YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F) -> f2(-1 + A,-1 + B,A,B,-2 + A,F) [A >= 1 && B >= 1] (?,1) 1. f3(A,B,C,D,E,F) -> f2(A,B,C,D,E,F) True (1,1) 2. f2(A,B,C,D,E,F) -> f4(A,G,C,D,E,H) [0 >= B && 0 >= G] (?,1) 3. f2(A,B,C,D,E,F) -> f4(A,B,C,D,E,H) [B >= 1 && 0 >= A] (?,1) Signature: {(f2,6);(f3,6);(f4,6)} Flow Graph: [0->{0,2,3},1->{0,2,3},2->{},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. f2(A,B,C,D,E,F) -> f2(-1 + A,-1 + B,A,B,-2 + A,F) [A >= 1 && B >= 1] (?,1) 1. f3(A,B,C,D,E,F) -> f2(A,B,C,D,E,F) True (1,1) 2. f2(A,B,C,D,E,F) -> f4(A,G,C,D,E,H) [0 >= B && 0 >= G] (1,1) 3. f2(A,B,C,D,E,F) -> f4(A,B,C,D,E,H) [B >= 1 && 0 >= A] (1,1) Signature: {(f2,6);(f3,6);(f4,6)} Flow Graph: [0->{0,2,3},1->{0,2,3},2->{},3->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F) -> f2(-1 + A,-1 + B,A,B,-2 + A,F) [A >= 1 && B >= 1] (?,1) 1. f3(A,B,C,D,E,F) -> f2(A,B,C,D,E,F) True (1,1) 2. f2(A,B,C,D,E,F) -> f4(A,G,C,D,E,H) [0 >= B && 0 >= G] (?,1) 3. f2(A,B,C,D,E,F) -> f4(A,B,C,D,E,H) [B >= 1 && 0 >= A] (?,1) 4. f2(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(f2,6);(f3,6);(f4,6)} Flow Graph: [0->{0,2,3,4},1->{0,2,3,4},2->{},3->{},4->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[0] c: [0] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f2(A,B,C,D,E,F) -> f2(-1 + A,-1 + B,A,B,-2 + A,F) [A >= 1 && B >= 1] (?,1) 1. f3(A,B,C,D,E,F) -> f2(A,B,C,D,E,F) True (1,1) 2. f2(A,B,C,D,E,F) -> f4(A,G,C,D,E,H) [0 >= B && 0 >= G] (?,1) 3. f2(A,B,C,D,E,F) -> f4(A,B,C,D,E,H) [B >= 1 && 0 >= A] (?,1) 4. f2(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(f2,6);(f3,6);(f4,6)} Flow Graph: [0->{0,2,3,4},1->{0,2,3,4},2->{},3->{},4->{}] ,We construct a looptree: P: [0,1,2,3,4] | `- p:[0] c: [0]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0] f2 ~> f2 [A <= A, B <= B, C <= A, D <= B, E <= A, F <= F] f3 ~> f2 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] f2 ~> f4 [A <= A, B <= unknown, C <= C, D <= D, E <= E, F <= unknown] f2 ~> f4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= unknown] f2 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= A] f2 ~> f2 [A <= A, B <= B, C <= A, D <= B, E <= A, F <= F] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0] f2 ~> f2 [A ~=> C,A ~=> E,B ~=> D] f3 ~> f2 [] f2 ~> f4 [huge ~=> B,huge ~=> F] f2 ~> f4 [huge ~=> F] f2 ~> exitus616 [] + Loop: [A ~=> 0.0] f2 ~> f2 [A ~=> C,A ~=> E,B ~=> D] + Applied Processor: LareProcessor + Details: f3 ~> exitus616 [A ~=> C,A ~=> E,A ~=> 0.0,B ~=> D,A ~+> tick,tick ~+> tick] f3 ~> f4 [A ~=> C,A ~=> E,A ~=> 0.0,B ~=> D,huge ~=> B,huge ~=> F,A ~+> tick,tick ~+> tick] + f2> [A ~=> C,A ~=> E,A ~=> 0.0,B ~=> D,A ~+> tick,tick ~+> tick] YES(?,O(n^1))