YES(?,O(n^1)) 5.32/1.60 YES(?,O(n^1)) 5.32/1.60 5.32/1.60 We are left with following problem, upon which TcT provides the 5.32/1.60 certificate YES(?,O(n^1)). 5.32/1.60 5.32/1.60 Strict Trs: 5.32/1.60 { group3(@l) -> group3#1(@l) 5.32/1.60 , group3#1(::(@x, @xs)) -> group3#2(@xs, @x) 5.32/1.60 , group3#1(nil()) -> nil() 5.32/1.60 , group3#2(::(@y, @ys), @x) -> group3#3(@ys, @x, @y) 5.32/1.60 , group3#2(nil(), @x) -> nil() 5.32/1.60 , group3#3(::(@z, @zs), @x, @y) -> 5.32/1.60 ::(tuple#3(@x, @y, @z), group3(@zs)) 5.32/1.60 , group3#3(nil(), @x, @y) -> nil() 5.32/1.60 , zip3(@l1, @l2, @l3) -> zip3#1(@l1, @l2, @l3) 5.32/1.60 , zip3#1(::(@x, @xs), @l2, @l3) -> zip3#2(@l2, @l3, @x, @xs) 5.32/1.60 , zip3#1(nil(), @l2, @l3) -> nil() 5.32/1.60 , zip3#2(::(@y, @ys), @l3, @x, @xs) -> 5.32/1.60 zip3#3(@l3, @x, @xs, @y, @ys) 5.32/1.60 , zip3#2(nil(), @l3, @x, @xs) -> nil() 5.32/1.60 , zip3#3(::(@z, @zs), @x, @xs, @y, @ys) -> 5.32/1.60 ::(tuple#3(@x, @y, @z), zip3(@xs, @ys, @zs)) 5.32/1.60 , zip3#3(nil(), @x, @xs, @y, @ys) -> nil() } 5.32/1.60 Obligation: 5.32/1.60 innermost runtime complexity 5.32/1.60 Answer: 5.32/1.60 YES(?,O(n^1)) 5.32/1.60 5.32/1.60 The problem is match-bounded by 2. The enriched problem is 5.32/1.60 compatible with the following automaton. 5.32/1.60 { group3_0(2) -> 1 5.32/1.60 , group3_1(2) -> 4 5.32/1.60 , group3#1_0(2) -> 1 5.32/1.60 , group3#1_1(2) -> 1 5.32/1.60 , group3#1_2(2) -> 4 5.32/1.60 , ::_0(2, 2) -> 2 5.32/1.60 , ::_1(3, 4) -> 1 5.32/1.60 , ::_1(3, 4) -> 4 5.32/1.60 , group3#2_0(2, 2) -> 1 5.32/1.60 , group3#2_1(2, 2) -> 1 5.32/1.60 , group3#2_1(2, 2) -> 4 5.32/1.60 , nil_0() -> 2 5.32/1.60 , nil_1() -> 1 5.32/1.60 , nil_1() -> 4 5.32/1.60 , group3#3_0(2, 2, 2) -> 1 5.32/1.60 , group3#3_1(2, 2, 2) -> 1 5.32/1.60 , group3#3_1(2, 2, 2) -> 4 5.32/1.60 , tuple#3_0(2, 2, 2) -> 2 5.32/1.60 , tuple#3_1(2, 2, 2) -> 3 5.32/1.60 , zip3_0(2, 2, 2) -> 1 5.32/1.60 , zip3_1(2, 2, 2) -> 4 5.32/1.60 , zip3#1_0(2, 2, 2) -> 1 5.32/1.60 , zip3#1_1(2, 2, 2) -> 1 5.32/1.60 , zip3#1_2(2, 2, 2) -> 4 5.32/1.60 , zip3#2_0(2, 2, 2, 2) -> 1 5.32/1.60 , zip3#2_1(2, 2, 2, 2) -> 1 5.32/1.60 , zip3#2_1(2, 2, 2, 2) -> 4 5.32/1.60 , zip3#3_0(2, 2, 2, 2, 2) -> 1 5.32/1.60 , zip3#3_1(2, 2, 2, 2, 2) -> 1 5.32/1.60 , zip3#3_1(2, 2, 2, 2, 2) -> 4 } 5.32/1.60 5.32/1.60 Hurray, we answered YES(?,O(n^1)) 5.32/1.61 EOF