*** 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: Full 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: Full basic terms: {++,flatten,rev}/{nil,unit} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).