YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = A && C = D && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl71(A,-1 + B,-1 + C,D,1 + E,F) [A >= 1 && B = A && C = D && E = F] (?,1) 2. lbl71(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D >= 1 + C && B = 0 && C + E = D + F && A + C = D] (?,1) 3. lbl71(A,B,C,D,E,F) -> lbl71(A,-1 + B,-1 + C,D,1 + E,F) [A + C >= 1 + D && D >= 1 + C && A + C >= D && C + E = D + F && B + D = A + C] (?,1) 4. start0(A,B,C,D,E,F) -> start(A,A,D,D,F,F) True (1,1) Signature: {(lbl71,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{2,3},2->{},3->{2,3},4->{0,1}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = A && C = D && E = F] (1,1) 1. start(A,B,C,D,E,F) -> lbl71(A,-1 + B,-1 + C,D,1 + E,F) [A >= 1 && B = A && C = D && E = F] (1,1) 2. lbl71(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D >= 1 + C && B = 0 && C + E = D + F && A + C = D] (1,1) 3. lbl71(A,B,C,D,E,F) -> lbl71(A,-1 + B,-1 + C,D,1 + E,F) [A + C >= 1 + D && D >= 1 + C && A + C >= D && C + E = D + F && B + D = A + C] (?,1) 4. start0(A,B,C,D,E,F) -> start(A,A,D,D,F,F) True (1,1) Signature: {(lbl71,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{2,3},2->{},3->{2,3},4->{0,1}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = A && C = D && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl71(A,-1 + B,-1 + C,D,1 + E,F) [A >= 1 && B = A && C = D && E = F] (?,1) 2. lbl71(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D >= 1 + C && B = 0 && C + E = D + F && A + C = D] (?,1) 3. lbl71(A,B,C,D,E,F) -> lbl71(A,-1 + B,-1 + C,D,1 + E,F) [A + C >= 1 + D && D >= 1 + C && A + C >= D && C + E = D + F && B + D = A + C] (?,1) 4. start0(A,B,C,D,E,F) -> start(A,A,D,D,F,F) True (1,1) 5. lbl71(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 6. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl71,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{2,3,5},2->{},3->{2,3,5},4->{0,1,6},5->{},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[3] c: [3] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = A && C = D && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl71(A,-1 + B,-1 + C,D,1 + E,F) [A >= 1 && B = A && C = D && E = F] (?,1) 2. lbl71(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D >= 1 + C && B = 0 && C + E = D + F && A + C = D] (?,1) 3. lbl71(A,B,C,D,E,F) -> lbl71(A,-1 + B,-1 + C,D,1 + E,F) [A + C >= 1 + D && D >= 1 + C && A + C >= D && C + E = D + F && B + D = A + C] (?,1) 4. start0(A,B,C,D,E,F) -> start(A,A,D,D,F,F) True (1,1) 5. lbl71(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 6. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl71,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{2,3,5},2->{},3->{2,3,5},4->{0,1,6},5->{},6->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[3] c: [3]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] start ~> lbl71 [A <= A, B <= B, C <= K + D, D <= D, E <= K + F, F <= F] lbl71 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl71 ~> lbl71 [A <= A, B <= B, C <= B + C, D <= D, E <= K + E, F <= F] start0 ~> start [A <= A, B <= A, C <= D, D <= D, E <= F, F <= F] lbl71 ~> 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 + A + C + D] lbl71 ~> lbl71 [A <= A, B <= B, C <= B + C, D <= D, E <= K + E, F <= F] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0] start ~> stop [] start ~> lbl71 [D ~+> C,F ~+> E,K ~+> C,K ~+> E] lbl71 ~> stop [] lbl71 ~> lbl71 [B ~+> C,C ~+> C,E ~+> E,K ~+> E] start0 ~> start [A ~=> B,D ~=> C,F ~=> E] lbl71 ~> exitus616 [] start ~> exitus616 [] + Loop: [A ~+> 0.0,C ~+> 0.0,D ~+> 0.0,K ~+> 0.0] lbl71 ~> lbl71 [B ~+> C,C ~+> C,E ~+> E,K ~+> E] + Applied Processor: LareProcessor + Details: start0 ~> stop [A ~=> B ,D ~=> C ,F ~=> E ,A ~+> C ,A ~+> 0.0 ,A ~+> tick ,D ~+> C ,D ~+> 0.0 ,D ~+> tick ,F ~+> E ,tick ~+> tick ,K ~+> C ,K ~+> E ,K ~+> 0.0 ,K ~+> tick ,A ~*> C ,A ~*> E ,D ~*> C ,D ~*> E ,D ~*> 0.0 ,D ~*> tick ,K ~*> C ,K ~*> E ,K ~*> 0.0 ,K ~*> tick] start0 ~> exitus616 [A ~=> B ,D ~=> C ,F ~=> E ,A ~+> C ,A ~+> 0.0 ,A ~+> tick ,D ~+> C ,D ~+> 0.0 ,D ~+> tick ,F ~+> E ,tick ~+> tick ,K ~+> C ,K ~+> E ,K ~+> 0.0 ,K ~+> tick ,A ~*> C ,A ~*> E ,D ~*> C ,D ~*> E ,D ~*> 0.0 ,D ~*> tick ,K ~*> C ,K ~*> E ,K ~*> 0.0 ,K ~*> tick] + lbl71> [A ~+> 0.0 ,A ~+> tick ,B ~+> C ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,E ~+> E ,tick ~+> tick ,K ~+> E ,K ~+> 0.0 ,K ~+> tick ,A ~*> C ,A ~*> E ,B ~*> C ,C ~*> C ,C ~*> E ,D ~*> C ,D ~*> E ,K ~*> C ,K ~*> E] YES(?,POLY)