YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 3. lbl52(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= D && B >= 0 && D >= 1 && A >= D && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 8. lbl72(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && 0 >= A && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{6,7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatRules WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (1,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (1,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (1,1) 3. lbl52(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= D && B >= 0 && D >= 1 && A >= D && F = A] (1,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (1,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 8. lbl72(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && 0 >= A && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{6,7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [8] * Step 3: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (1,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (1,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (1,1) 3. lbl52(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= D && B >= 0 && D >= 1 && A >= D && F = A] (1,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (1,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{6,7},3->{},4->{3,4,5},5->{6,7},6->{},7->{3,4,5},9->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3),(4,3),(7,3),(7,5)] * Step 4: UnreachableRules WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (1,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (1,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (1,1) 3. lbl52(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= D && B >= 0 && D >= 1 && A >= D && F = A] (1,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (1,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{6,7},3->{},4->{4,5},5->{6,7},6->{},7->{4},9->{0,1,2}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [3] * Step 5: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (1,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (1,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (1,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (1,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{6,7},4->{4,5},5->{6,7},6->{},7->{4},9->{0,1,2}] + Applied Processor: AddSinks + Details: () * Step 6: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) 10. lbl72(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 11. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{6,7,10},4->{4,5},5->{6,7,10},6->{},7->{4,5},9->{0,1,2,11},10->{},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,5)] * Step 7: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) 10. lbl72(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 11. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{6,7,10},4->{4,5},5->{6,7,10},6->{},7->{4},9->{0,1,2,11},10->{},11->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,4,5,6,7,9,10,11] | `- p:[4,7,5] c: [7] | `- p:[4] c: [4] * Step 8: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) 10. lbl72(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 11. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{6,7,10},4->{4,5},5->{6,7,10},6->{},7->{4},9->{0,1,2,11},10->{},11->{}] ,We construct a looptree: P: [0,1,2,4,5,6,7,9,10,11] | `- p:[4,7,5] c: [7] | `- p:[4] c: [4]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 9: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.0.0] start ~> stop [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] start ~> lbl52 [A <= A, B <= C, C <= C, D <= F, E <= E, F <= F] start ~> lbl72 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] lbl52 ~> lbl52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl52 ~> lbl72 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] lbl72 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl72 ~> lbl52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] start0 ~> start [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] lbl72 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] start ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= K + D] lbl52 ~> lbl52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl72 ~> lbl52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl52 ~> lbl72 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] + Loop: [0.0.0 <= K + B] lbl52 ~> lbl52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Applied Processor: FlowAbstraction + Details: () * Step 10: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.0.0] start ~> stop [F ~=> D] start ~> lbl52 [C ~=> B,F ~=> D] start ~> lbl72 [F ~=> B,F ~=> D] lbl52 ~> lbl52 [] lbl52 ~> lbl72 [F ~=> B,F ~=> D] lbl72 ~> stop [] lbl72 ~> lbl52 [] start0 ~> start [A ~=> F,C ~=> B,E ~=> D] lbl72 ~> exitus616 [] start ~> exitus616 [] + Loop: [D ~+> 0.0,K ~+> 0.0] lbl52 ~> lbl52 [] lbl72 ~> lbl52 [] lbl52 ~> lbl72 [F ~=> B,F ~=> D] + Loop: [B ~+> 0.0.0,K ~+> 0.0.0] lbl52 ~> lbl52 [] + Applied Processor: LareProcessor + Details: start0 ~> stop [A ~=> B ,A ~=> D ,A ~=> F ,C ~=> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> tick ,K ~*> tick] start0 ~> exitus616 [A ~=> B ,A ~=> D ,A ~=> F ,C ~=> B ,E ~=> D ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> tick ,K ~*> tick] + lbl72> [F ~=> B ,F ~=> D ,B ~+> 0.0.0 ,B ~+> tick ,D ~+> 0.0 ,D ~+> tick ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> tick ,D ~*> tick ,F ~*> tick ,K ~*> tick] lbl72> [F ~=> B ,F ~=> D ,B ~+> 0.0.0 ,B ~+> tick ,D ~+> 0.0 ,D ~+> tick ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> tick ,D ~*> tick ,F ~*> tick ,K ~*> tick] + lbl52> [B ~+> 0.0.0,B ~+> tick,tick ~+> tick,K ~+> 0.0.0,K ~+> tick] YES(?,POLY)