* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 2nd(mark(X)) -> mark(2nd(X)) 2nd(ok(X)) -> ok(2nd(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) from(mark(X)) -> mark(from(X)) from(ok(X)) -> ok(from(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {2nd/1,cons/2,from/1,s/1,top/1} / {active/1,mark/1,ok/1,proper/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,cons,from,s,top} and constructors {active,mark,ok ,proper} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. 2nd_0(2) -> 1 2nd_1(2) -> 3 active_0(2) -> 2 active_1(2) -> 4 cons_0(2,2) -> 1 cons_1(2,2) -> 3 from_0(2) -> 1 from_1(2) -> 3 mark_0(2) -> 2 mark_1(3) -> 1 mark_1(3) -> 3 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 3 proper_0(2) -> 2 proper_1(2) -> 4 s_0(2) -> 1 s_1(2) -> 3 top_0(2) -> 1 top_1(4) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: 2nd(mark(X)) -> mark(2nd(X)) 2nd(ok(X)) -> ok(2nd(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) from(mark(X)) -> mark(from(X)) from(ok(X)) -> ok(from(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {2nd/1,cons/2,from/1,s/1,top/1} / {active/1,mark/1,ok/1,proper/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,cons,from,s,top} and constructors {active,mark,ok ,proper} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))