We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). 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() } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The problem is match-bounded by 2. The enriched problem is compatible with the following automaton. { group3_0(2) -> 1 , group3_1(2) -> 4 , group3#1_0(2) -> 1 , group3#1_1(2) -> 1 , group3#1_2(2) -> 4 , ::_0(2, 2) -> 2 , ::_1(3, 4) -> 1 , ::_1(3, 4) -> 4 , group3#2_0(2, 2) -> 1 , group3#2_1(2, 2) -> 1 , group3#2_1(2, 2) -> 4 , nil_0() -> 2 , nil_1() -> 1 , nil_1() -> 4 , group3#3_0(2, 2, 2) -> 1 , group3#3_1(2, 2, 2) -> 1 , group3#3_1(2, 2, 2) -> 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 } Hurray, we answered YES(?,O(n^1))