* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: any(X) -> s(X) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) eq(ok(X1),ok(X2)) -> ok(eq(X1,X2)) inf(mark(X)) -> mark(inf(X)) inf(ok(X)) -> ok(inf(X)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(false()) -> ok(false()) proper(nil()) -> ok(nil()) proper(true()) -> ok(true()) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {any/1,cons/2,eq/2,inf/1,length/1,proper/1,s/1,take/2,top/1} / {0/0,active/1,false/0,mark/1,nil/0,ok/1 ,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {any,cons,eq,inf,length,proper,s,take ,top} and constructors {0,active,false,mark,nil,ok,true} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 3 active_0(2) -> 2 active_1(2) -> 5 active_2(3) -> 6 any_0(2) -> 1 cons_0(2,2) -> 1 cons_1(2,2) -> 3 eq_0(2,2) -> 1 eq_1(2,2) -> 3 false_0() -> 2 false_1() -> 3 inf_0(2) -> 1 inf_1(2) -> 4 length_0(2) -> 1 length_1(2) -> 4 mark_0(2) -> 2 mark_1(4) -> 1 mark_1(4) -> 4 nil_0() -> 2 nil_1() -> 3 ok_0(2) -> 2 ok_1(1) -> 1 ok_1(3) -> 1 ok_1(3) -> 3 ok_1(3) -> 5 ok_1(4) -> 1 ok_1(4) -> 4 proper_0(2) -> 1 proper_1(2) -> 5 s_0(2) -> 1 s_1(2) -> 1 take_0(2,2) -> 1 take_1(2,2) -> 4 top_0(2) -> 1 top_1(5) -> 1 top_2(6) -> 1 true_0() -> 2 true_1() -> 3 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: any(X) -> s(X) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) eq(ok(X1),ok(X2)) -> ok(eq(X1,X2)) inf(mark(X)) -> mark(inf(X)) inf(ok(X)) -> ok(inf(X)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(false()) -> ok(false()) proper(nil()) -> ok(nil()) proper(true()) -> ok(true()) s(ok(X)) -> ok(s(X)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(mark(X1),X2) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {any/1,cons/2,eq/2,inf/1,length/1,proper/1,s/1,take/2,top/1} / {0/0,active/1,false/0,mark/1,nil/0,ok/1 ,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {any,cons,eq,inf,length,proper,s,take ,top} and constructors {0,active,false,mark,nil,ok,true} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))