WORST_CASE(?,O(n^1)) * Step 1: InnermostRuleRemoval WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: c(y) -> y c(a(a(0(),x),y)) -> a(c(c(c(0()))),y) c(c(c(y))) -> c(c(a(y,0()))) - Signature: {c/1} / {0/0,a/2} - Obligation: innermost runtime complexity wrt. defined symbols {c} and constructors {0,a} + Applied Processor: InnermostRuleRemoval + Details: Arguments of following rules are not normal-forms. c(c(c(y))) -> c(c(a(y,0()))) All above mentioned rules can be savely removed. * Step 2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: c(y) -> y c(a(a(0(),x),y)) -> a(c(c(c(0()))),y) - Signature: {c/1} / {0/0,a/2} - Obligation: innermost runtime complexity wrt. defined symbols {c} and constructors {0,a} + 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() -> 3 0_1() -> 4 0_1() -> 5 0_1() -> 6 a_0(2,2) -> 1 a_0(2,2) -> 2 a_1(3,2) -> 1 c_0(2) -> 1 c_1(4) -> 3 c_1(5) -> 3 c_1(5) -> 4 c_1(6) -> 3 c_1(6) -> 4 c_1(6) -> 5 2 -> 1 4 -> 3 5 -> 3 5 -> 4 6 -> 3 6 -> 4 6 -> 5 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: c(y) -> y c(a(a(0(),x),y)) -> a(c(c(c(0()))),y) - Signature: {c/1} / {0/0,a/2} - Obligation: innermost runtime complexity wrt. defined symbols {c} and constructors {0,a} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))