* Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add0(0(),x2) -> x2 add0(S(x),x2) -> +(S(0()),add0(x2,x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,add0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add0(0(),x2) -> x2 add0(S(x),x2) -> +(S(0()),add0(x2,x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,add0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,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(2,2) -> 1 +_1(3,4) -> 1 +_1(3,4) -> 4 0_0() -> 1 0_0() -> 2 0_0() -> 4 0_1() -> 5 S_0(2) -> 1 S_0(2) -> 2 S_0(2) -> 4 S_1(3) -> 1 S_1(3) -> 4 S_1(4) -> 1 S_1(4) -> 4 S_1(5) -> 3 add0_0(2,2) -> 1 add0_1(2,2) -> 4 2 -> 1 2 -> 4 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) add0(0(),x2) -> x2 add0(S(x),x2) -> +(S(0()),add0(x2,x)) - Signature: {+/2,add0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))