YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] (?,1) 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] (?,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] (?,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] (?,1) 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] (?,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{4,5,6,7},9->{4,5,6,7}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] (?,1) 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] (1,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] (1,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] (1,1) 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] (1,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{4,5,6,7},9->{4,5,6,7}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(8,4),(9,4)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] (?,1) 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] (1,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] (1,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] (1,1) 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] (1,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] (?,1) 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] (?,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] (?,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] (?,1) 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] (?,1) 10. f16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7,10},6->{4,5,6,7,10},7->{},8->{4,5,6,7,10},9->{4 ,5,6,7,10},10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(8,4),(9,4)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] (?,1) 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] (?,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] (?,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] (?,1) 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] (?,1) 10. f16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7,10},6->{4,5,6,7,10},7->{},8->{5,6,7,10},9->{5,6 ,7,10},10->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1,3,2] c: [3] | `- p:[5,6] c: [6] | `- p:[5] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] (?,1) 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] (?,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] (?,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] (?,1) 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] (?,1) 10. f16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7,10},6->{4,5,6,7,10},7->{},8->{5,6,7,10},9->{5,6 ,7,10},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1,3,2] c: [3] | `- p:[5,6] c: [6] | `- p:[5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,0.0,0.1,0.1.0] f0 ~> f9 [A <= 0*K, B <= 0*K, C <= unknown, D <= D, E <= E, F <= F, G <= G] f9 ~> f10 [A <= A, B <= B, C <= C, D <= C, E <= E, F <= F, G <= G] f9 ~> f10 [A <= A, B <= B, C <= C, D <= C, E <= E, F <= F, G <= G] f10 ~> f9 [A <= K + A, B <= K + A, C <= unknown, D <= D, E <= E, F <= F, G <= G] f16 ~> f28 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f16 ~> f16 [A <= K + A, B <= B, C <= C, D <= D, E <= A, F <= unknown, G <= unknown] f16 ~> f16 [A <= K + A, B <= B, C <= C, D <= D, E <= A, F <= unknown, G <= unknown] f16 ~> f28 [A <= A, B <= B, C <= C, D <= D, E <= A, F <= 0*K, G <= 0*K] f10 ~> f16 [A <= 0*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f9 ~> f16 [A <= 0*K, B <= B, C <= 0*K, D <= 0*K, E <= E, F <= F, G <= G] f16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= 10*K + A] f9 ~> f10 [A <= A, B <= B, C <= C, D <= C, E <= E, F <= F, G <= G] f10 ~> f9 [A <= K + A, B <= K + A, C <= unknown, D <= D, E <= E, F <= F, G <= G] f9 ~> f10 [A <= A, B <= B, C <= C, D <= C, E <= E, F <= F, G <= G] + Loop: [0.1 <= 10*K + A] f16 ~> f16 [A <= K + A, B <= B, C <= C, D <= D, E <= A, F <= unknown, G <= unknown] f16 ~> f16 [A <= K + A, B <= B, C <= C, D <= D, E <= A, F <= unknown, G <= unknown] + Loop: [0.1.0 <= 10*K + A] f16 ~> f16 [A <= K + A, B <= B, C <= C, D <= D, E <= A, F <= unknown, G <= unknown] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,0.0,0.1,0.1.0] f0 ~> f9 [K ~=> A,K ~=> B,huge ~=> C] f9 ~> f10 [C ~=> D] f9 ~> f10 [C ~=> D] f10 ~> f9 [huge ~=> C,A ~+> A,A ~+> B,K ~+> A,K ~+> B] f16 ~> f28 [] f16 ~> f16 [A ~=> E,huge ~=> F,huge ~=> G,A ~+> A,K ~+> A] f16 ~> f16 [A ~=> E,huge ~=> F,huge ~=> G,A ~+> A,K ~+> A] f16 ~> f28 [A ~=> E,K ~=> F,K ~=> G] f10 ~> f16 [K ~=> A] f9 ~> f16 [K ~=> A,K ~=> C,K ~=> D] f16 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f9 ~> f10 [C ~=> D] f10 ~> f9 [huge ~=> C,A ~+> A,A ~+> B,K ~+> A,K ~+> B] f9 ~> f10 [C ~=> D] + Loop: [A ~+> 0.1,K ~*> 0.1] f16 ~> f16 [A ~=> E,huge ~=> F,huge ~=> G,A ~+> A,K ~+> A] f16 ~> f16 [A ~=> E,huge ~=> F,huge ~=> G,A ~+> A,K ~+> A] + Loop: [A ~+> 0.1.0,K ~*> 0.1.0] f16 ~> f16 [A ~=> E,huge ~=> F,huge ~=> G,A ~+> A,K ~+> A] + Applied Processor: LareProcessor + Details: f0 ~> f28 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,huge ~=> C ,huge ~=> D ,huge ~=> F ,huge ~=> G ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> E ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> tick ,K ~*> A ,K ~*> B ,K ~*> E ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> tick ,K ~^> A ,K ~^> E] f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,huge ~=> C ,huge ~=> D ,huge ~=> F ,huge ~=> G ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> E ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> tick ,K ~*> A ,K ~*> B ,K ~*> E ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> tick ,K ~^> A] + f10> [C ~=> D ,huge ~=> C ,huge ~=> D ,A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,A ~*> A ,A ~*> B ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] f9> [C ~=> D ,huge ~=> C ,huge ~=> D ,A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,A ~*> A ,A ~*> B ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] + f16> [A ~=> E ,huge ~=> F ,huge ~=> G ,A ~+> A ,A ~+> E ,A ~+> 0.1 ,A ~+> 0.1.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> E ,K ~+> 0.1.0 ,K ~+> tick ,A ~*> A ,A ~*> E ,A ~*> 0.1.0 ,A ~*> tick ,K ~*> A ,K ~*> E ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> tick ,A ~^> A ,K ~^> A] + f16> [A ~=> E ,huge ~=> F ,huge ~=> G ,A ~+> A ,A ~+> E ,A ~+> 0.1.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> E ,A ~*> A ,K ~*> A ,K ~*> E ,K ~*> 0.1.0 ,K ~*> tick] YES(?,O(1))