YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F) True (1,1) 1. f5(A,B,C,D,E,F) -> f11(A,B,0,0,0,F) [B >= A && C = 0] (?,1) 2. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [C >= 1] (?,1) 3. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [0 >= 1 + C] (?,1) 4. f7(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) True (?,1) 5. f8(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) True (?,1) 6. f5(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) [A >= 1 + B && C = 0] (?,1) Signature: {(f10,6);(f11,6);(f12,6);(f5,6);(f7,6);(f8,6)} Flow Graph: [0->{1,2,3,6},1->{},2->{},3->{},4->{1,2,3,6},5->{1,2,3,6},6->{1,2,3,6}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F) True (1,1) 1. f5(A,B,C,D,E,F) -> f11(A,B,0,0,0,F) [B >= A && C = 0] (1,1) 2. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [C >= 1] (1,1) 3. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [0 >= 1 + C] (1,1) 4. f7(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) True (1,1) 5. f8(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) True (1,1) 6. f5(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) [A >= 1 + B && C = 0] (?,1) Signature: {(f10,6);(f11,6);(f12,6);(f5,6);(f7,6);(f8,6)} Flow Graph: [0->{1,2,3,6},1->{},2->{},3->{},4->{1,2,3,6},5->{1,2,3,6},6->{1,2,3,6}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(0,2),(0,3)] * Step 3: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F) True (1,1) 1. f5(A,B,C,D,E,F) -> f11(A,B,0,0,0,F) [B >= A && C = 0] (1,1) 2. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [C >= 1] (1,1) 3. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [0 >= 1 + C] (1,1) 4. f7(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) True (1,1) 5. f8(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) True (1,1) 6. f5(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) [A >= 1 + B && C = 0] (?,1) Signature: {(f10,6);(f11,6);(f12,6);(f5,6);(f7,6);(f8,6)} Flow Graph: [0->{6},1->{},2->{},3->{},4->{1,2,3,6},5->{1,2,3,6},6->{1,2,3,6}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [4,5] * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F) True (1,1) 1. f5(A,B,C,D,E,F) -> f11(A,B,0,0,0,F) [B >= A && C = 0] (1,1) 2. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [C >= 1] (1,1) 3. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [0 >= 1 + C] (1,1) 6. f5(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) [A >= 1 + B && C = 0] (?,1) Signature: {(f10,6);(f11,6);(f12,6);(f5,6);(f7,6);(f8,6)} Flow Graph: [0->{6},1->{},2->{},3->{},6->{1,2,3,6}] + Applied Processor: AddSinks + Details: () * Step 5: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F) True (1,1) 1. f5(A,B,C,D,E,F) -> f11(A,B,0,0,0,F) [B >= A && C = 0] (?,1) 2. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [C >= 1] (?,1) 3. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [0 >= 1 + C] (?,1) 6. f5(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) [A >= 1 + B && C = 0] (?,1) 7. f5(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(f10,6);(f11,6);(f12,6);(f5,6);(f7,6);(f8,6)} Flow Graph: [0->{1,2,3,6,7},1->{},2->{},3->{},6->{1,2,3,6,7},7->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(0,2),(0,3)] * Step 6: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F) True (1,1) 1. f5(A,B,C,D,E,F) -> f11(A,B,0,0,0,F) [B >= A && C = 0] (?,1) 2. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [C >= 1] (?,1) 3. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [0 >= 1 + C] (?,1) 6. f5(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) [A >= 1 + B && C = 0] (?,1) 7. f5(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(f10,6);(f11,6);(f12,6);(f5,6);(f7,6);(f8,6)} Flow Graph: [0->{6,7},1->{},2->{},3->{},6->{1,2,3,6,7},7->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,6,7] | `- p:[6] c: [6] * Step 7: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F) True (1,1) 1. f5(A,B,C,D,E,F) -> f11(A,B,0,0,0,F) [B >= A && C = 0] (?,1) 2. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [C >= 1] (?,1) 3. f5(A,B,C,D,E,F) -> f10(A,B,C,C,C,F) [0 >= 1 + C] (?,1) 6. f5(A,B,C,D,E,F) -> f5(A,1 + B,G,H,E,G) [A >= 1 + B && C = 0] (?,1) 7. f5(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(f10,6);(f11,6);(f12,6);(f5,6);(f7,6);(f8,6)} Flow Graph: [0->{6,7},1->{},2->{},3->{},6->{1,2,3,6,7},7->{}] ,We construct a looptree: P: [0,1,2,3,6,7] | `- p:[6] c: [6]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 8: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0] f12 ~> f5 [A <= 4*K, B <= 0*K, C <= 0*K, D <= D, E <= E, F <= F] f5 ~> f11 [A <= A, B <= B, C <= 0*K, D <= 0*K, E <= 0*K, F <= F] f5 ~> f10 [A <= A, B <= B, C <= C, D <= C, E <= C, F <= F] f5 ~> f10 [A <= A, B <= B, C <= C, D <= C, E <= C, F <= F] f5 ~> f5 [A <= A, B <= A + B, C <= unknown, D <= unknown, E <= E, F <= unknown] f5 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= A + B] f5 ~> f5 [A <= A, B <= A + B, C <= unknown, D <= unknown, E <= E, F <= unknown] + Applied Processor: FlowAbstraction + Details: () * Step 9: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0] f12 ~> f5 [K ~=> A,K ~=> B,K ~=> C] f5 ~> f11 [K ~=> C,K ~=> D,K ~=> E] f5 ~> f10 [C ~=> D,C ~=> E] f5 ~> f10 [C ~=> D,C ~=> E] f5 ~> f5 [huge ~=> C,huge ~=> D,huge ~=> F,A ~+> B,B ~+> B] f5 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] f5 ~> f5 [huge ~=> C,huge ~=> D,huge ~=> F,A ~+> B,B ~+> B] + Applied Processor: LareProcessor + Details: f12 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,huge ~=> C ,huge ~=> D ,huge ~=> F ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] f12 ~> f10 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,huge ~=> C ,huge ~=> D ,huge ~=> E ,huge ~=> F ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] f12 ~> f11 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,huge ~=> F ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] + f5> [huge ~=> C ,huge ~=> D ,huge ~=> F ,A ~+> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> B ,B ~*> B] YES(?,O(1))