* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: merge(x,nil()) -> x merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v()))) merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v())) merge(nil(),y) -> y - Signature: {merge/2} / {++/2,nil/0,u/0,v/0} - Obligation: innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. ++_0(1,1) -> 1 ++_0(1,1) -> 2 ++_0(1,3) -> 1 ++_0(1,3) -> 2 ++_0(1,4) -> 1 ++_0(1,4) -> 2 ++_0(1,5) -> 1 ++_0(1,5) -> 2 ++_0(3,1) -> 1 ++_0(3,1) -> 2 ++_0(3,3) -> 1 ++_0(3,3) -> 2 ++_0(3,4) -> 1 ++_0(3,4) -> 2 ++_0(3,5) -> 1 ++_0(3,5) -> 2 ++_0(4,1) -> 1 ++_0(4,1) -> 2 ++_0(4,3) -> 1 ++_0(4,3) -> 2 ++_0(4,4) -> 1 ++_0(4,4) -> 2 ++_0(4,5) -> 1 ++_0(4,5) -> 2 ++_0(5,1) -> 1 ++_0(5,1) -> 2 ++_0(5,3) -> 1 ++_0(5,3) -> 2 ++_0(5,4) -> 1 ++_0(5,4) -> 2 ++_0(5,5) -> 1 ++_0(5,5) -> 2 ++_1(1,1) -> 11 ++_1(1,3) -> 11 ++_1(1,4) -> 11 ++_1(1,5) -> 11 ++_1(1,6) -> 2 ++_1(1,6) -> 6 ++_1(3,1) -> 11 ++_1(3,3) -> 11 ++_1(3,4) -> 11 ++_1(3,5) -> 11 ++_1(3,6) -> 2 ++_1(3,6) -> 6 ++_1(4,1) -> 11 ++_1(4,3) -> 11 ++_1(4,4) -> 11 ++_1(4,5) -> 11 ++_1(4,6) -> 2 ++_1(4,6) -> 6 ++_1(5,1) -> 11 ++_1(5,3) -> 11 ++_1(5,4) -> 11 ++_1(5,5) -> 11 ++_1(5,6) -> 2 ++_1(5,6) -> 6 ++_1(8,9) -> 6 ++_1(8,9) -> 7 ++_1(8,10) -> 2 ++_1(8,10) -> 6 merge_0(1,1) -> 2 merge_0(1,3) -> 2 merge_0(1,4) -> 2 merge_0(1,5) -> 2 merge_0(3,1) -> 2 merge_0(3,3) -> 2 merge_0(3,4) -> 2 merge_0(3,5) -> 2 merge_0(4,1) -> 2 merge_0(4,3) -> 2 merge_0(4,4) -> 2 merge_0(4,5) -> 2 merge_0(5,1) -> 2 merge_0(5,3) -> 2 merge_0(5,4) -> 2 merge_0(5,5) -> 2 merge_1(1,7) -> 6 merge_1(3,7) -> 6 merge_1(4,7) -> 6 merge_1(5,7) -> 6 merge_1(11,9) -> 10 nil_0() -> 2 nil_0() -> 3 u_0() -> 2 u_0() -> 4 u_1() -> 8 v_0() -> 2 v_0() -> 5 v_1() -> 9 1 -> 2 3 -> 2 4 -> 2 5 -> 2 7 -> 6 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: merge(x,nil()) -> x merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v()))) merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v())) merge(nil(),y) -> y - Signature: {merge/2} / {++/2,nil/0,u/0,v/0} - Obligation: innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))