WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__FROM(z0) -> c(MARK(z0)) A__FROM(z0) -> c1() A__SEL(z0,z1) -> c5() A__SEL(0(),cons(z0,z1)) -> c2(MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c3(A__SEL(mark(z0),mark(z2)),MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c4(A__SEL(mark(z0),mark(z2)),MARK(z2)) MARK(0()) -> c11() MARK(cons(z0,z1)) -> c9(MARK(z0)) MARK(from(z0)) -> c6(A__FROM(mark(z0)),MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(sel(z0,z1)) -> c7(A__SEL(mark(z0),mark(z1)),MARK(z0)) MARK(sel(z0,z1)) -> c8(A__SEL(mark(z0),mark(z1)),MARK(z1)) - Weak TRS: a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) a__sel(z0,z1) -> sel(z0,z1) a__sel(0(),cons(z0,z1)) -> mark(z0) a__sel(s(z0),cons(z1,z2)) -> a__sel(mark(z0),mark(z2)) mark(0()) -> 0() mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(from(z0)) -> a__from(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(sel(z0,z1)) -> a__sel(mark(z0),mark(z1)) - Signature: {A__FROM/1,A__SEL/2,MARK/1,a__from/1,a__sel/2,mark/1} / {0/0,c/1,c1/0,c10/1,c11/0,c2/1,c3/2,c4/2,c5/0,c6/2 ,c7/2,c8/2,c9/1,cons/2,from/1,s/1,sel/2} - Obligation: innermost runtime complexity wrt. defined symbols {A__FROM,A__SEL,MARK,a__from,a__sel ,mark} and constructors {0,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,cons,from,s,sel} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__FROM(z0) -> c(MARK(z0)) A__FROM(z0) -> c1() A__SEL(z0,z1) -> c5() A__SEL(0(),cons(z0,z1)) -> c2(MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c3(A__SEL(mark(z0),mark(z2)),MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c4(A__SEL(mark(z0),mark(z2)),MARK(z2)) MARK(0()) -> c11() MARK(cons(z0,z1)) -> c9(MARK(z0)) MARK(from(z0)) -> c6(A__FROM(mark(z0)),MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(sel(z0,z1)) -> c7(A__SEL(mark(z0),mark(z1)),MARK(z0)) MARK(sel(z0,z1)) -> c8(A__SEL(mark(z0),mark(z1)),MARK(z1)) - Weak TRS: a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) a__sel(z0,z1) -> sel(z0,z1) a__sel(0(),cons(z0,z1)) -> mark(z0) a__sel(s(z0),cons(z1,z2)) -> a__sel(mark(z0),mark(z2)) mark(0()) -> 0() mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(from(z0)) -> a__from(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(sel(z0,z1)) -> a__sel(mark(z0),mark(z1)) - Signature: {A__FROM/1,A__SEL/2,MARK/1,a__from/1,a__sel/2,mark/1} / {0/0,c/1,c1/0,c10/1,c11/0,c2/1,c3/2,c4/2,c5/0,c6/2 ,c7/2,c8/2,c9/1,cons/2,from/1,s/1,sel/2} - Obligation: innermost runtime complexity wrt. defined symbols {A__FROM,A__SEL,MARK,a__from,a__sel ,mark} and constructors {0,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,cons,from,s,sel} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__FROM(z0) -> c(MARK(z0)) A__FROM(z0) -> c1() A__SEL(z0,z1) -> c5() A__SEL(0(),cons(z0,z1)) -> c2(MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c3(A__SEL(mark(z0),mark(z2)),MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c4(A__SEL(mark(z0),mark(z2)),MARK(z2)) MARK(0()) -> c11() MARK(cons(z0,z1)) -> c9(MARK(z0)) MARK(from(z0)) -> c6(A__FROM(mark(z0)),MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(sel(z0,z1)) -> c7(A__SEL(mark(z0),mark(z1)),MARK(z0)) MARK(sel(z0,z1)) -> c8(A__SEL(mark(z0),mark(z1)),MARK(z1)) - Weak TRS: a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) a__sel(z0,z1) -> sel(z0,z1) a__sel(0(),cons(z0,z1)) -> mark(z0) a__sel(s(z0),cons(z1,z2)) -> a__sel(mark(z0),mark(z2)) mark(0()) -> 0() mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(from(z0)) -> a__from(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(sel(z0,z1)) -> a__sel(mark(z0),mark(z1)) - Signature: {A__FROM/1,A__SEL/2,MARK/1,a__from/1,a__sel/2,mark/1} / {0/0,c/1,c1/0,c10/1,c11/0,c2/1,c3/2,c4/2,c5/0,c6/2 ,c7/2,c8/2,c9/1,cons/2,from/1,s/1,sel/2} - Obligation: innermost runtime complexity wrt. defined symbols {A__FROM,A__SEL,MARK,a__from,a__sel ,mark} and constructors {0,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,cons,from,s,sel} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: MARK(x){x -> cons(x,y)} = MARK(cons(x,y)) ->^+ c9(MARK(x)) = C[MARK(x) = MARK(x){}] WORST_CASE(Omega(n^1),?)