* Step 1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + 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: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. cons_0(2,2) -> 1 cons_0(2,2) -> 2 cons_1(2,2) -> 1 cons_1(2,2) -> 3 cons_1(2,3) -> 1 cons_1(2,3) -> 3 empty_0() -> 1 empty_0() -> 2 empty_1() -> 1 empty_1() -> 3 r1_0(2,2) -> 1 r1_1(2,3) -> 1 rev_0(2) -> 1 2 -> 1 3 -> 1 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))