The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

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

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
group3(::(@x2_0, ::(@y44_0, ::(@z128_0, @zs129_0)))) →⁺ ::(tuple#3(@x2_0, @y44_0, @z128_0), group3(@zs129_0))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [@zs129_0 / ::(@x2_0, ::(@y44_0, ::(@z128_0, @zs129_0)))].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)