YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] (1,1) 1. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] (?,1) 2. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 (?,1) && D >= 0 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] 3. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] (?,1) 4. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 && D >= 0 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] (?,1) Signature: {(m1,6);(start,6)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(0,2),(1,2),(1,3),(1,4),(2,3),(2,4),(3,1),(4,2)] * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] (1,1) 1. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] (?,1) 2. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 (?,1) && D >= 0 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] 3. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] (?,1) 4. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 && D >= 0 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] (?,1) Signature: {(m1,6);(start,6)} Flow Graph: [0->{3,4},1->{1},2->{1,2},3->{2,3,4},4->{1,3,4}] + Applied Processor: AddSinks + Details: () * Step 3: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] (1,1) 1. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] (?,1) 2. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 (?,1) && D >= 0 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] 3. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] (?,1) 4. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 && D >= 0 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] (?,1) 5. m1(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(m1,6);(start,6)} Flow Graph: [0->{1,2,3,4,5},1->{1,2,3,4,5},2->{1,2,3,4,5},3->{1,2,3,4,5},4->{1,2,3,4,5},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(0,2),(1,2),(1,3),(1,4),(2,3),(2,4),(3,1),(4,2)] * Step 4: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] (1,1) 1. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] (?,1) 2. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 (?,1) && D >= 0 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] 3. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] (?,1) 4. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 && D >= 0 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] (?,1) 5. m1(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(m1,6);(start,6)} Flow Graph: [0->{3,4,5},1->{1,5},2->{1,2,5},3->{2,3,4,5},4->{1,3,4,5},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[3,4] c: [4] | | | `- p:[3] c: [3] | +- p:[2] c: [2] | `- p:[1] c: [1] * Step 5: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] (1,1) 1. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] (?,1) 2. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 (?,1) && D >= 0 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] 3. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [B >= 1 && D >= 0 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] (?,1) 4. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [B >= 1 && D >= 0 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] (?,1) 5. m1(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(m1,6);(start,6)} Flow Graph: [0->{3,4,5},1->{1,5},2->{1,2,5},3->{2,3,4,5},4->{1,3,4,5},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- p:[3,4] c: [4] | | | `- p:[3] c: [3] | +- p:[2] c: [2] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 6: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.0.0,0.1,0.2] start ~> m1 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] m1 ~> m1 [A <= A, B <= B, C <= K + C, D <= D, E <= E, F <= B + F] m1 ~> m1 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= B + F] m1 ~> m1 [A <= A, B <= B, C <= B + C, D <= D, E <= E, F <= B + F] m1 ~> m1 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= B + F] m1 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= K + A + E] m1 ~> m1 [A <= A, B <= B, C <= B + C, D <= D, E <= E, F <= B + F] m1 ~> m1 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= B + F] + Loop: [0.0.0 <= K + B + F] m1 ~> m1 [A <= A, B <= B, C <= B + C, D <= D, E <= E, F <= B + F] + Loop: [0.1 <= K + B + F] m1 ~> m1 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= B + F] + Loop: [0.2 <= K + B + F] m1 ~> m1 [A <= A, B <= B, C <= K + C, D <= D, E <= E, F <= B + F] + Applied Processor: FlowAbstraction + Details: () * Step 7: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.0.0,0.1,0.2] start ~> m1 [] m1 ~> m1 [B ~+> F,C ~+> C,F ~+> F,K ~+> C] m1 ~> m1 [A ~+> A,B ~+> F,F ~+> F,K ~+> A] m1 ~> m1 [B ~+> C,B ~+> F,C ~+> C,F ~+> F] m1 ~> m1 [A ~+> A,B ~+> F,F ~+> F,K ~+> A] m1 ~> exitus616 [] + Loop: [A ~+> 0.0,E ~+> 0.0,K ~+> 0.0] m1 ~> m1 [B ~+> C,B ~+> F,C ~+> C,F ~+> F] m1 ~> m1 [A ~+> A,B ~+> F,F ~+> F,K ~+> A] + Loop: [B ~+> 0.0.0,F ~+> 0.0.0,K ~+> 0.0.0] m1 ~> m1 [B ~+> C,B ~+> F,C ~+> C,F ~+> F] + Loop: [B ~+> 0.1,F ~+> 0.1,K ~+> 0.1] m1 ~> m1 [A ~+> A,B ~+> F,F ~+> F,K ~+> A] + Loop: [B ~+> 0.2,F ~+> 0.2,K ~+> 0.2] m1 ~> m1 [B ~+> F,C ~+> C,F ~+> F,K ~+> C] + Applied Processor: LareProcessor + Details: start ~> exitus616 [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> C ,B ~+> F ,B ~+> 0.0.0 ,B ~+> 0.1 ,B ~+> 0.2 ,B ~+> tick ,C ~+> C ,E ~+> 0.0 ,E ~+> tick ,F ~+> F ,F ~+> 0.0.0 ,F ~+> 0.1 ,F ~+> 0.2 ,F ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,A ~*> A ,A ~*> C ,A ~*> F ,A ~*> tick ,B ~*> A ,B ~*> C ,B ~*> F ,E ~*> A ,E ~*> C ,E ~*> F ,E ~*> tick ,F ~*> A ,F ~*> C ,F ~*> F ,K ~*> A ,K ~*> C ,K ~*> F ,K ~*> tick ,A ~^> F ,E ~^> F ,K ~^> F] + m1> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> C ,B ~+> F ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> C ,E ~+> 0.0 ,E ~+> tick ,F ~+> F ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> C ,A ~*> F ,A ~*> tick ,B ~*> C ,B ~*> F ,E ~*> A ,E ~*> C ,E ~*> F ,E ~*> tick ,F ~*> C ,F ~*> F ,K ~*> A ,K ~*> C ,K ~*> F ,K ~*> tick ,A ~^> F ,E ~^> F ,K ~^> F] + m1> [B ~+> C ,B ~+> F ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> C ,F ~+> F ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> C ,B ~*> F ,F ~*> C ,F ~*> F ,K ~*> C ,K ~*> F] + m1> [A ~+> A ,B ~+> F ,B ~+> 0.1 ,B ~+> tick ,F ~+> F ,F ~+> 0.1 ,F ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.1 ,K ~+> tick ,B ~*> A ,B ~*> F ,F ~*> A ,F ~*> F ,K ~*> A ,K ~*> F] + m1> [B ~+> F ,B ~+> 0.2 ,B ~+> tick ,C ~+> C ,F ~+> F ,F ~+> 0.2 ,F ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.2 ,K ~+> tick ,B ~*> C ,B ~*> F ,F ~*> C ,F ~*> F ,K ~*> C ,K ~*> F] YES(?,POLY)