WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__tail(X) -> tail(X) a__tail(cons(X,XS)) -> mark(XS) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(tail(X)) -> a__tail(mark(X)) mark(zeros()) -> a__zeros() - Signature: {a__tail/1,a__zeros/0,mark/1} / {0/0,cons/2,tail/1,zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__tail,a__zeros,mark} and constructors {0,cons,tail ,zeros} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 4. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 1 0_1() -> 3 0_2() -> 5 0_3() -> 7 0_4() -> 9 a__tail_0(2) -> 1 a__tail_1(1) -> 1 a__zeros_0() -> 1 a__zeros_1() -> 1 a__zeros_2() -> 1 a__zeros_3() -> 1 cons_0(2,2) -> 2 cons_1(1,2) -> 1 cons_1(3,4) -> 1 cons_2(5,6) -> 1 cons_3(7,8) -> 1 cons_4(9,10) -> 1 mark_0(2) -> 1 mark_1(2) -> 1 mark_2(2) -> 1 mark_2(4) -> 1 mark_2(6) -> 1 mark_2(8) -> 1 mark_2(10) -> 1 tail_0(2) -> 2 tail_1(2) -> 1 tail_2(1) -> 1 zeros_0() -> 2 zeros_1() -> 1 zeros_1() -> 4 zeros_2() -> 1 zeros_2() -> 6 zeros_3() -> 1 zeros_3() -> 8 zeros_4() -> 1 zeros_4() -> 10 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: a__tail(X) -> tail(X) a__tail(cons(X,XS)) -> mark(XS) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(tail(X)) -> a__tail(mark(X)) mark(zeros()) -> a__zeros() - Signature: {a__tail/1,a__zeros/0,mark/1} / {0/0,cons/2,tail/1,zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__tail,a__zeros,mark} and constructors {0,cons,tail ,zeros} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))