YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,1,F,G,H,I,J) [A >= 1 && B >= 1 + C && D = B && E = F && G = C && H = I && J = A] (?,1) 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,1 + D,1,F,G,H,I,J) [A >= 1 && C >= B && D = B && E = F && G = C && H = I && J = A] (?,1) 2. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,-1,F,G,H,I,J) [B >= 1 + C && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 3. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,1 + D,-1,F,G,H,I,J) [C >= B && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 4. lbl71(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [C >= B && A >= 1 && D = 1 + C && E = 1 && J = A && H = I && G = C] (?,1) 5. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && D >= 1 + B && 1 + C >= D && E = 1 && J = A && H = I && G = C] (?,1) 6. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && A >= 1 && E = 1 && J = A && H = I && G = C] (?,1) 7. lbl81(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [0 >= A && C >= B && D = 1 + C && 1 + E = 0 && J = A && H = I && G = C] (?,1) 8. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 9. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,B,C,B,F,F,C,I,I,A) True (1,1) Signature: {(lbl71,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5,6},2->{},3->{7,8,9},4->{},5->{4,5,6},6->{7,8,9},7->{},8->{4,5,6},9->{7,8,9},10->{0,1,2,3}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,1,F,G,H,I,J) [A >= 1 && B >= 1 + C && D = B && E = F && G = C && H = I && J = A] (1,1) 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,1 + D,1,F,G,H,I,J) [A >= 1 && C >= B && D = B && E = F && G = C && H = I && J = A] (1,1) 2. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,-1,F,G,H,I,J) [B >= 1 + C && 0 >= A && D = B && E = F && G = C && H = I && J = A] (1,1) 3. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,1 + D,-1,F,G,H,I,J) [C >= B && 0 >= A && D = B && E = F && G = C && H = I && J = A] (1,1) 4. lbl71(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [C >= B && A >= 1 && D = 1 + C && E = 1 && J = A && H = I && G = C] (1,1) 5. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && D >= 1 + B && 1 + C >= D && E = 1 && J = A && H = I && G = C] (?,1) 6. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && A >= 1 && E = 1 && J = A && H = I && G = C] (?,1) 7. lbl81(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [0 >= A && C >= B && D = 1 + C && 1 + E = 0 && J = A && H = I && G = C] (1,1) 8. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 9. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,B,C,B,F,F,C,I,I,A) True (1,1) Signature: {(lbl71,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5,6},2->{},3->{7,8,9},4->{},5->{4,5,6},6->{7,8,9},7->{},8->{4,5,6},9->{7,8,9},10->{0,1,2,3}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [6,8] * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,1,F,G,H,I,J) [A >= 1 && B >= 1 + C && D = B && E = F && G = C && H = I && J = A] (1,1) 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,1 + D,1,F,G,H,I,J) [A >= 1 && C >= B && D = B && E = F && G = C && H = I && J = A] (1,1) 2. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,-1,F,G,H,I,J) [B >= 1 + C && 0 >= A && D = B && E = F && G = C && H = I && J = A] (1,1) 3. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,1 + D,-1,F,G,H,I,J) [C >= B && 0 >= A && D = B && E = F && G = C && H = I && J = A] (1,1) 4. lbl71(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [C >= B && A >= 1 && D = 1 + C && E = 1 && J = A && H = I && G = C] (1,1) 5. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && D >= 1 + B && 1 + C >= D && E = 1 && J = A && H = I && G = C] (?,1) 7. lbl81(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [0 >= A && C >= B && D = 1 + C && 1 + E = 0 && J = A && H = I && G = C] (1,1) 9. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,B,C,B,F,F,C,I,I,A) True (1,1) Signature: {(lbl71,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5},2->{},3->{7,9},4->{},5->{4,5},7->{},9->{7,9},10->{0,1,2,3}] + Applied Processor: AddSinks + Details: () * Step 4: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,1,F,G,H,I,J) [A >= 1 && B >= 1 + C && D = B && E = F && G = C && H = I && J = A] (?,1) 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,1 + D,1,F,G,H,I,J) [A >= 1 && C >= B && D = B && E = F && G = C && H = I && J = A] (?,1) 2. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,-1,F,G,H,I,J) [B >= 1 + C && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 3. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,1 + D,-1,F,G,H,I,J) [C >= B && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 4. lbl71(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [C >= B && A >= 1 && D = 1 + C && E = 1 && J = A && H = I && G = C] (?,1) 5. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && D >= 1 + B && 1 + C >= D && E = 1 && J = A && H = I && G = C] (?,1) 7. lbl81(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [0 >= A && C >= B && D = 1 + C && 1 + E = 0 && J = A && H = I && G = C] (?,1) 9. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,B,C,B,F,F,C,I,I,A) True (1,1) 11. lbl81(A,B,C,D,E,F,G,H,I,J) -> exitus616(A,B,C,D,E,F,G,H,I,J) True (?,1) 12. start(A,B,C,D,E,F,G,H,I,J) -> exitus616(A,B,C,D,E,F,G,H,I,J) True (?,1) 13. lbl71(A,B,C,D,E,F,G,H,I,J) -> exitus616(A,B,C,D,E,F,G,H,I,J) True (?,1) Signature: {(exitus616,10);(lbl71,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5,13},2->{},3->{7,9,11},4->{},5->{4,5,13},7->{},9->{7,9,11},10->{0,1,2,3,12},11->{},12->{} ,13->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,7,9,10,11,12,13] | +- p:[9] c: [9] | `- p:[5] c: [5] * Step 5: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,1,F,G,H,I,J) [A >= 1 && B >= 1 + C && D = B && E = F && G = C && H = I && J = A] (?,1) 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,1 + D,1,F,G,H,I,J) [A >= 1 && C >= B && D = B && E = F && G = C && H = I && J = A] (?,1) 2. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,-1,F,G,H,I,J) [B >= 1 + C && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 3. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,1 + D,-1,F,G,H,I,J) [C >= B && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 4. lbl71(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [C >= B && A >= 1 && D = 1 + C && E = 1 && J = A && H = I && G = C] (?,1) 5. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && D >= 1 + B && 1 + C >= D && E = 1 && J = A && H = I && G = C] (?,1) 7. lbl81(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [0 >= A && C >= B && D = 1 + C && 1 + E = 0 && J = A && H = I && G = C] (?,1) 9. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,B,C,B,F,F,C,I,I,A) True (1,1) 11. lbl81(A,B,C,D,E,F,G,H,I,J) -> exitus616(A,B,C,D,E,F,G,H,I,J) True (?,1) 12. start(A,B,C,D,E,F,G,H,I,J) -> exitus616(A,B,C,D,E,F,G,H,I,J) True (?,1) 13. lbl71(A,B,C,D,E,F,G,H,I,J) -> exitus616(A,B,C,D,E,F,G,H,I,J) True (?,1) Signature: {(exitus616,10);(lbl71,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5,13},2->{},3->{7,9,11},4->{},5->{4,5,13},7->{},9->{7,9,11},10->{0,1,2,3,12},11->{},12->{} ,13->{}] ,We construct a looptree: P: [0,1,2,3,4,5,7,9,10,11,12,13] | +- p:[9] c: [9] | `- p:[5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 6: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,I,J,0.0,0.1] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= K, F <= F, G <= G, H <= H, I <= I, J <= J] start ~> lbl71 [A <= A, B <= B, C <= C, D <= K + B, E <= K, F <= F, G <= G, H <= H, I <= I, J <= J] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= K, F <= F, G <= G, H <= H, I <= I, J <= J] start ~> lbl81 [A <= A, B <= B, C <= C, D <= K + B, E <= K, F <= F, G <= G, H <= H, I <= I, J <= J] lbl71 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] lbl71 ~> lbl71 [A <= A, B <= B, C <= C, D <= D + E, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] lbl81 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] lbl81 ~> lbl81 [A <= A, B <= B, C <= C, D <= D + E, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] start0 ~> start [A <= A, B <= B, C <= C, D <= B, E <= F, F <= F, G <= C, H <= I, I <= I, J <= A] lbl81 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] start ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] lbl71 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] + Loop: [0.0 <= K + C + D] lbl81 ~> lbl81 [A <= A, B <= B, C <= C, D <= D + E, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] + Loop: [0.1 <= K + C + D] lbl71 ~> lbl71 [A <= A, B <= B, C <= C, D <= D + E, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] + Applied Processor: FlowAbstraction + Details: () * Step 7: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,I,J,0.0,0.1] start ~> stop [K ~=> E] start ~> lbl71 [K ~=> E,B ~+> D,K ~+> D] start ~> stop [K ~=> E] start ~> lbl81 [K ~=> E,B ~+> D,K ~+> D] lbl71 ~> stop [] lbl71 ~> lbl71 [D ~+> D,E ~+> D] lbl81 ~> stop [] lbl81 ~> lbl81 [D ~+> D,E ~+> D] start0 ~> start [A ~=> J,B ~=> D,C ~=> G,F ~=> E,I ~=> H] lbl81 ~> exitus616 [] start ~> exitus616 [] lbl71 ~> exitus616 [] + Loop: [C ~+> 0.0,D ~+> 0.0,K ~+> 0.0] lbl81 ~> lbl81 [D ~+> D,E ~+> D] + Loop: [C ~+> 0.1,D ~+> 0.1,K ~+> 0.1] lbl71 ~> lbl71 [D ~+> D,E ~+> D] + Applied Processor: LareProcessor + Details: start0 ~> exitus616 [A ~=> J ,B ~=> D ,C ~=> G ,F ~=> E ,I ~=> H ,K ~=> E ,B ~+> D ,B ~+> 0.0 ,B ~+> 0.1 ,B ~+> tick ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,B ~*> D ,C ~*> D ,K ~*> D ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] start0 ~> stop [A ~=> J ,B ~=> D ,C ~=> G ,I ~=> H ,K ~=> E ,B ~+> D ,B ~+> 0.0 ,B ~+> 0.1 ,B ~+> tick ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,B ~*> D ,C ~*> D ,K ~*> D ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + lbl81> [C ~+> 0.0 ,C ~+> tick ,D ~+> D ,D ~+> 0.0 ,D ~+> tick ,E ~+> D ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,C ~*> D ,D ~*> D ,E ~*> D ,K ~*> D] + lbl71> [C ~+> 0.1 ,C ~+> tick ,D ~+> D ,D ~+> 0.1 ,D ~+> tick ,E ~+> D ,tick ~+> tick ,K ~+> 0.1 ,K ~+> tick ,C ~*> D ,D ~*> D ,E ~*> D ,K ~*> D] YES(?,O(n^1))