YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop1(A,B,C,D) [A >= 0 && B >= 0 && C >= 0 && D = 0] (?,1) 1. start(A,B,C,D) -> cont1(A,B,C,D) [D >= 1 && A >= 0 && B >= 0 && C >= 0 && D >= 0 && A >= D] (?,1) 2. cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [D >= 1 && B >= 0 && A >= D && C = 0] (?,1) 3. cont1(A,B,C,D) -> a(A,B,-1 + C,D) [C >= 1 && D >= 1 && C >= 0 && B >= 0 && A >= D] (?,1) 4. a(A,B,C,D) -> b(A,B,E,-1 + D) [A >= D && B >= 0 && C >= 0 && D >= 1] (?,1) 5. b(A,B,C,D) -> start(A,B,C,D) [C >= 0 && D >= 0 && B >= 0 && A >= 1 + D] (?,1) 6. b(A,B,C,D) -> stop3(A,B,C,D) [0 >= 1 + C && D >= 0 && B >= 0 && A >= 1 + D] (?,1) 7. start0(A,B,C,D) -> start(A,B,B,A) [A >= 0 && B >= 0] (1,1) Signature: {(a,4);(b,4);(cont1,4);(start,4);(start0,4);(stop1,4);(stop2,4);(stop3,4)} Flow Graph: [0->{},1->{2,3},2->{},3->{4},4->{5,6},5->{0,1},6->{},7->{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) -> stop1(A,B,C,D) [A >= 0 && B >= 0 && C >= 0 && D = 0] (1,1) 1. start(A,B,C,D) -> cont1(A,B,C,D) [D >= 1 && A >= 0 && B >= 0 && C >= 0 && D >= 0 && A >= D] (?,1) 2. cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [D >= 1 && B >= 0 && A >= D && C = 0] (1,1) 3. cont1(A,B,C,D) -> a(A,B,-1 + C,D) [C >= 1 && D >= 1 && C >= 0 && B >= 0 && A >= D] (?,1) 4. a(A,B,C,D) -> b(A,B,E,-1 + D) [A >= D && B >= 0 && C >= 0 && D >= 1] (?,1) 5. b(A,B,C,D) -> start(A,B,C,D) [C >= 0 && D >= 0 && B >= 0 && A >= 1 + D] (?,1) 6. b(A,B,C,D) -> stop3(A,B,C,D) [0 >= 1 + C && D >= 0 && B >= 0 && A >= 1 + D] (1,1) 7. start0(A,B,C,D) -> start(A,B,B,A) [A >= 0 && B >= 0] (1,1) Signature: {(a,4);(b,4);(cont1,4);(start,4);(start0,4);(stop1,4);(stop2,4);(stop3,4)} Flow Graph: [0->{},1->{2,3},2->{},3->{4},4->{5,6},5->{0,1},6->{},7->{0,1}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop1(A,B,C,D) [A >= 0 && B >= 0 && C >= 0 && D = 0] (?,1) 1. start(A,B,C,D) -> cont1(A,B,C,D) [D >= 1 && A >= 0 && B >= 0 && C >= 0 && D >= 0 && A >= D] (?,1) 2. cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [D >= 1 && B >= 0 && A >= D && C = 0] (?,1) 3. cont1(A,B,C,D) -> a(A,B,-1 + C,D) [C >= 1 && D >= 1 && C >= 0 && B >= 0 && A >= D] (?,1) 4. a(A,B,C,D) -> b(A,B,E,-1 + D) [A >= D && B >= 0 && C >= 0 && D >= 1] (?,1) 5. b(A,B,C,D) -> start(A,B,C,D) [C >= 0 && D >= 0 && B >= 0 && A >= 1 + D] (?,1) 6. b(A,B,C,D) -> stop3(A,B,C,D) [0 >= 1 + C && D >= 0 && B >= 0 && A >= 1 + D] (?,1) 7. start0(A,B,C,D) -> start(A,B,B,A) [A >= 0 && B >= 0] (1,1) 8. b(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) 9. cont1(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) 10. start(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(a,4);(b,4);(cont1,4);(exitus616,4);(start,4);(start0,4);(stop1,4);(stop2,4);(stop3,4)} Flow Graph: [0->{},1->{2,3,9},2->{},3->{4},4->{5,6,8},5->{0,1,10},6->{},7->{0,1,10},8->{},9->{},10->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[1,5,4,3] c: [5] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. start(A,B,C,D) -> stop1(A,B,C,D) [A >= 0 && B >= 0 && C >= 0 && D = 0] (?,1) 1. start(A,B,C,D) -> cont1(A,B,C,D) [D >= 1 && A >= 0 && B >= 0 && C >= 0 && D >= 0 && A >= D] (?,1) 2. cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [D >= 1 && B >= 0 && A >= D && C = 0] (?,1) 3. cont1(A,B,C,D) -> a(A,B,-1 + C,D) [C >= 1 && D >= 1 && C >= 0 && B >= 0 && A >= D] (?,1) 4. a(A,B,C,D) -> b(A,B,E,-1 + D) [A >= D && B >= 0 && C >= 0 && D >= 1] (?,1) 5. b(A,B,C,D) -> start(A,B,C,D) [C >= 0 && D >= 0 && B >= 0 && A >= 1 + D] (?,1) 6. b(A,B,C,D) -> stop3(A,B,C,D) [0 >= 1 + C && D >= 0 && B >= 0 && A >= 1 + D] (?,1) 7. start0(A,B,C,D) -> start(A,B,B,A) [A >= 0 && B >= 0] (1,1) 8. b(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) 9. cont1(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) 10. start(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(a,4);(b,4);(cont1,4);(exitus616,4);(start,4);(start0,4);(stop1,4);(stop2,4);(stop3,4)} Flow Graph: [0->{},1->{2,3,9},2->{},3->{4},4->{5,6,8},5->{0,1,10},6->{},7->{0,1,10},8->{},9->{},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[1,5,4,3] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0] start ~> stop1 [A <= A, B <= B, C <= C, D <= D] start ~> cont1 [A <= A, B <= B, C <= C, D <= D] cont1 ~> stop2 [A <= A, B <= B, C <= K, D <= D] cont1 ~> a [A <= A, B <= B, C <= C, D <= D] a ~> b [A <= A, B <= B, C <= unknown, D <= D] b ~> start [A <= A, B <= B, C <= C, D <= D] b ~> stop3 [A <= A, B <= B, C <= C, D <= D] start0 ~> start [A <= A, B <= B, C <= B, D <= A] b ~> exitus616 [A <= A, B <= B, C <= C, D <= D] cont1 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] start ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= K + D] start ~> cont1 [A <= A, B <= B, C <= C, D <= D] b ~> start [A <= A, B <= B, C <= C, D <= D] a ~> b [A <= A, B <= B, C <= unknown, D <= D] cont1 ~> a [A <= A, B <= B, C <= C, D <= D] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0] start ~> stop1 [] start ~> cont1 [] cont1 ~> stop2 [K ~=> C] cont1 ~> a [] a ~> b [huge ~=> C] b ~> start [] b ~> stop3 [] start0 ~> start [A ~=> D,B ~=> C] b ~> exitus616 [] cont1 ~> exitus616 [] start ~> exitus616 [] + Loop: [D ~+> 0.0,K ~+> 0.0] start ~> cont1 [] b ~> start [] a ~> b [huge ~=> C] cont1 ~> a [] + Applied Processor: LareProcessor + Details: start0 ~> stop3 [A ~=> D ,B ~=> C ,huge ~=> C ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> tick ,K ~*> tick] start0 ~> stop1 [A ~=> D ,B ~=> C ,huge ~=> C ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] start0 ~> exitus616 [A ~=> D ,B ~=> C ,huge ~=> C ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> tick ,K ~*> tick] start0 ~> stop2 [A ~=> D ,K ~=> C ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> tick ,K ~*> tick] + b> [huge ~=> C,D ~+> 0.0,D ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] cont1> [huge ~=> C,D ~+> 0.0,D ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] start> [huge ~=> C,D ~+> 0.0,D ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] YES(?,POLY)