YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B,C) -> f300(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B,C) -> f1(A,B,D) [A >= 0] (?,1) 4. f2(A,B,C) -> f300(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{},4->{0,1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,0),(0,2),(0,3),(1,0),(1,2),(2,1)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B,C) -> f300(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B,C) -> f1(A,B,D) [A >= 0] (?,1) 4. f2(A,B,C) -> f300(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1},1->{1,3},2->{0,2,3},3->{},4->{0,1,2,3}] + Applied Processor: FromIts + Details: () * Step 3: Unfold WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f300(A,B,C) -> f300(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300(A,B,C) -> f1(A,B,D) [A >= 0] f2(A,B,C) -> f300(A,B,C) True Signature: {(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{1},1->{1,3},2->{0,2,3},3->{},4->{0,1,2,3}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f300.0(A,B,C) -> f300.1(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] f300.1(A,B,C) -> f300.1(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] f300.1(A,B,C) -> f300.3(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] f300.2(A,B,C) -> f300.0(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B,C) -> f300.2(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B,C) -> f300.3(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300.3(A,B,C) -> f1.5(A,B,D) [A >= 0] f2.4(A,B,C) -> f300.0(A,B,C) True f2.4(A,B,C) -> f300.1(A,B,C) True f2.4(A,B,C) -> f300.2(A,B,C) True f2.4(A,B,C) -> f300.3(A,B,C) True Signature: {(f1.5,3);(f2.4,3);(f300.0,3);(f300.1,3);(f300.2,3);(f300.3,3)} Rule Graph: [0->{1,2},1->{1,2},2->{6},3->{0},4->{3,4,5},5->{6},6->{},7->{0},8->{1,2},9->{3,4,5},10->{6}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f300.0(A,B,C) -> f300.1(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] f300.1(A,B,C) -> f300.1(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] f300.1(A,B,C) -> f300.3(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] f300.2(A,B,C) -> f300.0(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B,C) -> f300.2(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B,C) -> f300.3(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300.3(A,B,C) -> f1.5(A,B,D) [A >= 0] f2.4(A,B,C) -> f300.0(A,B,C) True f2.4(A,B,C) -> f300.1(A,B,C) True f2.4(A,B,C) -> f300.2(A,B,C) True f2.4(A,B,C) -> f300.3(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f1.5,3);(f2.4,3);(f300.0,3);(f300.1,3);(f300.2,3);(f300.3,3)} Rule Graph: [0->{1,2},1->{1,2},2->{6},3->{0},4->{3,4,5},5->{6},6->{11,12,13,14,15},7->{0},8->{1,2},9->{3,4,5},10->{6}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | +- p:[4] c: [4] | `- p:[1] c: [1] * Step 6: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f300.0(A,B,C) -> f300.1(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] f300.1(A,B,C) -> f300.1(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] f300.1(A,B,C) -> f300.3(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] f300.2(A,B,C) -> f300.0(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B,C) -> f300.2(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B,C) -> f300.3(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300.3(A,B,C) -> f1.5(A,B,D) [A >= 0] f2.4(A,B,C) -> f300.0(A,B,C) True f2.4(A,B,C) -> f300.1(A,B,C) True f2.4(A,B,C) -> f300.2(A,B,C) True f2.4(A,B,C) -> f300.3(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True f1.5(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f1.5,3);(f2.4,3);(f300.0,3);(f300.1,3);(f300.2,3);(f300.3,3)} Rule Graph: [0->{1,2},1->{1,2},2->{6},3->{0},4->{3,4,5},5->{6},6->{11,12,13,14,15},7->{0},8->{1,2},9->{3,4,5},10->{6}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | +- p:[4] c: [4] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0,0.1] f300.0 ~> f300.1 [A <= 99*K + A, B <= 0*K, C <= C] f300.1 ~> f300.1 [A <= A, B <= K + B, C <= C] f300.1 ~> f300.3 [A <= A, B <= K + B, C <= C] f300.2 ~> f300.0 [A <= A, B <= B, C <= C] f300.2 ~> f300.2 [A <= A, B <= B, C <= C] f300.2 ~> f300.3 [A <= A, B <= B, C <= C] f300.3 ~> f1.5 [A <= A, B <= B, C <= unknown] f2.4 ~> f300.0 [A <= A, B <= B, C <= C] f2.4 ~> f300.1 [A <= A, B <= B, C <= C] f2.4 ~> f300.2 [A <= A, B <= B, C <= C] f2.4 ~> f300.3 [A <= A, B <= B, C <= C] f1.5 ~> exitus616 [A <= A, B <= B, C <= C] f1.5 ~> exitus616 [A <= A, B <= B, C <= C] f1.5 ~> exitus616 [A <= A, B <= B, C <= C] f1.5 ~> exitus616 [A <= A, B <= B, C <= C] f1.5 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 2*K + B] f300.2 ~> f300.2 [A <= A, B <= B, C <= C] + Loop: [0.1 <= K + A] f300.1 ~> f300.1 [A <= A, B <= K + B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.1] f300.0 ~> f300.1 [K ~=> B,A ~+> A,K ~*> A] f300.1 ~> f300.1 [B ~+> B,K ~+> B] f300.1 ~> f300.3 [B ~+> B,K ~+> B] f300.2 ~> f300.0 [] f300.2 ~> f300.2 [] f300.2 ~> f300.3 [] f300.3 ~> f1.5 [huge ~=> C] f2.4 ~> f300.0 [] f2.4 ~> f300.1 [] f2.4 ~> f300.2 [] f2.4 ~> f300.3 [] f1.5 ~> exitus616 [] f1.5 ~> exitus616 [] f1.5 ~> exitus616 [] f1.5 ~> exitus616 [] f1.5 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f300.2 ~> f300.2 [] + Loop: [A ~+> 0.1,K ~+> 0.1] f300.1 ~> f300.1 [B ~+> B,K ~+> B] + Applied Processor: Lare + Details: f2.4 ~> exitus616 [huge ~=> C ,A ~+> A ,A ~+> 0.1 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f300.2> [B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f300.1> [A ~+> 0.1 ,A ~+> tick ,B ~+> B ,tick ~+> tick ,K ~+> B ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,K ~*> B] YES(?,O(n^1))