* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: rev(++(x,x)) -> rev(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(a()) -> a() rev(b()) -> b() - Signature: {rev/1} / {++/2,a/0,b/0} - Obligation: innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: rev(++(x,x)) -> rev(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(a()) -> a() rev(b()) -> b() - Signature: {rev/1} / {++/2,a/0,b/0} - Obligation: innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: rev(y){y -> ++(x,y)} = rev(++(x,y)) ->^+ ++(rev(y),rev(x)) = C[rev(y) = rev(y){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: rev(++(x,x)) -> rev(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(a()) -> a() rev(b()) -> b() - Signature: {rev/1} / {++/2,a/0,b/0} - Obligation: innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. ++_0(1,1) -> 1 ++_0(1,2) -> 1 ++_0(1,3) -> 1 ++_0(2,1) -> 1 ++_0(2,2) -> 1 ++_0(2,3) -> 1 ++_0(3,1) -> 1 ++_0(3,2) -> 1 ++_0(3,3) -> 1 ++_1(4,4) -> 4 a_0() -> 2 a_1() -> 4 b_0() -> 3 b_1() -> 4 rev_0(1) -> 4 rev_0(2) -> 4 rev_0(3) -> 4 rev_1(1) -> 4 rev_1(2) -> 4 rev_1(3) -> 4 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: rev(++(x,x)) -> rev(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(a()) -> a() rev(b()) -> b() - Signature: {rev/1} / {++/2,a/0,b/0} - Obligation: innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))