*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
++(x,nil()) -> x
++(++(x,y),z) -> ++(x,++(y,z))
++(nil(),y) -> y
flatten(++(x,y)) -> ++(flatten(x),flatten(y))
flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
flatten(flatten(x)) -> flatten(x)
flatten(nil()) -> nil()
flatten(unit(x)) -> flatten(x)
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(nil()) -> nil()
rev(rev(x)) -> x
rev(unit(x)) -> unit(x)
Weak DP Rules:
Weak TRS Rules:
Signature:
{++/2,flatten/1,rev/1} / {nil/0,unit/1}
Obligation:
Innermost
basic terms: {++,flatten,rev}/{nil,unit}
Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
Proof:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
++_0(2,2) -> 1
flatten_0(2) -> 1
flatten_1(2) -> 1
nil_0() -> 1
nil_0() -> 2
nil_1() -> 1
rev_0(2) -> 1
unit_0(2) -> 1
unit_0(2) -> 2
unit_1(2) -> 1
2 -> 1
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
++(x,nil()) -> x
++(++(x,y),z) -> ++(x,++(y,z))
++(nil(),y) -> y
flatten(++(x,y)) -> ++(flatten(x),flatten(y))
flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
flatten(flatten(x)) -> flatten(x)
flatten(nil()) -> nil()
flatten(unit(x)) -> flatten(x)
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(nil()) -> nil()
rev(rev(x)) -> x
rev(unit(x)) -> unit(x)
Signature:
{++/2,flatten/1,rev/1} / {nil/0,unit/1}
Obligation:
Innermost
basic terms: {++,flatten,rev}/{nil,unit}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).