* Step 1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),y) -> +(x,s(y)) +(s(x),y) -> s(+(x,y)) - Signature: {+/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {+} and constructors {0,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: +(0(),y) -> y +(s(x),y) -> +(x,s(y)) +(s(x),y) -> s(+(x,y)) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} 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(2,2) -> 4 +_1(2,3) -> 1 +_1(2,3) -> 4 0_0() -> 1 0_0() -> 2 0_0() -> 4 s_0(2) -> 1 s_0(2) -> 2 s_0(2) -> 4 s_1(1) -> 1 s_1(2) -> 1 s_1(2) -> 3 s_1(2) -> 4 s_1(3) -> 1 s_1(3) -> 3 s_1(3) -> 4 s_1(4) -> 1 s_1(4) -> 4 2 -> 1 2 -> 4 3 -> 1 3 -> 4 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: +(0(),y) -> y +(s(x),y) -> +(x,s(y)) +(s(x),y) -> s(+(x,y)) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))