WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            F(0(),z0) -> c3()
            F(S(z0),0()) -> c2()
            F(S(z0),S(z1)) -> c(H(g(z0,S(z1)),f(S(S(S(z0))),z1)),G(z0,S(z1)))
            F(S(z0),S(z1)) -> c1(H(g(z0,S(z1)),f(S(S(S(z0))),z1)),F(S(S(S(z0))),z1))
            G(0(),z0) -> c7()
            G(S(z0),0()) -> c6()
            G(S(z0),S(z1)) -> c4(H(f(S(z0),S(z1)),g(z0,S(S(S(z1))))),F(S(z0),S(z1)))
            G(S(z0),S(z1)) -> c5(H(f(S(z0),S(z1)),g(z0,S(S(S(z1))))),G(z0,S(S(S(z1)))))
            H(0(),0()) -> c9()
            H(0(),S(z0)) -> c8(H(0(),z0))
            H(S(z0),z1) -> c10(H(z0,z1))
        - Weak TRS:
            f(0(),z0) -> 0()
            f(S(z0),0()) -> 0()
            f(S(z0),S(z1)) -> h(g(z0,S(z1)),f(S(S(S(z0))),z1))
            g(0(),z0) -> 0()
            g(S(z0),0()) -> 0()
            g(S(z0),S(z1)) -> h(f(S(z0),S(z1)),g(z0,S(S(S(z1)))))
            h(0(),0()) -> 0()
            h(0(),S(z0)) -> h(0(),z0)
            h(S(z0),z1) -> h(z0,z1)
        - Signature:
            {F/2,G/2,H/2,f/2,g/2,h/2} / {0/0,S/1,c/2,c1/2,c10/1,c2/0,c3/0,c4/2,c5/2,c6/0,c7/0,c8/1,c9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F,G,H,f,g,h} and constructors {0,S,c,c1,c10,c2,c3,c4,c5
            ,c6,c7,c8,c9}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            F(0(),z0) -> c3()
            F(S(z0),0()) -> c2()
            F(S(z0),S(z1)) -> c(H(g(z0,S(z1)),f(S(S(S(z0))),z1)),G(z0,S(z1)))
            F(S(z0),S(z1)) -> c1(H(g(z0,S(z1)),f(S(S(S(z0))),z1)),F(S(S(S(z0))),z1))
            G(0(),z0) -> c7()
            G(S(z0),0()) -> c6()
            G(S(z0),S(z1)) -> c4(H(f(S(z0),S(z1)),g(z0,S(S(S(z1))))),F(S(z0),S(z1)))
            G(S(z0),S(z1)) -> c5(H(f(S(z0),S(z1)),g(z0,S(S(S(z1))))),G(z0,S(S(S(z1)))))
            H(0(),0()) -> c9()
            H(0(),S(z0)) -> c8(H(0(),z0))
            H(S(z0),z1) -> c10(H(z0,z1))
        - Weak TRS:
            f(0(),z0) -> 0()
            f(S(z0),0()) -> 0()
            f(S(z0),S(z1)) -> h(g(z0,S(z1)),f(S(S(S(z0))),z1))
            g(0(),z0) -> 0()
            g(S(z0),0()) -> 0()
            g(S(z0),S(z1)) -> h(f(S(z0),S(z1)),g(z0,S(S(S(z1)))))
            h(0(),0()) -> 0()
            h(0(),S(z0)) -> h(0(),z0)
            h(S(z0),z1) -> h(z0,z1)
        - Signature:
            {F/2,G/2,H/2,f/2,g/2,h/2} / {0/0,S/1,c/2,c1/2,c10/1,c2/0,c3/0,c4/2,c5/2,c6/0,c7/0,c8/1,c9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F,G,H,f,g,h} and constructors {0,S,c,c1,c10,c2,c3,c4,c5
            ,c6,c7,c8,c9}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            F(0(),z0) -> c3()
            F(S(z0),0()) -> c2()
            F(S(z0),S(z1)) -> c(H(g(z0,S(z1)),f(S(S(S(z0))),z1)),G(z0,S(z1)))
            F(S(z0),S(z1)) -> c1(H(g(z0,S(z1)),f(S(S(S(z0))),z1)),F(S(S(S(z0))),z1))
            G(0(),z0) -> c7()
            G(S(z0),0()) -> c6()
            G(S(z0),S(z1)) -> c4(H(f(S(z0),S(z1)),g(z0,S(S(S(z1))))),F(S(z0),S(z1)))
            G(S(z0),S(z1)) -> c5(H(f(S(z0),S(z1)),g(z0,S(S(S(z1))))),G(z0,S(S(S(z1)))))
            H(0(),0()) -> c9()
            H(0(),S(z0)) -> c8(H(0(),z0))
            H(S(z0),z1) -> c10(H(z0,z1))
        - Weak TRS:
            f(0(),z0) -> 0()
            f(S(z0),0()) -> 0()
            f(S(z0),S(z1)) -> h(g(z0,S(z1)),f(S(S(S(z0))),z1))
            g(0(),z0) -> 0()
            g(S(z0),0()) -> 0()
            g(S(z0),S(z1)) -> h(f(S(z0),S(z1)),g(z0,S(S(S(z1)))))
            h(0(),0()) -> 0()
            h(0(),S(z0)) -> h(0(),z0)
            h(S(z0),z1) -> h(z0,z1)
        - Signature:
            {F/2,G/2,H/2,f/2,g/2,h/2} / {0/0,S/1,c/2,c1/2,c10/1,c2/0,c3/0,c4/2,c5/2,c6/0,c7/0,c8/1,c9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F,G,H,f,g,h} and constructors {0,S,c,c1,c10,c2,c3,c4,c5
            ,c6,c7,c8,c9}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          F(S(x),y){y -> S(y)} =
            F(S(x),S(y)) ->^+ c1(H(g(x,S(y)),f(S(S(S(x))),y)),F(S(S(S(x))),y))
              = C[F(S(S(S(x))),y) = F(S(x),y){x -> S(S(x))}]

WORST_CASE(Omega(n^1),?)