YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = A] (?,1) 1. start(A,B,C,D) -> lbl32(A,B,C,-1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = A] (?,1) 2. lbl32(A,B,C,D) -> stop(A,B,C,D) [-1 + A + -1*D >= 0 (?,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && A >= 2 && D = 1 && B = C] 3. lbl32(A,B,C,D) -> lbl32(A,B,C,-1 + D) [-1 + A + -1*D >= 0 (?,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && D >= 2 && D >= 1 && A >= 1 + D && B = C] 4. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl32,4);(start,4);(start0,4);(stop,4)} 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(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = A] (1,1) 1. start(A,B,C,D) -> lbl32(A,B,C,-1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = A] (1,1) 2. lbl32(A,B,C,D) -> stop(A,B,C,D) [-1 + A + -1*D >= 0 (1,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && A >= 2 && D = 1 && B = C] 3. lbl32(A,B,C,D) -> lbl32(A,B,C,-1 + D) [-1 + A + -1*D >= 0 (?,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && D >= 2 && D >= 1 && A >= 1 + D && B = C] 4. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl32,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{2,3},2->{},3->{2,3},4->{0,1}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = A] (?,1) 1. start(A,B,C,D) -> lbl32(A,B,C,-1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = A] (?,1) 2. lbl32(A,B,C,D) -> stop(A,B,C,D) [-1 + A + -1*D >= 0 (?,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && A >= 2 && D = 1 && B = C] 3. lbl32(A,B,C,D) -> lbl32(A,B,C,-1 + D) [-1 + A + -1*D >= 0 (?,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && D >= 2 && D >= 1 && A >= 1 + D && B = C] 4. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) 5. lbl32(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) 6. start(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(lbl32,4);(start,4);(start0,4);(stop,4)} 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(?,O(n^1)) + Considered Problem: (Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = A] (?,1) 1. start(A,B,C,D) -> lbl32(A,B,C,-1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = A] (?,1) 2. lbl32(A,B,C,D) -> stop(A,B,C,D) [-1 + A + -1*D >= 0 (?,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && A >= 2 && D = 1 && B = C] 3. lbl32(A,B,C,D) -> lbl32(A,B,C,-1 + D) [-1 + A + -1*D >= 0 (?,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && D >= 2 && D >= 1 && A >= 1 + D && B = C] 4. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) 5. lbl32(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) 6. start(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(lbl32,4);(start,4);(start0,4);(stop,4)} 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(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,0.0] start ~> stop [A <= A, B <= B, C <= C, D <= D] start ~> lbl32 [A <= A, B <= B, C <= C, D <= D] lbl32 ~> stop [A <= A, B <= B, C <= C, D <= D] lbl32 ~> lbl32 [A <= A, B <= B, C <= C, D <= D] start0 ~> start [A <= A, B <= C, C <= C, D <= A] lbl32 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] start ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= D] lbl32 ~> lbl32 [A <= A, B <= B, C <= C, D <= D] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0] start ~> stop [] start ~> lbl32 [] lbl32 ~> stop [] lbl32 ~> lbl32 [] start0 ~> start [A ~=> D,C ~=> B] lbl32 ~> exitus616 [] start ~> exitus616 [] + Loop: [D ~=> 0.0] lbl32 ~> lbl32 [] + Applied Processor: LareProcessor + Details: start0 ~> stop [A ~=> D,A ~=> 0.0,C ~=> B,A ~+> tick,tick ~+> tick] start0 ~> exitus616 [A ~=> D,A ~=> 0.0,C ~=> B,A ~+> tick,tick ~+> tick] + lbl32> [D ~=> 0.0,D ~+> tick,tick ~+> tick] YES(?,O(n^1))