WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__2ND(z0) -> c3() A__2ND(cons(z0,z1)) -> c1(A__2ND(cons1(mark(z0),mark(z1))),MARK(z0)) A__2ND(cons(z0,z1)) -> c2(A__2ND(cons1(mark(z0),mark(z1))),MARK(z1)) A__2ND(cons1(z0,cons(z1,z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) A__FROM(z0) -> c5() MARK(2nd(z0)) -> c6(A__2ND(mark(z0)),MARK(z0)) MARK(cons(z0,z1)) -> c8(MARK(z0)) MARK(cons1(z0,z1)) -> c10(MARK(z0)) MARK(cons1(z0,z1)) -> c11(MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)),MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) - Weak TRS: a__2nd(z0) -> 2nd(z0) a__2nd(cons(z0,z1)) -> a__2nd(cons1(mark(z0),mark(z1))) a__2nd(cons1(z0,cons(z1,z2))) -> mark(z1) a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(cons1(z0,z1)) -> cons1(mark(z0),mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(s(z0)) -> s(mark(z0)) - Signature: {A__2ND/1,A__FROM/1,MARK/1,a__2nd/1,a__from/1,mark/1} / {2nd/1,c/1,c1/2,c10/1,c11/1,c2/2,c3/0,c4/1,c5/0,c6/2 ,c7/2,c8/1,c9/1,cons/2,cons1/2,from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {A__2ND,A__FROM,MARK,a__2nd,a__from ,mark} and constructors {2nd,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,cons,cons1,from,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__2ND(z0) -> c3() A__2ND(cons(z0,z1)) -> c1(A__2ND(cons1(mark(z0),mark(z1))),MARK(z0)) A__2ND(cons(z0,z1)) -> c2(A__2ND(cons1(mark(z0),mark(z1))),MARK(z1)) A__2ND(cons1(z0,cons(z1,z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) A__FROM(z0) -> c5() MARK(2nd(z0)) -> c6(A__2ND(mark(z0)),MARK(z0)) MARK(cons(z0,z1)) -> c8(MARK(z0)) MARK(cons1(z0,z1)) -> c10(MARK(z0)) MARK(cons1(z0,z1)) -> c11(MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)),MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) - Weak TRS: a__2nd(z0) -> 2nd(z0) a__2nd(cons(z0,z1)) -> a__2nd(cons1(mark(z0),mark(z1))) a__2nd(cons1(z0,cons(z1,z2))) -> mark(z1) a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(cons1(z0,z1)) -> cons1(mark(z0),mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(s(z0)) -> s(mark(z0)) - Signature: {A__2ND/1,A__FROM/1,MARK/1,a__2nd/1,a__from/1,mark/1} / {2nd/1,c/1,c1/2,c10/1,c11/1,c2/2,c3/0,c4/1,c5/0,c6/2 ,c7/2,c8/1,c9/1,cons/2,cons1/2,from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {A__2ND,A__FROM,MARK,a__2nd,a__from ,mark} and constructors {2nd,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,cons,cons1,from,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__2ND(z0) -> c3() A__2ND(cons(z0,z1)) -> c1(A__2ND(cons1(mark(z0),mark(z1))),MARK(z0)) A__2ND(cons(z0,z1)) -> c2(A__2ND(cons1(mark(z0),mark(z1))),MARK(z1)) A__2ND(cons1(z0,cons(z1,z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) A__FROM(z0) -> c5() MARK(2nd(z0)) -> c6(A__2ND(mark(z0)),MARK(z0)) MARK(cons(z0,z1)) -> c8(MARK(z0)) MARK(cons1(z0,z1)) -> c10(MARK(z0)) MARK(cons1(z0,z1)) -> c11(MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)),MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) - Weak TRS: a__2nd(z0) -> 2nd(z0) a__2nd(cons(z0,z1)) -> a__2nd(cons1(mark(z0),mark(z1))) a__2nd(cons1(z0,cons(z1,z2))) -> mark(z1) a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(cons1(z0,z1)) -> cons1(mark(z0),mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(s(z0)) -> s(mark(z0)) - Signature: {A__2ND/1,A__FROM/1,MARK/1,a__2nd/1,a__from/1,mark/1} / {2nd/1,c/1,c1/2,c10/1,c11/1,c2/2,c3/0,c4/1,c5/0,c6/2 ,c7/2,c8/1,c9/1,cons/2,cons1/2,from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {A__2ND,A__FROM,MARK,a__2nd,a__from ,mark} and constructors {2nd,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,cons,cons1,from,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: MARK(x){x -> 2nd(x)} = MARK(2nd(x)) ->^+ c6(A__2ND(mark(x)),MARK(x)) = C[MARK(x) = MARK(x){}] WORST_CASE(Omega(n^1),?)