*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS 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()
Weak DP Rules:
Weak TRS Rules:
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
basic terms: {group3,group3#1,group3#2,group3#3,zip3,zip3#1,zip3#2,zip3#3}/{::,nil,tuple#3}
Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
Proof:
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
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS 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()
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
basic terms: {group3,group3#1,group3#2,group3#3,zip3,zip3#1,zip3#2,zip3#3}/{::,nil,tuple#3}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).