YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evaleasy2start(A) -> evaleasy2entryin(A) True (1,1) 1. evaleasy2entryin(A) -> evaleasy2bb1in(A) True (?,1) 2. evaleasy2bb1in(A) -> evaleasy2bbin(A) [A >= 1] (?,1) 3. evaleasy2bb1in(A) -> evaleasy2returnin(A) [0 >= A] (?,1) 4. evaleasy2bbin(A) -> evaleasy2bb1in(-1 + A) [-1 + A >= 0] (?,1) 5. evaleasy2returnin(A) -> evaleasy2stop(A) [-1*A >= 0] (?,1) Signature: {(evaleasy2bb1in,1) ;(evaleasy2bbin,1) ;(evaleasy2entryin,1) ;(evaleasy2returnin,1) ;(evaleasy2start,1) ;(evaleasy2stop,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evaleasy2start(A) -> evaleasy2entryin(A) True (1,1) 1. evaleasy2entryin(A) -> evaleasy2bb1in(A) True (1,1) 2. evaleasy2bb1in(A) -> evaleasy2bbin(A) [A >= 1] (?,1) 3. evaleasy2bb1in(A) -> evaleasy2returnin(A) [0 >= A] (1,1) 4. evaleasy2bbin(A) -> evaleasy2bb1in(-1 + A) [-1 + A >= 0] (?,1) 5. evaleasy2returnin(A) -> evaleasy2stop(A) [-1*A >= 0] (1,1) Signature: {(evaleasy2bb1in,1) ;(evaleasy2bbin,1) ;(evaleasy2entryin,1) ;(evaleasy2returnin,1) ;(evaleasy2start,1) ;(evaleasy2stop,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evaleasy2start(A) -> evaleasy2entryin(A) True (1,1) 1. evaleasy2entryin(A) -> evaleasy2bb1in(A) True (?,1) 2. evaleasy2bb1in(A) -> evaleasy2bbin(A) [A >= 1] (?,1) 3. evaleasy2bb1in(A) -> evaleasy2returnin(A) [0 >= A] (?,1) 4. evaleasy2bbin(A) -> evaleasy2bb1in(-1 + A) [-1 + A >= 0] (?,1) 5. evaleasy2returnin(A) -> evaleasy2stop(A) [-1*A >= 0] (?,1) 6. evaleasy2returnin(A) -> exitus616(A) True (?,1) Signature: {(evaleasy2bb1in,1) ;(evaleasy2bbin,1) ;(evaleasy2entryin,1) ;(evaleasy2returnin,1) ;(evaleasy2start,1) ;(evaleasy2stop,1) ;(exitus616,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{2,3},5->{},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[2,4] c: [4] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. evaleasy2start(A) -> evaleasy2entryin(A) True (1,1) 1. evaleasy2entryin(A) -> evaleasy2bb1in(A) True (?,1) 2. evaleasy2bb1in(A) -> evaleasy2bbin(A) [A >= 1] (?,1) 3. evaleasy2bb1in(A) -> evaleasy2returnin(A) [0 >= A] (?,1) 4. evaleasy2bbin(A) -> evaleasy2bb1in(-1 + A) [-1 + A >= 0] (?,1) 5. evaleasy2returnin(A) -> evaleasy2stop(A) [-1*A >= 0] (?,1) 6. evaleasy2returnin(A) -> exitus616(A) True (?,1) Signature: {(evaleasy2bb1in,1) ;(evaleasy2bbin,1) ;(evaleasy2entryin,1) ;(evaleasy2returnin,1) ;(evaleasy2start,1) ;(evaleasy2stop,1) ;(exitus616,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{2,3},5->{},6->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[2,4] c: [4]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,0.0] evaleasy2start ~> evaleasy2entryin [A <= A] evaleasy2entryin ~> evaleasy2bb1in [A <= A] evaleasy2bb1in ~> evaleasy2bbin [A <= A] evaleasy2bb1in ~> evaleasy2returnin [A <= A] evaleasy2bbin ~> evaleasy2bb1in [A <= A] evaleasy2returnin ~> evaleasy2stop [A <= A] evaleasy2returnin ~> exitus616 [A <= A] + Loop: [0.0 <= A] evaleasy2bb1in ~> evaleasy2bbin [A <= A] evaleasy2bbin ~> evaleasy2bb1in [A <= A] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] evaleasy2start ~> evaleasy2entryin [] evaleasy2entryin ~> evaleasy2bb1in [] evaleasy2bb1in ~> evaleasy2bbin [] evaleasy2bb1in ~> evaleasy2returnin [] evaleasy2bbin ~> evaleasy2bb1in [] evaleasy2returnin ~> evaleasy2stop [] evaleasy2returnin ~> exitus616 [] + Loop: [A ~=> 0.0] evaleasy2bb1in ~> evaleasy2bbin [] evaleasy2bbin ~> evaleasy2bb1in [] + Applied Processor: LareProcessor + Details: evaleasy2start ~> exitus616 [A ~=> 0.0,A ~+> tick,tick ~+> tick] evaleasy2start ~> evaleasy2stop [A ~=> 0.0,A ~+> tick,tick ~+> tick] + evaleasy2bb1in> [A ~=> 0.0,A ~+> tick,tick ~+> tick] YES(?,O(n^1))