*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: ++(x,++(y,z)) -> ++(++(x,y),z) ++(x,nil()) -> x ++(.(x,y),z) -> .(x,++(y,z)) ++(nil(),y) -> y make(x) -> .(x,nil()) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(nil()) -> nil() rev(rev(x)) -> x Weak DP Rules: Weak TRS Rules: Signature: {++/2,make/1,rev/1} / {./2,nil/0} Obligation: Full basic terms: {++,make,rev}/{.,nil} Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} Proof: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. ++_0(2,2) -> 1 ++_0(2,4) -> 1 ++_0(4,2) -> 1 ++_0(4,4) -> 1 ++_1(2,2) -> 6 ++_1(2,4) -> 6 ++_1(4,2) -> 6 ++_1(4,4) -> 6 ._0(2,2) -> 1 ._0(2,2) -> 2 ._0(2,2) -> 6 ._0(2,4) -> 1 ._0(2,4) -> 2 ._0(2,4) -> 6 ._0(4,2) -> 1 ._0(4,2) -> 2 ._0(4,2) -> 6 ._0(4,4) -> 1 ._0(4,4) -> 2 ._0(4,4) -> 6 ._1(2,6) -> 1 ._1(2,6) -> 6 ._1(2,7) -> 3 ._1(4,6) -> 1 ._1(4,6) -> 6 ._1(4,7) -> 3 make_0(2) -> 3 make_0(4) -> 3 nil_0() -> 1 nil_0() -> 4 nil_0() -> 6 nil_1() -> 5 nil_1() -> 7 rev_0(2) -> 5 rev_0(4) -> 5 2 -> 1 2 -> 6 4 -> 1 4 -> 6 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: ++(x,++(y,z)) -> ++(++(x,y),z) ++(x,nil()) -> x ++(.(x,y),z) -> .(x,++(y,z)) ++(nil(),y) -> y make(x) -> .(x,nil()) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(nil()) -> nil() rev(rev(x)) -> x Signature: {++/2,make/1,rev/1} / {./2,nil/0} Obligation: Full basic terms: {++,make,rev}/{.,nil} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).