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

WORST_CASE(Omega(n^1),?)