WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: group3(l) -> group3#1(l) group3#1(cons(x,xs)) -> group3#2(xs,x) group3#1(nil()) -> nil() group3#2(cons(y,ys),x) -> group3#3(ys,x,y) group3#2(nil(),x) -> nil() group3#3(cons(z,zs),x,y) -> cons(tuple#3(x,y,z),group3(zs)) group3#3(nil(),x,y) -> nil() zip3(l1,l2,l3) -> zip3#1(l1,l2,l3) zip3#1(cons(x,xs),l2,l3) -> zip3#2(l2,l3,x,xs) zip3#1(nil(),l2,l3) -> nil() zip3#2(cons(y,ys),l3,x,xs) -> zip3#3(l3,x,xs,y,ys) zip3#2(nil(),l3,x,xs) -> nil() zip3#3(cons(z,zs),x,xs,y,ys) -> cons(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} / {cons/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 {cons,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. cons_0(2,2) -> 2 cons_1(3,4) -> 1 cons_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 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: group3(l) -> group3#1(l) group3#1(cons(x,xs)) -> group3#2(xs,x) group3#1(nil()) -> nil() group3#2(cons(y,ys),x) -> group3#3(ys,x,y) group3#2(nil(),x) -> nil() group3#3(cons(z,zs),x,y) -> cons(tuple#3(x,y,z),group3(zs)) group3#3(nil(),x,y) -> nil() zip3(l1,l2,l3) -> zip3#1(l1,l2,l3) zip3#1(cons(x,xs),l2,l3) -> zip3#2(l2,l3,x,xs) zip3#1(nil(),l2,l3) -> nil() zip3#2(cons(y,ys),l3,x,xs) -> zip3#3(l3,x,xs,y,ys) zip3#2(nil(),l3,x,xs) -> nil() zip3#3(cons(z,zs),x,xs,y,ys) -> cons(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} / {cons/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 {cons,nil,tuple#3} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))