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) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] 1. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 3. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] 4. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 5. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) Signature: {(lbl101,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{3,4,5},3->{},4->{3,4,5},5->{3,4,5},6->{0,1,2}] + 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) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] 1. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 3. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 (1,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] 4. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 5. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) Signature: {(lbl101,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{3,4,5},3->{},4->{3,4,5},5->{3,4,5},6->{0,1,2}] + 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) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] 1. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 3. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] 4. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 5. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) 7. lbl101(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 8. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl101,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5,7},2->{3,4,5,7},3->{},4->{3,4,5,7},5->{3,4,5,7},6->{0,1,2,8},7->{},8->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[4,5] c: [5] | `- p:[4] c: [4] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] 1. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 3. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] 4. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 5. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) 7. lbl101(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 8. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl101,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5,7},2->{3,4,5,7},3->{},4->{3,4,5,7},5->{3,4,5,7},6->{0,1,2,8},7->{},8->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[4,5] c: [5] | `- p:[4] c: [4]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: 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 <= D, E <= E, F <= F] start ~> lbl101 [A <= A, B <= 2*K, C <= C, D <= D, E <= K, F <= F] start ~> lbl101 [A <= A, B <= 2*K, C <= C, D <= D, E <= K, F <= F] lbl101 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl101 ~> lbl101 [A <= A, B <= A + D, C <= C, D <= D, E <= A, F <= F] lbl101 ~> lbl101 [A <= A, B <= A + D, C <= C, D <= D, E <= B, F <= F] start0 ~> start [A <= A, B <= C, C <= C, D <= A, E <= F, F <= F] lbl101 ~> 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 + B] lbl101 ~> lbl101 [A <= A, B <= A + D, C <= C, D <= D, E <= A, F <= F] lbl101 ~> lbl101 [A <= A, B <= A + D, C <= C, D <= D, E <= B, F <= F] + Loop: [0.0.0 <= K + A + B] lbl101 ~> lbl101 [A <= A, B <= A + D, C <= C, D <= D, E <= A, 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,0.0,0.0.0] start ~> stop [] start ~> lbl101 [K ~=> B,K ~=> E] start ~> lbl101 [K ~=> B,K ~=> E] lbl101 ~> stop [] lbl101 ~> lbl101 [A ~=> E,A ~+> B,D ~+> B] lbl101 ~> lbl101 [B ~=> E,A ~+> B,D ~+> B] start0 ~> start [A ~=> D,C ~=> B,F ~=> E] lbl101 ~> exitus616 [] start ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] lbl101 ~> lbl101 [A ~=> E,A ~+> B,D ~+> B] lbl101 ~> lbl101 [B ~=> E,A ~+> B,D ~+> B] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0,K ~+> 0.0.0] lbl101 ~> lbl101 [A ~=> E,A ~+> B,D ~+> B] + Applied Processor: LareProcessor + Details: start0 ~> stop [A ~=> D ,A ~=> E ,C ~=> B ,F ~=> E ,K ~=> B ,K ~=> E ,A ~+> B ,A ~+> E ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,A ~*> E ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] start0 ~> exitus616 [A ~=> D ,A ~=> E ,C ~=> B ,F ~=> E ,K ~=> B ,K ~=> E ,A ~+> B ,A ~+> E ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,A ~*> E ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + lbl101> [A ~=> E ,B ~=> E ,A ~+> B ,A ~+> E ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,D ~+> B ,D ~+> E ,D ~+> 0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> tick ,D ~*> tick ,K ~*> tick] + lbl101> [A ~=> E ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,D ~+> B ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)