YES(?,O(n^1)) * Step 1: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. a(A) -> a(-1 + A) [A >= 1] (?,1) 1. start(A) -> a(100) [A = 100] (1,1) 2. start(A) -> a(A) [A >= 1] (1,1) Signature: {(a,1);(start,1)} Flow Graph: [0->{0},1->{0},2->{0}] + Applied Processor: AddSinks + Details: () * Step 2: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. a(A) -> a(-1 + A) [A >= 1] (?,1) 1. start(A) -> a(100) [A = 100] (1,1) 2. start(A) -> a(A) [A >= 1] (1,1) 3. a(A) -> exitus616(A) True (?,1) Signature: {(a,1);(exitus616,1);(start,1)} Flow Graph: [0->{0,3},1->{0,3},2->{0,3},3->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3] | `- p:[0] c: [0] * Step 3: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. a(A) -> a(-1 + A) [A >= 1] (?,1) 1. start(A) -> a(100) [A = 100] (1,1) 2. start(A) -> a(A) [A >= 1] (1,1) 3. a(A) -> exitus616(A) True (?,1) Signature: {(a,1);(exitus616,1);(start,1)} Flow Graph: [0->{0,3},1->{0,3},2->{0,3},3->{}] ,We construct a looptree: P: [0,1,2,3] | `- p:[0] c: [0]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 4: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,0.0] a ~> a [A <= A] start ~> a [A <= 100*K] start ~> a [A <= A] a ~> exitus616 [A <= A] + Loop: [0.0 <= A] a ~> a [A <= A] + Applied Processor: FlowAbstraction + Details: () * Step 5: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] a ~> a [] start ~> a [K ~=> A] start ~> a [] a ~> exitus616 [] + Loop: [A ~=> 0.0] a ~> a [] + Applied Processor: LareProcessor + Details: start ~> exitus616 [A ~=> 0.0,K ~=> A,K ~=> 0.0,A ~+> tick,tick ~+> tick,K ~+> tick] + a> [A ~=> 0.0,A ~+> tick,tick ~+> tick] YES(?,O(n^1))