WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            BITITER(z0,z1) -> c10(IF(zero(z0),z0,inc(z1)),ZERO(z0))
            BITITER(z0,z1) -> c11(IF(zero(z0),z0,inc(z1)),INC(z1))
            BITS(z0) -> c9(BITITER(z0,0()))
            HALF(0()) -> c()
            HALF(s(0())) -> c1()
            HALF(s(s(z0))) -> c2(HALF(z0))
            IF(false(),z0,z1) -> c13(BITITER(half(z0),z1),HALF(z0))
            IF(true(),z0,z1) -> c12(P(z1))
            INC(0()) -> c3()
            INC(s(z0)) -> c4(INC(z0))
            P(0()) -> c7()
            P(s(z0)) -> c8()
            ZERO(0()) -> c5()
            ZERO(s(z0)) -> c6()
        - Weak TRS:
            bitIter(z0,z1) -> if(zero(z0),z0,inc(z1))
            bits(z0) -> bitIter(z0,0())
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(z0))) -> s(half(z0))
            if(false(),z0,z1) -> bitIter(half(z0),z1)
            if(true(),z0,z1) -> p(z1)
            inc(0()) -> 0()
            inc(s(z0)) -> s(inc(z0))
            p(0()) -> 0()
            p(s(z0)) -> z0
            zero(0()) -> true()
            zero(s(z0)) -> false()
        - Signature:
            {BITITER/2,BITS/1,HALF/1,IF/3,INC/1,P/1,ZERO/1,bitIter/2,bits/1,half/1,if/3,inc/1,p/1,zero/1} / {0/0,c/0
            ,c1/0,c10/2,c11/2,c12/1,c13/2,c2/1,c3/0,c4/1,c5/0,c6/0,c7/0,c8/0,c9/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {BITITER,BITS,HALF,IF,INC,P,ZERO,bitIter,bits,half,if,inc
            ,p,zero} and constructors {0,c,c1,c10,c11,c12,c13,c2,c3,c4,c5,c6,c7,c8,c9,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            BITITER(z0,z1) -> c10(IF(zero(z0),z0,inc(z1)),ZERO(z0))
            BITITER(z0,z1) -> c11(IF(zero(z0),z0,inc(z1)),INC(z1))
            BITS(z0) -> c9(BITITER(z0,0()))
            HALF(0()) -> c()
            HALF(s(0())) -> c1()
            HALF(s(s(z0))) -> c2(HALF(z0))
            IF(false(),z0,z1) -> c13(BITITER(half(z0),z1),HALF(z0))
            IF(true(),z0,z1) -> c12(P(z1))
            INC(0()) -> c3()
            INC(s(z0)) -> c4(INC(z0))
            P(0()) -> c7()
            P(s(z0)) -> c8()
            ZERO(0()) -> c5()
            ZERO(s(z0)) -> c6()
        - Weak TRS:
            bitIter(z0,z1) -> if(zero(z0),z0,inc(z1))
            bits(z0) -> bitIter(z0,0())
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(z0))) -> s(half(z0))
            if(false(),z0,z1) -> bitIter(half(z0),z1)
            if(true(),z0,z1) -> p(z1)
            inc(0()) -> 0()
            inc(s(z0)) -> s(inc(z0))
            p(0()) -> 0()
            p(s(z0)) -> z0
            zero(0()) -> true()
            zero(s(z0)) -> false()
        - Signature:
            {BITITER/2,BITS/1,HALF/1,IF/3,INC/1,P/1,ZERO/1,bitIter/2,bits/1,half/1,if/3,inc/1,p/1,zero/1} / {0/0,c/0
            ,c1/0,c10/2,c11/2,c12/1,c13/2,c2/1,c3/0,c4/1,c5/0,c6/0,c7/0,c8/0,c9/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {BITITER,BITS,HALF,IF,INC,P,ZERO,bitIter,bits,half,if,inc
            ,p,zero} and constructors {0,c,c1,c10,c11,c12,c13,c2,c3,c4,c5,c6,c7,c8,c9,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            BITITER(z0,z1) -> c10(IF(zero(z0),z0,inc(z1)),ZERO(z0))
            BITITER(z0,z1) -> c11(IF(zero(z0),z0,inc(z1)),INC(z1))
            BITS(z0) -> c9(BITITER(z0,0()))
            HALF(0()) -> c()
            HALF(s(0())) -> c1()
            HALF(s(s(z0))) -> c2(HALF(z0))
            IF(false(),z0,z1) -> c13(BITITER(half(z0),z1),HALF(z0))
            IF(true(),z0,z1) -> c12(P(z1))
            INC(0()) -> c3()
            INC(s(z0)) -> c4(INC(z0))
            P(0()) -> c7()
            P(s(z0)) -> c8()
            ZERO(0()) -> c5()
            ZERO(s(z0)) -> c6()
        - Weak TRS:
            bitIter(z0,z1) -> if(zero(z0),z0,inc(z1))
            bits(z0) -> bitIter(z0,0())
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(z0))) -> s(half(z0))
            if(false(),z0,z1) -> bitIter(half(z0),z1)
            if(true(),z0,z1) -> p(z1)
            inc(0()) -> 0()
            inc(s(z0)) -> s(inc(z0))
            p(0()) -> 0()
            p(s(z0)) -> z0
            zero(0()) -> true()
            zero(s(z0)) -> false()
        - Signature:
            {BITITER/2,BITS/1,HALF/1,IF/3,INC/1,P/1,ZERO/1,bitIter/2,bits/1,half/1,if/3,inc/1,p/1,zero/1} / {0/0,c/0
            ,c1/0,c10/2,c11/2,c12/1,c13/2,c2/1,c3/0,c4/1,c5/0,c6/0,c7/0,c8/0,c9/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {BITITER,BITS,HALF,IF,INC,P,ZERO,bitIter,bits,half,if,inc
            ,p,zero} and constructors {0,c,c1,c10,c11,c12,c13,c2,c3,c4,c5,c6,c7,c8,c9,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          HALF(x){x -> s(s(x))} =
            HALF(s(s(x))) ->^+ c2(HALF(x))
              = C[HALF(x) = HALF(x){}]

WORST_CASE(Omega(n^1),?)