YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f2(A,B) True (1,1) 1. f2(A,B) -> f2(-1 + A,B) [A >= 1] (?,1) 2. f2(A,B) -> f1(-1 + A,C) [0 >= A] (?,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + 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. f300(A,B) -> f2(A,B) True (1,1) 1. f2(A,B) -> f2(-1 + A,B) [A >= 1] (?,1) 2. f2(A,B) -> f1(-1 + A,C) [0 >= A] (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f2(A,B) True (1,1) 1. f2(A,B) -> f2(-1 + A,B) [A >= 1] (?,1) 2. f2(A,B) -> f1(-1 + A,C) [0 >= A] (?,1) 3. f2(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f300(A,B) -> f2(A,B) True (1,1) 1. f2(A,B) -> f2(-1 + A,B) [A >= 1] (?,1) 2. f2(A,B) -> f1(-1 + A,C) [0 >= A] (?,1) 3. f2(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] ,We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0] f300 ~> f2 [A <= A, B <= B] f2 ~> f2 [A <= A, B <= B] f2 ~> f1 [A <= K + A, B <= unknown] f2 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= A] f2 ~> f2 [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] f300 ~> f2 [] f2 ~> f2 [] f2 ~> f1 [huge ~=> B,A ~+> A,K ~+> A] f2 ~> exitus616 [] + Loop: [A ~=> 0.0] f2 ~> f2 [] + Applied Processor: LareProcessor + Details: f300 ~> exitus616 [A ~=> 0.0,A ~+> tick,tick ~+> tick] f300 ~> f1 [A ~=> 0.0,huge ~=> B,A ~+> A,A ~+> tick,tick ~+> tick,K ~+> A] + f2> [A ~=> 0.0,A ~+> tick,tick ~+> tick] YES(?,O(n^1))