* Step 1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {f/1,p/1} / {0/0,cons/1,s/1} - Obligation: runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s} + Applied Processor: ToInnermost + Details: switch to innermost, as the system is overlay and right linear and does not contain weak rules * Step 2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {f/1,p/1} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 4 0_1() -> 6 0_1() -> 7 0_2() -> 9 cons_0(1) -> 2 cons_0(1) -> 4 cons_0(2) -> 2 cons_0(2) -> 4 cons_0(5) -> 2 cons_0(5) -> 4 cons_1(6) -> 3 cons_2(9) -> 3 f_0(1) -> 3 f_0(2) -> 3 f_0(5) -> 3 f_1(7) -> 3 p_0(1) -> 4 p_0(2) -> 4 p_0(5) -> 4 p_1(8) -> 7 s_0(1) -> 4 s_0(1) -> 5 s_0(2) -> 4 s_0(2) -> 5 s_0(5) -> 4 s_0(5) -> 5 s_1(6) -> 8 1 -> 4 2 -> 4 5 -> 4 6 -> 7 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {f/1,p/1} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))