YES(?,O(1)) * Step 1: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f10(1,B,C) True (1,1) 1. f10(A,B,C) -> f13(A,1,C) [-1 + A >= 0 && 5 >= A] (?,1) 2. f13(A,B,C) -> f13(A,1 + B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] (?,1) 3. f21(A,B,C) -> f24(A,1,C) [-1 + A >= 0 && 5 >= A] (?,1) 4. f24(A,B,C) -> f27(A,B,1) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] (?,1) 5. f27(A,B,C) -> f27(A,B,1 + C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= C] 6. f27(A,B,C) -> f24(A,1 + B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && C >= 6] 7. f24(A,B,C) -> f21(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] (?,1) 8. f21(A,B,C) -> f39(A,B,C) [-1 + A >= 0 && A >= 6] (?,1) 9. f13(A,B,C) -> f10(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] (?,1) 10. f10(A,B,C) -> f21(1,B,C) [-1 + A >= 0 && A >= 6] (?,1) Signature: {(f0,3);(f10,3);(f13,3);(f21,3);(f24,3);(f27,3);(f39,3)} Flow Graph: [0->{1,10},1->{2,9},2->{2,9},3->{4,7},4->{5,6},5->{5,6},6->{4,7},7->{3,8},8->{},9->{1,10},10->{3,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,10),(1,9),(3,7),(4,6),(10,8)] * Step 2: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f10(1,B,C) True (1,1) 1. f10(A,B,C) -> f13(A,1,C) [-1 + A >= 0 && 5 >= A] (?,1) 2. f13(A,B,C) -> f13(A,1 + B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] (?,1) 3. f21(A,B,C) -> f24(A,1,C) [-1 + A >= 0 && 5 >= A] (?,1) 4. f24(A,B,C) -> f27(A,B,1) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] (?,1) 5. f27(A,B,C) -> f27(A,B,1 + C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= C] 6. f27(A,B,C) -> f24(A,1 + B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && C >= 6] 7. f24(A,B,C) -> f21(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] (?,1) 8. f21(A,B,C) -> f39(A,B,C) [-1 + A >= 0 && A >= 6] (?,1) 9. f13(A,B,C) -> f10(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] (?,1) 10. f10(A,B,C) -> f21(1,B,C) [-1 + A >= 0 && A >= 6] (?,1) Signature: {(f0,3);(f10,3);(f13,3);(f21,3);(f24,3);(f27,3);(f39,3)} Flow Graph: [0->{1},1->{2},2->{2,9},3->{4},4->{5},5->{5,6},6->{4,7},7->{3,8},8->{},9->{1,10},10->{3}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,B,C) -> f10(1,B,C) True f10(A,B,C) -> f13(A,1,C) [-1 + A >= 0 && 5 >= A] f13(A,B,C) -> f13(A,1 + B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] f21(A,B,C) -> f24(A,1,C) [-1 + A >= 0 && 5 >= A] f24(A,B,C) -> f27(A,B,1) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] f27(A,B,C) -> f27(A,B,1 + C) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= C] f27(A,B,C) -> f24(A,1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && C >= 6] f24(A,B,C) -> f21(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] f21(A,B,C) -> f39(A,B,C) [-1 + A >= 0 && A >= 6] f13(A,B,C) -> f10(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] f10(A,B,C) -> f21(1,B,C) [-1 + A >= 0 && A >= 6] Signature: {(f0,3);(f10,3);(f13,3);(f21,3);(f24,3);(f27,3);(f39,3)} Rule Graph: [0->{1},1->{2},2->{2,9},3->{4},4->{5},5->{5,6},6->{4,7},7->{3,8},8->{},9->{1,10},10->{3}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,B,C) -> f10(1,B,C) True f10(A,B,C) -> f13(A,1,C) [-1 + A >= 0 && 5 >= A] f13(A,B,C) -> f13(A,1 + B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] f21(A,B,C) -> f24(A,1,C) [-1 + A >= 0 && 5 >= A] f24(A,B,C) -> f27(A,B,1) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] f27(A,B,C) -> f27(A,B,1 + C) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= C] f27(A,B,C) -> f24(A,1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && C >= 6] f24(A,B,C) -> f21(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] f21(A,B,C) -> f39(A,B,C) [-1 + A >= 0 && A >= 6] f13(A,B,C) -> f10(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] f10(A,B,C) -> f21(1,B,C) [-1 + A >= 0 && A >= 6] f39(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0,3);(f10,3);(f13,3);(f21,3);(f24,3);(f27,3);(f39,3)} Rule Graph: [0->{1},1->{2},2->{2,9},3->{4},4->{5},5->{5,6},6->{4,7},7->{3,8},8->{11},9->{1,10},10->{3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | +- p:[1,9,2] c: [1,9] | | | `- p:[2] c: [2] | `- p:[3,7,6,5,4] c: [3,7] | `- p:[4,6,5] c: [4,6] | `- p:[5] c: [5] * Step 5: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0(A,B,C) -> f10(1,B,C) True f10(A,B,C) -> f13(A,1,C) [-1 + A >= 0 && 5 >= A] f13(A,B,C) -> f13(A,1 + B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] f21(A,B,C) -> f24(A,1,C) [-1 + A >= 0 && 5 >= A] f24(A,B,C) -> f27(A,B,1) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= B] f27(A,B,C) -> f27(A,B,1 + C) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 5 >= C] f27(A,B,C) -> f24(A,1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && C >= 6] f24(A,B,C) -> f21(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] f21(A,B,C) -> f39(A,B,C) [-1 + A >= 0 && A >= 6] f13(A,B,C) -> f10(1 + A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= 6] f10(A,B,C) -> f21(1,B,C) [-1 + A >= 0 && A >= 6] f39(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0,3);(f10,3);(f13,3);(f21,3);(f24,3);(f27,3);(f39,3)} Rule Graph: [0->{1},1->{2},2->{2,9},3->{4},4->{5},5->{5,6},6->{4,7},7->{3,8},8->{11},9->{1,10},10->{3}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | +- p:[1,9,2] c: [1,9] | | | `- p:[2] c: [2] | `- p:[3,7,6,5,4] c: [3,7] | `- p:[4,6,5] c: [4,6] | `- p:[5] c: [5]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0,0.1,0.1.0,0.1.0.0] f0 ~> f10 [A <= K, B <= B, C <= C] f10 ~> f13 [A <= A, B <= K, C <= C] f13 ~> f13 [A <= A, B <= 6*K, C <= C] f21 ~> f24 [A <= A, B <= K, C <= C] f24 ~> f27 [A <= A, B <= B, C <= K] f27 ~> f27 [A <= A, B <= B, C <= 6*K] f27 ~> f24 [A <= A, B <= B + C, C <= C] f24 ~> f21 [A <= A + B, B <= B, C <= C] f21 ~> f39 [A <= A, B <= B, C <= C] f13 ~> f10 [A <= A + B, B <= B, C <= C] f10 ~> f21 [A <= K, B <= B, C <= C] f39 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 5*K + A] f10 ~> f13 [A <= A, B <= K, C <= C] f13 ~> f10 [A <= A + B, B <= B, C <= C] f13 ~> f13 [A <= A, B <= 6*K, C <= C] + Loop: [0.0.0 <= 5*K + B] f13 ~> f13 [A <= A, B <= 6*K, C <= C] + Loop: [0.1 <= 5*K + A] f21 ~> f24 [A <= A, B <= K, C <= C] f24 ~> f21 [A <= A + B, B <= B, C <= C] f27 ~> f24 [A <= A, B <= B + C, C <= C] f27 ~> f27 [A <= A, B <= B, C <= 6*K] f24 ~> f27 [A <= A, B <= B, C <= K] + Loop: [0.1.0 <= 5*K + B] f24 ~> f27 [A <= A, B <= B, C <= K] f27 ~> f24 [A <= A, B <= B + C, C <= C] f27 ~> f27 [A <= A, B <= B, C <= 6*K] + Loop: [0.1.0.0 <= 5*K + C] f27 ~> f27 [A <= A, B <= B, C <= 6*K] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0,0.1,0.1.0,0.1.0.0] f0 ~> f10 [K ~=> A] f10 ~> f13 [K ~=> B] f13 ~> f13 [K ~=> B] f21 ~> f24 [K ~=> B] f24 ~> f27 [K ~=> C] f27 ~> f27 [K ~=> C] f27 ~> f24 [B ~+> B,C ~+> B] f24 ~> f21 [A ~+> A,B ~+> A] f21 ~> f39 [] f13 ~> f10 [A ~+> A,B ~+> A] f10 ~> f21 [K ~=> A] f39 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f10 ~> f13 [K ~=> B] f13 ~> f10 [A ~+> A,B ~+> A] f13 ~> f13 [K ~=> B] + Loop: [B ~+> 0.0.0,K ~*> 0.0.0] f13 ~> f13 [K ~=> B] + Loop: [A ~+> 0.1,K ~*> 0.1] f21 ~> f24 [K ~=> B] f24 ~> f21 [A ~+> A,B ~+> A] f27 ~> f24 [B ~+> B,C ~+> B] f27 ~> f27 [K ~=> C] f24 ~> f27 [K ~=> C] + Loop: [B ~+> 0.1.0,K ~*> 0.1.0] f24 ~> f27 [K ~=> C] f27 ~> f24 [B ~+> B,C ~+> B] f27 ~> f27 [K ~=> C] + Loop: [C ~+> 0.1.0.0,K ~*> 0.1.0.0] f27 ~> f27 [K ~=> C] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,K ~^> A ,K ~^> B] + f10> [K ~=> B ,A ~+> A ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> tick ,K ~*> A ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + f13> [K ~=> B,B ~+> 0.0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0.0,K ~*> tick] + f21> [K ~=> B ,K ~=> C ,A ~+> A ,A ~+> 0.1 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,A ~^> A ,A ~^> B ,K ~^> A ,K ~^> B] + f24> [K ~=> C ,B ~+> B ,B ~+> 0.1.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.1.0.0 ,K ~+> tick ,B ~*> B ,B ~*> tick ,K ~*> B ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick] + f27> [K ~=> C,C ~+> 0.1.0.0,C ~+> tick,tick ~+> tick,K ~*> 0.1.0.0,K ~*> tick] YES(?,O(1))