*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
append(@l1,@l2) -> append#1(@l1,@l2)
append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
append#1(nil(),@l2) -> @l2
appendAll(@l) -> appendAll#1(@l)
appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
appendAll#1(nil()) -> nil()
appendAll2(@l) -> appendAll2#1(@l)
appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
appendAll2#1(nil()) -> nil()
appendAll3(@l) -> appendAll3#1(@l)
appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
appendAll3#1(nil()) -> nil()
Weak DP Rules:
Weak TRS Rules:
Signature:
{append/2,append#1/2,appendAll/1,appendAll#1/1,appendAll2/1,appendAll2#1/1,appendAll3/1,appendAll3#1/1} / {::/2,nil/0}
Obligation:
Innermost
basic terms: {append,append#1,appendAll,appendAll#1,appendAll2,appendAll2#1,appendAll3,appendAll3#1}/{::,nil}
Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
Proof:
The problem is match-bounded by 4.
The enriched problem is compatible with follwoing automaton.
::_0(2,2) -> 1
::_0(2,2) -> 2
::_0(2,2) -> 3
::_1(2,1) -> 1
::_1(2,3) -> 1
::_1(2,3) -> 3
::_1(2,4) -> 1
::_1(2,4) -> 4
::_2(2,7) -> 1
::_2(2,7) -> 5
::_2(2,7) -> 7
::_3(2,8) -> 1
::_3(2,8) -> 6
::_3(2,8) -> 8
append_0(2,2) -> 1
append_1(2,2) -> 3
append_1(2,4) -> 1
append_1(2,4) -> 4
append_1(4,5) -> 1
append_1(4,5) -> 5
append_1(4,5) -> 7
append_1(5,6) -> 1
append_1(5,6) -> 6
append_1(5,6) -> 8
append_2(4,5) -> 7
append_3(7,6) -> 8
append#1_0(2,2) -> 1
append#1_1(2,2) -> 1
append#1_2(2,2) -> 3
append#1_2(2,4) -> 1
append#1_2(2,4) -> 4
append#1_2(4,5) -> 1
append#1_2(4,5) -> 5
append#1_2(4,5) -> 7
append#1_2(5,6) -> 1
append#1_2(5,6) -> 6
append#1_2(5,6) -> 8
append#1_3(4,5) -> 7
append#1_4(7,6) -> 8
appendAll_0(2) -> 1
appendAll_1(2) -> 1
appendAll_1(2) -> 4
appendAll#1_0(2) -> 1
appendAll#1_1(2) -> 1
appendAll#1_2(2) -> 1
appendAll#1_2(2) -> 4
appendAll2_0(2) -> 1
appendAll2_1(2) -> 1
appendAll2_1(2) -> 5
appendAll2_1(2) -> 7
appendAll2#1_0(2) -> 1
appendAll2#1_1(2) -> 1
appendAll2#1_2(2) -> 1
appendAll2#1_2(2) -> 5
appendAll2#1_2(2) -> 7
appendAll3_0(2) -> 1
appendAll3_1(2) -> 1
appendAll3_1(2) -> 6
appendAll3_1(2) -> 8
appendAll3#1_0(2) -> 1
appendAll3#1_1(2) -> 1
appendAll3#1_2(2) -> 1
appendAll3#1_2(2) -> 6
appendAll3#1_2(2) -> 8
nil_0() -> 1
nil_0() -> 2
nil_0() -> 3
nil_1() -> 1
nil_1() -> 4
nil_1() -> 5
nil_1() -> 6
nil_1() -> 7
nil_1() -> 8
2 -> 1
2 -> 3
4 -> 1
5 -> 1
5 -> 7
6 -> 1
6 -> 8
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
append(@l1,@l2) -> append#1(@l1,@l2)
append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
append#1(nil(),@l2) -> @l2
appendAll(@l) -> appendAll#1(@l)
appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
appendAll#1(nil()) -> nil()
appendAll2(@l) -> appendAll2#1(@l)
appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
appendAll2#1(nil()) -> nil()
appendAll3(@l) -> appendAll3#1(@l)
appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
appendAll3#1(nil()) -> nil()
Signature:
{append/2,append#1/2,appendAll/1,appendAll#1/1,appendAll2/1,appendAll2#1/1,appendAll3/1,appendAll3#1/1} / {::/2,nil/0}
Obligation:
Innermost
basic terms: {append,append#1,appendAll,appendAll#1,appendAll2,appendAll2#1,appendAll3,appendAll3#1}/{::,nil}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).