YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> lbl51(E,B,0,D) [A = B && C = D] (?,1) 1. lbl51(A,B,C,D) -> stop(A,B,C,D) [C >= A && C >= 0 && 9 >= C] (?,1) 2. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 3 + C && C >= 0 && 9 >= C] (?,1) 3. lbl51(A,B,C,D) -> cut(A,B,C,D) [A >= 1 + C && 2 + C >= A && 9 >= A && C >= 0 && 9 >= C] (?,1) 4. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 10 && A >= 1 + C && 2 + C >= A && C >= 0 && 9 >= C] (?,1) 5. cut(A,B,C,D) -> lbl51(E,B,A,D) [2 + C >= A && 9 >= A && C >= 0 && A >= 1 + C] (?,1) 6. start0(A,B,C,D) -> start(B,B,D,D) True (1,1) Signature: {(cut,4);(lbl51,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{5},4->{},5->{1,2,3,4},6->{0}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> lbl51(E,B,0,D) [A = B && C = D] (1,1) 1. lbl51(A,B,C,D) -> stop(A,B,C,D) [C >= A && C >= 0 && 9 >= C] (1,1) 2. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 3 + C && C >= 0 && 9 >= C] (1,1) 3. lbl51(A,B,C,D) -> cut(A,B,C,D) [A >= 1 + C && 2 + C >= A && 9 >= A && C >= 0 && 9 >= C] (?,1) 4. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 10 && A >= 1 + C && 2 + C >= A && C >= 0 && 9 >= C] (1,1) 5. cut(A,B,C,D) -> lbl51(E,B,A,D) [2 + C >= A && 9 >= A && C >= 0 && A >= 1 + C] (?,1) 6. start0(A,B,C,D) -> start(B,B,D,D) True (1,1) Signature: {(cut,4);(lbl51,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{5},4->{},5->{1,2,3,4},6->{0}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> lbl51(E,B,0,D) [A = B && C = D] (1,1) 1. lbl51(A,B,C,D) -> stop(A,B,C,D) [C >= A && C >= 0 && 9 >= C] (1,1) 2. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 3 + C && C >= 0 && 9 >= C] (1,1) 3. lbl51(A,B,C,D) -> cut(A,B,C,D) [A >= 1 + C && 2 + C >= A && 9 >= A && C >= 0 && 9 >= C] (?,1) 4. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 10 && A >= 1 + C && 2 + C >= A && C >= 0 && 9 >= C] (1,1) 5. cut(A,B,C,D) -> lbl51(E,B,A,D) [2 + C >= A && 9 >= A && C >= 0 && A >= 1 + C] (?,1) 6. start0(A,B,C,D) -> start(B,B,D,D) True (1,1) Signature: {(cut,4);(lbl51,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{5},4->{},5->{1,2,3,4},6->{0}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> lbl51(E,B,0,D) [A = B && C = D] (?,1) 1. lbl51(A,B,C,D) -> stop(A,B,C,D) [C >= A && C >= 0 && 9 >= C] (?,1) 2. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 3 + C && C >= 0 && 9 >= C] (?,1) 3. lbl51(A,B,C,D) -> cut(A,B,C,D) [A >= 1 + C && 2 + C >= A && 9 >= A && C >= 0 && 9 >= C] (?,1) 4. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 10 && A >= 1 + C && 2 + C >= A && C >= 0 && 9 >= C] (?,1) 5. cut(A,B,C,D) -> lbl51(E,B,A,D) [2 + C >= A && 9 >= A && C >= 0 && A >= 1 + C] (?,1) 6. start0(A,B,C,D) -> start(B,B,D,D) True (1,1) 7. lbl51(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(cut,4);(exitus616,4);(lbl51,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{1,2,3,4,7},1->{},2->{},3->{5},4->{},5->{1,2,3,4,7},6->{0},7->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> lbl51(E,B,0,D) [A = B && C = D] (?,1) 1. lbl51(A,B,C,D) -> stop(A,B,C,D) [C >= A && C >= 0 && 9 >= C] (?,1) 2. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 3 + C && C >= 0 && 9 >= C] (?,1) 3. lbl51(A,B,C,D) -> cut(A,B,C,D) [A >= 1 + C && 2 + C >= A && 9 >= A && C >= 0 && 9 >= C] (?,1) 4. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 10 && A >= 1 + C && 2 + C >= A && C >= 0 && 9 >= C] (?,1) 5. cut(A,B,C,D) -> lbl51(E,B,A,D) [2 + C >= A && 9 >= A && C >= 0 && A >= 1 + C] (?,1) 6. start0(A,B,C,D) -> start(B,B,D,D) True (1,1) 7. lbl51(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(cut,4);(exitus616,4);(lbl51,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{1,2,3,7},1->{},2->{},3->{5},4->{},5->{1,2,3,4,7},6->{0},7->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[3,5] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. start(A,B,C,D) -> lbl51(E,B,0,D) [A = B && C = D] (?,1) 1. lbl51(A,B,C,D) -> stop(A,B,C,D) [C >= A && C >= 0 && 9 >= C] (?,1) 2. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 3 + C && C >= 0 && 9 >= C] (?,1) 3. lbl51(A,B,C,D) -> cut(A,B,C,D) [A >= 1 + C && 2 + C >= A && 9 >= A && C >= 0 && 9 >= C] (?,1) 4. lbl51(A,B,C,D) -> stop(A,B,C,D) [A >= 10 && A >= 1 + C && 2 + C >= A && C >= 0 && 9 >= C] (?,1) 5. cut(A,B,C,D) -> lbl51(E,B,A,D) [2 + C >= A && 9 >= A && C >= 0 && A >= 1 + C] (?,1) 6. start0(A,B,C,D) -> start(B,B,D,D) True (1,1) 7. lbl51(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(cut,4);(exitus616,4);(lbl51,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{1,2,3,7},1->{},2->{},3->{5},4->{},5->{1,2,3,4,7},6->{0},7->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[3,5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,0.0] start ~> lbl51 [A <= unknown, B <= B, C <= 0*K, D <= D] lbl51 ~> stop [A <= A, B <= B, C <= C, D <= D] lbl51 ~> stop [A <= A, B <= B, C <= C, D <= D] lbl51 ~> cut [A <= A, B <= B, C <= C, D <= D] lbl51 ~> stop [A <= A, B <= B, C <= C, D <= D] cut ~> lbl51 [A <= unknown, B <= B, C <= A, D <= D] start0 ~> start [A <= B, B <= B, C <= D, D <= D] lbl51 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= 9*K + C] lbl51 ~> cut [A <= A, B <= B, C <= C, D <= D] cut ~> lbl51 [A <= unknown, B <= B, C <= A, D <= D] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0] start ~> lbl51 [K ~=> C,huge ~=> A] lbl51 ~> stop [] lbl51 ~> stop [] lbl51 ~> cut [] lbl51 ~> stop [] cut ~> lbl51 [A ~=> C,huge ~=> A] start0 ~> start [B ~=> A,D ~=> C] lbl51 ~> exitus616 [] + Loop: [C ~+> 0.0,K ~*> 0.0] lbl51 ~> cut [] cut ~> lbl51 [A ~=> C,huge ~=> A] + Applied Processor: LareProcessor + Details: start0 ~> stop [K ~=> C ,huge ~=> A ,huge ~=> C ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] start0 ~> exitus616 [K ~=> C ,huge ~=> A ,huge ~=> C ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] + lbl51> [A ~=> C ,huge ~=> A ,huge ~=> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~*> 0.0 ,K ~*> tick] YES(?,O(1))