f_0(z0) -> a()
            f_1(z0) -> g_1(z0,z0)
            f_2(z0) -> g_2(z0,z0)
            f_3(z0) -> g_3(z0,z0)
            f_4(z0) -> g_4(z0,z0)
            f_5(z0) -> g_5(z0,z0)
            g_1(s(z0),z1) -> b(f_0(z1),g_1(z0,z1))
            g_2(s(z0),z1) -> b(f_1(z1),g_2(z0,z1))
            g_3(s(z0),z1) -> b(f_2(z1),g_3(z0,z1))
            g_4(s(z0),z1) -> b(f_3(z1),g_4(z0,z1))
            g_5(s(z0),z1) -> b(f_4(z1),g_5(z0,z1))
        - Signature:
            {F_0/1,F_1/1,F_2/1,F_3/1,F_4/1,F_5/1,G_1/2,G_2/2,G_3/2,G_4/2,G_5/2,f_0/1,f_1/1,f_2/1,f_3/1,f_4/1,f_5/1,g_1/2
            ,g_2/2,g_3/2,g_4/2,g_5/2} / {a/0,b/2,c/0,c1/1,c10/1,c11/1,c12/1,c13/1,c14/1,c15/1,c2/1,c3/1,c4/1,c5/1,c6/1
            ,c7/1,c8/1,c9/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F_0,F_1,F_2,F_3,F_4,F_5,G_1,G_2,G_3,G_4,G_5,f_0,f_1,f_2
            ,f_3,f_4,f_5,g_1,g_2,g_3,g_4,g_5} and constructors {a,b,c,c1,c10,c11,c12,c13,c14,c15,c2,c3,c4,c5,c6,c7,c8,c9
            ,s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 1, araTimeout = 8, araRuleShifting = Just 1, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "F_0") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "F_1") :: ["A"(2)] -(1)-> "A"(0)
          F (TrsFun "F_2") :: ["A"(4)] -(1)-> "A"(0)
          F (TrsFun "F_3") :: ["A"(6)] -(1)-> "A"(0)
          F (TrsFun "F_4") :: ["A"(8)] -(1)-> "A"(0)
          F (TrsFun "F_5") :: ["A"(10)] -(1)-> "A"(0)
          F (TrsFun "G_1") :: ["A"(2) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "G_2") :: ["A"(2) x "A"(2)] -(0)-> "A"(0)
          F (TrsFun "G_3") :: ["A"(2) x "A"(4)] -(0)-> "A"(0)
          F (TrsFun "G_4") :: ["A"(2) x "A"(6)] -(0)-> "A"(0)
          F (TrsFun "G_5") :: ["A"(2) x "A"(8)] -(0)-> "A"(0)
          F (TrsFun "a") :: [] -(0)-> "A"(0)
          F (TrsFun "b") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "c") :: [] -(0)-> "A"(0)
          F (TrsFun "c1") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c10") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c11") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c12") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c13") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c14") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c15") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c2") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c3") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c4") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c5") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c6") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c7") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c8") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c9") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "f_0") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "f_1") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "f_2") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "f_3") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "f_4") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "f_5") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "g_1") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "g_2") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "g_3") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "g_4") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "g_5") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "s") :: ["A"(2)] -(2)-> "A"(2)
          F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          F_0(z0) -> c()
          F_1(z0) -> c1(G_1(z0,z0))
          F_2(z0) -> c4(G_2(z0,z0))
          F_3(z0) -> c7(G_3(z0,z0))
          F_4(z0) -> c10(G_4(z0,z0))
          F_5(z0) -> c13(G_5(z0,z0))
          G_1(s(z0),z1) -> c2(F_0(z1))
          G_1(s(z0),z1) -> c3(G_1(z0,z1))
          G_2(s(z0),z1) -> c5(F_1(z1))
          G_2(s(z0),z1) -> c6(G_2(z0,z1))
          G_3(s(z0),z1) -> c8(F_2(z1))
          G_3(s(z0),z1) -> c9(G_3(z0,z1))
          G_4(s(z0),z1) -> c11(F_3(z1))
          G_4(s(z0),z1) -> c12(G_4(z0,z1))
          G_5(s(z0),z1) -> c14(F_4(z1))
          G_5(s(z0),z1) -> c15(G_5(z0,z1))
        2. Weak:
          
        

WORST_CASE(Omega(n^1),O(n^1))