YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. l0(A,B,C,D) -> l1(0,B,C,D) True (1,1) 1. l1(A,B,C,D) -> l2(A,B,0,0) [A >= 0 && -1 + B >= 0] (?,1) 2. l2(A,B,C,D) -> l2(A,B,1 + C,C + D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && -1 + B >= C] 3. l2(A,B,C,D) -> l1(A + D,-1 + B,C,D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && C >= B] 4. l1(A,B,C,D) -> l3(A,B,C,D) [A >= 0 && 0 >= B] (?,1) 5. l3(A,B,C,D) -> l3(-1 + A,B,C,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0 && -1 + A >= 0] (?,1) Signature: {(l0,4);(l1,4);(l2,4);(l3,4)} Flow Graph: [0->{1,4},1->{2,3},2->{2,3},3->{1,4},4->{5},5->{5}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. l0(A,B,C,D) -> l1(0,B,C,D) True (1,1) 1. l1(A,B,C,D) -> l2(A,B,0,0) [A >= 0 && -1 + B >= 0] (?,1) 2. l2(A,B,C,D) -> l2(A,B,1 + C,C + D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && -1 + B >= C] 3. l2(A,B,C,D) -> l1(A + D,-1 + B,C,D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && C >= B] 4. l1(A,B,C,D) -> l3(A,B,C,D) [A >= 0 && 0 >= B] (1,1) 5. l3(A,B,C,D) -> l3(-1 + A,B,C,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0 && -1 + A >= 0] (?,1) Signature: {(l0,4);(l1,4);(l2,4);(l3,4)} Flow Graph: [0->{1,4},1->{2,3},2->{2,3},3->{1,4},4->{5},5->{5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. l0(A,B,C,D) -> l1(0,B,C,D) True (1,1) 1. l1(A,B,C,D) -> l2(A,B,0,0) [A >= 0 && -1 + B >= 0] (?,1) 2. l2(A,B,C,D) -> l2(A,B,1 + C,C + D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && -1 + B >= C] 3. l2(A,B,C,D) -> l1(A + D,-1 + B,C,D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && C >= B] 4. l1(A,B,C,D) -> l3(A,B,C,D) [A >= 0 && 0 >= B] (1,1) 5. l3(A,B,C,D) -> l3(-1 + A,B,C,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0 && -1 + A >= 0] (?,1) Signature: {(l0,4);(l1,4);(l2,4);(l3,4)} Flow Graph: [0->{1,4},1->{2},2->{2,3},3->{1,4},4->{5},5->{5}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. l0(A,B,C,D) -> l1(0,B,C,D) True (1,1) 1. l1(A,B,C,D) -> l2(A,B,0,0) [A >= 0 && -1 + B >= 0] (?,1) 2. l2(A,B,C,D) -> l2(A,B,1 + C,C + D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && -1 + B >= C] 3. l2(A,B,C,D) -> l1(A + D,-1 + B,C,D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && C >= B] 4. l1(A,B,C,D) -> l3(A,B,C,D) [A >= 0 && 0 >= B] (?,1) 5. l3(A,B,C,D) -> l3(-1 + A,B,C,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0 && -1 + A >= 0] (?,1) 6. l3(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(l0,4);(l1,4);(l2,4);(l3,4)} Flow Graph: [0->{1,4},1->{2,3},2->{2,3},3->{1,4},4->{5,6},5->{5,6},6->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. l0(A,B,C,D) -> l1(0,B,C,D) True (1,1) 1. l1(A,B,C,D) -> l2(A,B,0,0) [A >= 0 && -1 + B >= 0] (?,1) 2. l2(A,B,C,D) -> l2(A,B,1 + C,C + D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && -1 + B >= C] 3. l2(A,B,C,D) -> l1(A + D,-1 + B,C,D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && C >= B] 4. l1(A,B,C,D) -> l3(A,B,C,D) [A >= 0 && 0 >= B] (?,1) 5. l3(A,B,C,D) -> l3(-1 + A,B,C,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0 && -1 + A >= 0] (?,1) 6. l3(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(l0,4);(l1,4);(l2,4);(l3,4)} Flow Graph: [0->{1,4},1->{2},2->{2,3},3->{1,4},4->{5,6},5->{5,6},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | +- p:[1,3,2] c: [3] | | | `- p:[2] c: [2] | `- p:[5] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. l0(A,B,C,D) -> l1(0,B,C,D) True (1,1) 1. l1(A,B,C,D) -> l2(A,B,0,0) [A >= 0 && -1 + B >= 0] (?,1) 2. l2(A,B,C,D) -> l2(A,B,1 + C,C + D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && -1 + B >= C] 3. l2(A,B,C,D) -> l1(A + D,-1 + B,C,D) [D >= 0 (?,1) && C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && C >= B] 4. l1(A,B,C,D) -> l3(A,B,C,D) [A >= 0 && 0 >= B] (?,1) 5. l3(A,B,C,D) -> l3(-1 + A,B,C,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0 && -1 + A >= 0] (?,1) 6. l3(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(l0,4);(l1,4);(l2,4);(l3,4)} Flow Graph: [0->{1,4},1->{2},2->{2,3},3->{1,4},4->{5,6},5->{5,6},6->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | +- p:[1,3,2] c: [3] | | | `- p:[2] c: [2] | `- p:[5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0,0.1] l0 ~> l1 [A <= 0*K, B <= B, C <= C, D <= D] l1 ~> l2 [A <= A, B <= B, C <= 0*K, D <= 0*K] l2 ~> l2 [A <= A, B <= B, C <= B, D <= C + D] l2 ~> l1 [A <= A + D, B <= C, C <= C, D <= D] l1 ~> l3 [A <= A, B <= B, C <= C, D <= D] l3 ~> l3 [A <= A, B <= B, C <= C, D <= D] l3 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= B] l1 ~> l2 [A <= A, B <= B, C <= 0*K, D <= 0*K] l2 ~> l1 [A <= A + D, B <= C, C <= C, D <= D] l2 ~> l2 [A <= A, B <= B, C <= B, D <= C + D] + Loop: [0.0.0 <= B + C] l2 ~> l2 [A <= A, B <= B, C <= B, D <= C + D] + Loop: [0.1 <= K + A] l3 ~> l3 [A <= A, B <= B, C <= C, D <= D] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0,0.1] l0 ~> l1 [K ~=> A] l1 ~> l2 [K ~=> C,K ~=> D] l2 ~> l2 [B ~=> C,C ~+> D,D ~+> D] l2 ~> l1 [C ~=> B,A ~+> A,D ~+> A] l1 ~> l3 [] l3 ~> l3 [] l3 ~> exitus616 [] + Loop: [B ~=> 0.0] l1 ~> l2 [K ~=> C,K ~=> D] l2 ~> l1 [C ~=> B,A ~+> A,D ~+> A] l2 ~> l2 [B ~=> C,C ~+> D,D ~+> D] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0] l2 ~> l2 [B ~=> C,C ~+> D,D ~+> D] + Loop: [A ~+> 0.1,K ~+> 0.1] l3 ~> l3 [] + Applied Processor: LareProcessor + Details: l0 ~> exitus616 [B ~=> C ,B ~=> 0.0 ,K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,B ~+> A ,B ~+> D ,B ~+> 0.0.0 ,B ~+> 0.1 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> D ,K ~+> 0.0.0 ,K ~+> 0.1 ,K ~+> tick ,B ~*> A ,B ~*> D ,B ~*> 0.0.0 ,B ~*> 0.1 ,B ~*> tick ,K ~*> A ,K ~*> D ,K ~*> 0.0.0 ,K ~*> 0.1 ,K ~*> tick] + l1> [B ~=> C ,B ~=> 0.0 ,K ~=> B ,K ~=> C ,K ~=> D ,A ~+> A ,B ~+> A ,B ~+> D ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> D ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> A ,B ~*> D ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> D ,K ~*> 0.0.0 ,K ~*> tick] + l2> [B ~=> C ,B ~+> D ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> D ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> D ,tick ~+> tick ,B ~*> D ,C ~*> D] + l3> [A ~+> 0.1,A ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,POLY)