YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(0,0,C,D) True (1,1) 1. f6(A,B,C,D) -> f6(A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 2. f6(A,B,C,D) -> f6(2 + A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. f15(A,B,C,D) -> f19(1 + C,B,C,1) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A = 1 + C] (?,1) 4. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= A] (?,1) 5. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 2 + C] (?,1) 6. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && C >= 1 + A] (?,1) 7. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + C && B >= C] (?,1) 8. f6(A,B,C,D) -> f19(A,B,A,1) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && A = C] (?,1) Signature: {(f0,4);(f15,4);(f19,4);(f6,4)} Flow Graph: [0->{1,2,6,7,8},1->{1,2,6,7,8},2->{1,2,6,7,8},3->{},4->{},5->{},6->{3,4,5},7->{3,4,5},8->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(0,0,C,D) True (1,1) 1. f6(A,B,C,D) -> f6(A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 2. f6(A,B,C,D) -> f6(2 + A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. f15(A,B,C,D) -> f19(1 + C,B,C,1) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A = 1 + C] (1,1) 4. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= A] (1,1) 5. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 2 + C] (1,1) 6. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && C >= 1 + A] (1,1) 7. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + C && B >= C] (1,1) 8. f6(A,B,C,D) -> f19(A,B,A,1) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && A = C] (1,1) Signature: {(f0,4);(f15,4);(f19,4);(f6,4)} Flow Graph: [0->{1,2,6,7,8},1->{1,2,6,7,8},2->{1,2,6,7,8},3->{},4->{},5->{},6->{3,4,5},7->{3,4,5},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,6),(6,3),(6,5),(7,4)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(0,0,C,D) True (1,1) 1. f6(A,B,C,D) -> f6(A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 2. f6(A,B,C,D) -> f6(2 + A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. f15(A,B,C,D) -> f19(1 + C,B,C,1) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A = 1 + C] (1,1) 4. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= A] (1,1) 5. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 2 + C] (1,1) 6. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && C >= 1 + A] (1,1) 7. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + C && B >= C] (1,1) 8. f6(A,B,C,D) -> f19(A,B,A,1) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && A = C] (1,1) Signature: {(f0,4);(f15,4);(f19,4);(f6,4)} Flow Graph: [0->{1,2,7,8},1->{1,2,6,7,8},2->{1,2,6,7,8},3->{},4->{},5->{},6->{4},7->{3,5},8->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(0,0,C,D) True (1,1) 1. f6(A,B,C,D) -> f6(A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 2. f6(A,B,C,D) -> f6(2 + A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. f15(A,B,C,D) -> f19(1 + C,B,C,1) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A = 1 + C] (?,1) 4. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= A] (?,1) 5. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 2 + C] (?,1) 6. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && C >= 1 + A] (?,1) 7. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + C && B >= C] (?,1) 8. f6(A,B,C,D) -> f19(A,B,A,1) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && A = C] (?,1) 9. f6(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) 10. f15(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f0,4);(f15,4);(f19,4);(f6,4)} Flow Graph: [0->{1,2,6,7,8,9},1->{1,2,6,7,8,9},2->{1,2,6,7,8,9},3->{},4->{},5->{},6->{3,4,5,10},7->{3,4,5,10},8->{} ,9->{},10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,6),(6,3),(6,5),(7,4)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(0,0,C,D) True (1,1) 1. f6(A,B,C,D) -> f6(A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 2. f6(A,B,C,D) -> f6(2 + A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. f15(A,B,C,D) -> f19(1 + C,B,C,1) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A = 1 + C] (?,1) 4. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= A] (?,1) 5. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 2 + C] (?,1) 6. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && C >= 1 + A] (?,1) 7. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + C && B >= C] (?,1) 8. f6(A,B,C,D) -> f19(A,B,A,1) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && A = C] (?,1) 9. f6(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) 10. f15(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f0,4);(f15,4);(f19,4);(f6,4)} Flow Graph: [0->{1,2,7,8,9},1->{1,2,6,7,8,9},2->{1,2,6,7,8,9},3->{},4->{},5->{},6->{4,10},7->{3,5,10},8->{},9->{} ,10->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[1,2] c: [2] | `- p:[1] c: [1] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. f0(A,B,C,D) -> f6(0,0,C,D) True (1,1) 1. f6(A,B,C,D) -> f6(A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 2. f6(A,B,C,D) -> f6(2 + A,1 + B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. f15(A,B,C,D) -> f19(1 + C,B,C,1) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A = 1 + C] (?,1) 4. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= A] (?,1) 5. f15(A,B,C,D) -> f19(A,B,C,0) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 2 + C] (?,1) 6. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && C >= 1 + A] (?,1) 7. f6(A,B,C,D) -> f15(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + C && B >= C] (?,1) 8. f6(A,B,C,D) -> f19(A,B,A,1) [B >= 0 && A + B >= 0 && A >= 0 && B >= C && A = C] (?,1) 9. f6(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) 10. f15(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f0,4);(f15,4);(f19,4);(f6,4)} Flow Graph: [0->{1,2,7,8,9},1->{1,2,6,7,8,9},2->{1,2,6,7,8,9},3->{},4->{},5->{},6->{4,10},7->{3,5,10},8->{},9->{} ,10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[1,2] c: [2] | `- p:[1] c: [1]) + 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] f0 ~> f6 [A <= 0*K, B <= 0*K, C <= C, D <= D] f6 ~> f6 [A <= A, B <= C, C <= C, D <= D] f6 ~> f6 [A <= 2*K + A, B <= C, C <= C, D <= D] f15 ~> f19 [A <= A, B <= B, C <= C, D <= K] f15 ~> f19 [A <= A, B <= B, C <= C, D <= 0*K] f15 ~> f19 [A <= A, B <= B, C <= C, D <= 0*K] f6 ~> f15 [A <= A, B <= B, C <= C, D <= D] f6 ~> f15 [A <= A, B <= B, C <= C, D <= D] f6 ~> f19 [A <= A, B <= B, C <= A, D <= K] f6 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] f15 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= B + C] f6 ~> f6 [A <= A, B <= C, C <= C, D <= D] f6 ~> f6 [A <= 2*K + A, B <= C, C <= C, D <= D] + Loop: [0.0.0 <= B + C] f6 ~> f6 [A <= A, B <= C, 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] f0 ~> f6 [K ~=> A,K ~=> B] f6 ~> f6 [C ~=> B] f6 ~> f6 [C ~=> B,A ~+> A,K ~*> A] f15 ~> f19 [K ~=> D] f15 ~> f19 [K ~=> D] f15 ~> f19 [K ~=> D] f6 ~> f15 [] f6 ~> f15 [] f6 ~> f19 [A ~=> C,K ~=> D] f6 ~> exitus616 [] f15 ~> exitus616 [] + Loop: [B ~+> 0.0,C ~+> 0.0] f6 ~> f6 [C ~=> B] f6 ~> f6 [C ~=> B,A ~+> A,K ~*> A] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0] f6 ~> f6 [C ~=> B] + Applied Processor: LareProcessor + Details: f0 ~> f19 [C ~=> B ,K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,C ~+> 0.0 ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,C ~*> A ,C ~*> C ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> A ,K ~*> C ,K ~*> tick] f0 ~> exitus616 [C ~=> B ,K ~=> A ,K ~=> B ,C ~+> 0.0 ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,C ~*> A ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> A ,K ~*> tick] + f6> [C ~=> B ,A ~+> A ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,B ~*> A ,B ~*> tick ,C ~*> A ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> A] + f6> [C ~=> B,B ~+> 0.0.0,B ~+> tick,C ~+> 0.0.0,C ~+> tick,tick ~+> tick] YES(?,POLY)