YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f5(A,B) -> f5(-1 + A,B) [A >= 1] (?,1) 1. f5(A,B) -> f1(A,C) [0 >= A] (?,1) 2. f300(A,B) -> f5(-1 + A,B) [A >= 1] (1,1) 3. f300(A,B) -> f1(A,C) [0 >= A] (1,1) Signature: {(f1,2);(f300,2);(f5,2)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + 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. f5(A,B) -> f5(-1 + A,B) [A >= 1] (?,1) 1. f5(A,B) -> f1(A,C) [0 >= A] (1,1) 2. f300(A,B) -> f5(-1 + A,B) [A >= 1] (1,1) 3. f300(A,B) -> f1(A,C) [0 >= A] (1,1) Signature: {(f1,2);(f300,2);(f5,2)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f5(A,B) -> f5(-1 + A,B) [A >= 1] (?,1) 1. f5(A,B) -> f1(A,C) [0 >= A] (?,1) 2. f300(A,B) -> f5(-1 + A,B) [A >= 1] (1,1) 3. f300(A,B) -> f1(A,C) [0 >= A] (1,1) 4. f300(A,B) -> exitus616(A,B) True (1,1) 5. f5(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f1,2);(f300,2);(f5,2)} Flow Graph: [0->{0,1,5},1->{},2->{0,1,5},3->{},4->{},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0] c: [0] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f5(A,B) -> f5(-1 + A,B) [A >= 1] (?,1) 1. f5(A,B) -> f1(A,C) [0 >= A] (?,1) 2. f300(A,B) -> f5(-1 + A,B) [A >= 1] (1,1) 3. f300(A,B) -> f1(A,C) [0 >= A] (1,1) 4. f300(A,B) -> exitus616(A,B) True (1,1) 5. f5(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f1,2);(f300,2);(f5,2)} Flow Graph: [0->{0,1,5},1->{},2->{0,1,5},3->{},4->{},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0] c: [0]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0] f5 ~> f5 [A <= A, B <= B] f5 ~> f1 [A <= A, B <= unknown] f300 ~> f5 [A <= A, B <= B] f300 ~> f1 [A <= A, B <= unknown] f300 ~> exitus616 [A <= A, B <= B] f5 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= A] f5 ~> f5 [A <= A, B <= B] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0] f5 ~> f5 [] f5 ~> f1 [huge ~=> B] f300 ~> f5 [] f300 ~> f1 [huge ~=> B] f300 ~> exitus616 [] f5 ~> exitus616 [] + Loop: [A ~=> 0.0] f5 ~> f5 [] + Applied Processor: LareProcessor + Details: f300 ~> exitus616 [A ~=> 0.0,A ~+> tick,tick ~+> tick] f300 ~> f1 [A ~=> 0.0,huge ~=> B,A ~+> tick,tick ~+> tick] + f5> [A ~=> 0.0,A ~+> tick,tick ~+> tick] YES(?,O(n^1))