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 >= 1 + A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] (?,1) 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] (?,1) 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl101,6);(lbl121,6);(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->{6,7},7->{3,4,5},8->{0,1,2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= 1 + A && B = C && D = E && F = A] (1,1) 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] (1,1) 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] (1,1) 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] (1,1) 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl101,6);(lbl121,6);(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->{6,7},7->{3,4,5},8->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(4,5),(7,3)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= 1 + A && B = C && D = E && F = A] (1,1) 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] (1,1) 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] (1,1) 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] (1,1) 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4},2->{6,7},3->{},4->{3,4},5->{6,7},6->{6,7},7->{4,5},8->{0,1,2}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= 1 + A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] (?,1) 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] (?,1) 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) 9. lbl121(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 10. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5,9},2->{6,7},3->{},4->{3,4,5,9},5->{6,7},6->{6,7},7->{3,4,5,9},8->{0,1,2,10},9->{},10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(4,5),(7,3)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= 1 + A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] (?,1) 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] (?,1) 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) 9. lbl121(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 10. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,9},2->{6,7},3->{},4->{3,4,9},5->{6,7},6->{6,7},7->{4,5,9},8->{0,1,2,10},9->{},10->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[6,5,7] c: [7] | | | `- p:[6] c: [6] | `- p:[4] c: [4] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= 1 + A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] (?,1) 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] (?,1) 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) 9. lbl121(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 10. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,9},2->{6,7},3->{},4->{3,4,9},5->{6,7},6->{6,7},7->{4,5,9},8->{0,1,2,10},9->{},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[6,5,7] c: [7] | | | `- p:[6] c: [6] | `- p:[4] c: [4]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.0.0,0.1] start ~> stop [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] start ~> lbl121 [A <= A, B <= K, C <= C, D <= K, E <= E, F <= F] start ~> lbl101 [A <= A, B <= 2*K, C <= C, D <= F, E <= E, F <= F] lbl121 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl121 ~> lbl121 [A <= A, B <= K, C <= C, D <= K, E <= E, F <= F] lbl121 ~> lbl101 [A <= A, B <= 2*K, C <= C, D <= D, E <= E, F <= F] lbl101 ~> lbl101 [A <= A, B <= A + F, C <= C, D <= D, E <= E, F <= F] lbl101 ~> lbl121 [A <= A, B <= B, C <= C, D <= A, E <= E, F <= F] start0 ~> start [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] lbl121 ~> 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] lbl101 ~> lbl101 [A <= A, B <= A + F, C <= C, D <= D, E <= E, F <= F] lbl121 ~> lbl101 [A <= A, B <= 2*K, C <= C, D <= D, E <= E, F <= F] lbl101 ~> lbl121 [A <= A, B <= B, C <= C, D <= A, E <= E, F <= F] + Loop: [0.0.0 <= B + 2*D] lbl101 ~> lbl101 [A <= A, B <= A + F, C <= C, D <= D, E <= E, F <= F] + Loop: [0.1 <= K + D] lbl121 ~> lbl121 [A <= A, B <= K, C <= C, D <= K, E <= E, F <= F] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.0.0,0.1] start ~> stop [F ~=> D] start ~> lbl121 [K ~=> B,K ~=> D] start ~> lbl101 [F ~=> D,K ~=> B] lbl121 ~> stop [] lbl121 ~> lbl121 [K ~=> B,K ~=> D] lbl121 ~> lbl101 [K ~=> B] lbl101 ~> lbl101 [A ~+> B,F ~+> B] lbl101 ~> lbl121 [A ~=> D] start0 ~> start [A ~=> F,C ~=> B,E ~=> D] lbl121 ~> exitus616 [] start ~> exitus616 [] + Loop: [D ~+> 0.0,K ~+> 0.0] lbl101 ~> lbl101 [A ~+> B,F ~+> B] lbl121 ~> lbl101 [K ~=> B] lbl101 ~> lbl121 [A ~=> D] + Loop: [B ~+> 0.0.0,D ~*> 0.0.0] lbl101 ~> lbl101 [A ~+> B,F ~+> B] + Loop: [D ~+> 0.1,K ~+> 0.1] lbl121 ~> lbl121 [K ~=> B,K ~=> D] + Applied Processor: LareProcessor + Details: start0 ~> stop [A ~=> D ,A ~=> F ,C ~=> B ,K ~=> B ,K ~=> D ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> 0.1 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.1 ,K ~*> tick] start0 ~> exitus616 [A ~=> D ,A ~=> F ,C ~=> B ,E ~=> D ,K ~=> B ,K ~=> D ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> 0.1 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.1 ,K ~*> tick] + lbl121> [A ~=> D ,K ~=> B ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,D ~+> 0.0 ,D ~+> tick ,F ~+> B ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,D ~*> 0.0.0 ,D ~*> tick ,F ~*> tick ,K ~*> tick] lbl121> [A ~=> D ,K ~=> B ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,D ~+> 0.0 ,D ~+> tick ,F ~+> B ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> tick ,D ~*> 0.0.0 ,D ~*> tick ,F ~*> tick ,K ~*> tick] + lbl101> [A ~+> B,B ~+> 0.0.0,B ~+> tick,F ~+> B,tick ~+> tick,D ~*> 0.0.0,D ~*> tick] + lbl121> [K ~=> B,K ~=> D,D ~+> 0.1,D ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,POLY)