* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y)) anchored(Nil(),y) -> y goal(x,y) -> anchored(x,y) - Signature: {anchored/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {anchored,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: anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y)) anchored(Nil(),y) -> y goal(x,y) -> anchored(x,y) - Signature: {anchored/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: anchored(y,z){y -> Cons(x,y)} = anchored(Cons(x,y),z) ->^+ anchored(y,Cons(Cons(Nil(),Nil()),z)) = C[anchored(y,Cons(Cons(Nil(),Nil()),z)) = anchored(y,z){z -> Cons(Cons(Nil(),Nil()),z)}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y)) anchored(Nil(),y) -> y goal(x,y) -> anchored(x,y) - Signature: {anchored/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. Cons_0(1,1) -> 1 Cons_0(1,1) -> 3 Cons_0(1,1) -> 4 Cons_0(1,2) -> 1 Cons_0(1,2) -> 3 Cons_0(1,2) -> 4 Cons_0(2,1) -> 1 Cons_0(2,1) -> 3 Cons_0(2,1) -> 4 Cons_0(2,2) -> 1 Cons_0(2,2) -> 3 Cons_0(2,2) -> 4 Cons_1(6,1) -> 3 Cons_1(6,1) -> 4 Cons_1(6,1) -> 5 Cons_1(6,2) -> 3 Cons_1(6,2) -> 4 Cons_1(6,2) -> 5 Cons_1(6,5) -> 3 Cons_1(6,5) -> 4 Cons_1(6,5) -> 5 Cons_1(7,8) -> 6 Nil_0() -> 2 Nil_0() -> 3 Nil_0() -> 4 Nil_1() -> 7 Nil_1() -> 8 anchored_0(1,1) -> 3 anchored_0(1,2) -> 3 anchored_0(2,1) -> 3 anchored_0(2,2) -> 3 anchored_1(1,1) -> 4 anchored_1(1,2) -> 4 anchored_1(1,5) -> 3 anchored_1(1,5) -> 4 anchored_1(2,1) -> 4 anchored_1(2,2) -> 4 anchored_1(2,5) -> 3 anchored_1(2,5) -> 4 goal_0(1,1) -> 4 goal_0(1,2) -> 4 goal_0(2,1) -> 4 goal_0(2,2) -> 4 1 -> 3 1 -> 4 2 -> 3 2 -> 4 5 -> 3 5 -> 4 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y)) anchored(Nil(),y) -> y goal(x,y) -> anchored(x,y) - Signature: {anchored/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {anchored,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))