* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: append(Cons(x,xs),ys) -> Cons(x,append(xs,ys)) append(Nil(),ys) -> ys goal(x,y) -> append(x,y) - Signature: {append/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,goal} and constructors {Cons,Nil} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: append(Cons(x,xs),ys) -> Cons(x,append(xs,ys)) append(Nil(),ys) -> ys goal(x,y) -> append(x,y) - Signature: {append/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,goal} and constructors {Cons,Nil} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: append(y,z){y -> Cons(x,y)} = append(Cons(x,y),z) ->^+ Cons(x,append(y,z)) = C[append(y,z) = append(y,z){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: append(Cons(x,xs),ys) -> Cons(x,append(xs,ys)) append(Nil(),ys) -> ys goal(x,y) -> append(x,y) - Signature: {append/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,goal} and constructors {Cons,Nil} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. Cons_0(2,2) -> 1 Cons_0(2,2) -> 2 Cons_0(2,2) -> 3 Cons_1(2,3) -> 1 Cons_1(2,3) -> 3 Nil_0() -> 1 Nil_0() -> 2 Nil_0() -> 3 append_0(2,2) -> 1 append_1(2,2) -> 1 append_1(2,2) -> 3 goal_0(2,2) -> 1 2 -> 1 2 -> 3 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: append(Cons(x,xs),ys) -> Cons(x,append(xs,ys)) append(Nil(),ys) -> ys goal(x,y) -> append(x,y) - Signature: {append/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,goal} and constructors {Cons,Nil} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))