* Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: group3(@l) -> group3#1(@l) group3#1(::(@x,@xs)) -> group3#2(@xs,@x) group3#1(nil()) -> nil() group3#2(::(@y,@ys),@x) -> group3#3(@ys,@x,@y) group3#2(nil(),@x) -> nil() group3#3(::(@z,@zs),@x,@y) -> ::(tuple#3(@x,@y,@z),group3(@zs)) group3#3(nil(),@x,@y) -> nil() zip3(@l1,@l2,@l3) -> zip3#1(@l1,@l2,@l3) zip3#1(::(@x,@xs),@l2,@l3) -> zip3#2(@l2,@l3,@x,@xs) zip3#1(nil(),@l2,@l3) -> nil() zip3#2(::(@y,@ys),@l3,@x,@xs) -> zip3#3(@l3,@x,@xs,@y,@ys) zip3#2(nil(),@l3,@x,@xs) -> nil() zip3#3(::(@z,@zs),@x,@xs,@y,@ys) -> ::(tuple#3(@x,@y,@z),zip3(@xs,@ys,@zs)) zip3#3(nil(),@x,@xs,@y,@ys) -> nil() - Signature: {group3/1,group3#1/1,group3#2/2,group3#3/3,zip3/3,zip3#1/3,zip3#2/4,zip3#3/5} / {::/2,nil/0,tuple#3/3} - Obligation: innermost runtime complexity wrt. defined symbols {group3,group3#1,group3#2,group3#3,zip3,zip3#1,zip3#2 ,zip3#3} and constructors {::,nil,tuple#3} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: group3(@l) -> group3#1(@l) group3#1(::(@x,@xs)) -> group3#2(@xs,@x) group3#1(nil()) -> nil() group3#2(::(@y,@ys),@x) -> group3#3(@ys,@x,@y) group3#2(nil(),@x) -> nil() group3#3(::(@z,@zs),@x,@y) -> ::(tuple#3(@x,@y,@z),group3(@zs)) group3#3(nil(),@x,@y) -> nil() zip3(@l1,@l2,@l3) -> zip3#1(@l1,@l2,@l3) zip3#1(::(@x,@xs),@l2,@l3) -> zip3#2(@l2,@l3,@x,@xs) zip3#1(nil(),@l2,@l3) -> nil() zip3#2(::(@y,@ys),@l3,@x,@xs) -> zip3#3(@l3,@x,@xs,@y,@ys) zip3#2(nil(),@l3,@x,@xs) -> nil() zip3#3(::(@z,@zs),@x,@xs,@y,@ys) -> ::(tuple#3(@x,@y,@z),zip3(@xs,@ys,@zs)) zip3#3(nil(),@x,@xs,@y,@ys) -> nil() - Signature: {group3/1,group3#1/1,group3#2/2,group3#3/3,zip3/3,zip3#1/3,zip3#2/4,zip3#3/5} / {::/2,nil/0,tuple#3/3} - Obligation: innermost runtime complexity wrt. defined symbols {group3,group3#1,group3#2,group3#3,zip3,zip3#1,zip3#2 ,zip3#3} and constructors {::,nil,tuple#3} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. ::_0(2,2) -> 2 ::_1(3,4) -> 1 ::_1(3,4) -> 4 group3_0(2) -> 1 group3_1(2) -> 4 group3#1_0(2) -> 1 group3#1_1(2) -> 1 group3#1_2(2) -> 4 group3#2_0(2,2) -> 1 group3#2_1(2,2) -> 1 group3#2_1(2,2) -> 4 group3#3_0(2,2,2) -> 1 group3#3_1(2,2,2) -> 1 group3#3_1(2,2,2) -> 4 nil_0() -> 2 nil_1() -> 1 nil_1() -> 4 tuple#3_0(2,2,2) -> 2 tuple#3_1(2,2,2) -> 3 zip3_0(2,2,2) -> 1 zip3_1(2,2,2) -> 4 zip3#1_0(2,2,2) -> 1 zip3#1_1(2,2,2) -> 1 zip3#1_2(2,2,2) -> 4 zip3#2_0(2,2,2,2) -> 1 zip3#2_1(2,2,2,2) -> 1 zip3#2_1(2,2,2,2) -> 4 zip3#3_0(2,2,2,2,2) -> 1 zip3#3_1(2,2,2,2,2) -> 1 zip3#3_1(2,2,2,2,2) -> 4 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: group3(@l) -> group3#1(@l) group3#1(::(@x,@xs)) -> group3#2(@xs,@x) group3#1(nil()) -> nil() group3#2(::(@y,@ys),@x) -> group3#3(@ys,@x,@y) group3#2(nil(),@x) -> nil() group3#3(::(@z,@zs),@x,@y) -> ::(tuple#3(@x,@y,@z),group3(@zs)) group3#3(nil(),@x,@y) -> nil() zip3(@l1,@l2,@l3) -> zip3#1(@l1,@l2,@l3) zip3#1(::(@x,@xs),@l2,@l3) -> zip3#2(@l2,@l3,@x,@xs) zip3#1(nil(),@l2,@l3) -> nil() zip3#2(::(@y,@ys),@l3,@x,@xs) -> zip3#3(@l3,@x,@xs,@y,@ys) zip3#2(nil(),@l3,@x,@xs) -> nil() zip3#3(::(@z,@zs),@x,@xs,@y,@ys) -> ::(tuple#3(@x,@y,@z),zip3(@xs,@ys,@zs)) zip3#3(nil(),@x,@xs,@y,@ys) -> nil() - Signature: {group3/1,group3#1/1,group3#2/2,group3#3/3,zip3/3,zip3#1/3,zip3#2/4,zip3#3/5} / {::/2,nil/0,tuple#3/3} - Obligation: innermost runtime complexity wrt. defined symbols {group3,group3#1,group3#2,group3#3,zip3,zip3#1,zip3#2 ,zip3#3} and constructors {::,nil,tuple#3} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))