* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add(0(),X) -> X add(s(),Y) -> s() from(X) -> cons(X) fst(0(),Z) -> nil() fst(s(),cons(Y)) -> cons(Y) len(cons(X)) -> s() len(nil()) -> 0() - Signature: {add/2,from/1,fst/2,len/1} / {0/0,cons/1,nil/0,s/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,from,fst,len} and constructors {0,cons,nil,s} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 2 0_1() -> 1 add_0(2,2) -> 1 cons_0(2) -> 1 cons_0(2) -> 2 cons_1(2) -> 1 from_0(2) -> 1 fst_0(2,2) -> 1 len_0(2) -> 1 nil_0() -> 1 nil_0() -> 2 nil_1() -> 1 s_0() -> 1 s_0() -> 2 s_1() -> 1 2 -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: add(0(),X) -> X add(s(),Y) -> s() from(X) -> cons(X) fst(0(),Z) -> nil() fst(s(),cons(Y)) -> cons(Y) len(cons(X)) -> s() len(nil()) -> 0() - Signature: {add/2,from/1,fst/2,len/1} / {0/0,cons/1,nil/0,s/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,from,fst,len} and constructors {0,cons,nil,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))