YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f7(30,30,1,0,2,F,G,H,I) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I) -> f7(A,B,C + D,C,1 + E,C,G,H,I) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && B >= E] 2. f7(A,B,C,D,E,F,G,H,I) -> f19(A,B,C,D,E,F,C,C,C) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && E >= 1 + B] Signature: {(f0,9);(f19,9);(f7,9)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + 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. f0(A,B,C,D,E,F,G,H,I) -> f7(30,30,1,0,2,F,G,H,I) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I) -> f7(A,B,C + D,C,1 + E,C,G,H,I) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && B >= E] 2. f7(A,B,C,D,E,F,G,H,I) -> f19(A,B,C,D,E,F,C,C,C) [-2 + E >= 0 (1,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && E >= 1 + B] Signature: {(f0,9);(f19,9);(f7,9)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f7(30,30,1,0,2,F,G,H,I) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I) -> f7(A,B,C + D,C,1 + E,C,G,H,I) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && B >= E] 2. f7(A,B,C,D,E,F,G,H,I) -> f19(A,B,C,D,E,F,C,C,C) [-2 + E >= 0 (1,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && E >= 1 + B] Signature: {(f0,9);(f19,9);(f7,9)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f7(30,30,1,0,2,F,G,H,I) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I) -> f7(A,B,C + D,C,1 + E,C,G,H,I) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && B >= E] 2. f7(A,B,C,D,E,F,G,H,I) -> f19(A,B,C,D,E,F,C,C,C) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && E >= 1 + B] 3. f7(A,B,C,D,E,F,G,H,I) -> exitus616(A,B,C,D,E,F,G,H,I) True (?,1) Signature: {(exitus616,9);(f0,9);(f19,9);(f7,9)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f7(30,30,1,0,2,F,G,H,I) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I) -> f7(A,B,C + D,C,1 + E,C,G,H,I) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && B >= E] 2. f7(A,B,C,D,E,F,G,H,I) -> f19(A,B,C,D,E,F,C,C,C) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && E >= 1 + B] 3. f7(A,B,C,D,E,F,G,H,I) -> exitus616(A,B,C,D,E,F,G,H,I) True (?,1) Signature: {(exitus616,9);(f0,9);(f19,9);(f7,9)} Flow Graph: [0->{1,3},1->{1,2,3},2->{},3->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f7(30,30,1,0,2,F,G,H,I) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I) -> f7(A,B,C + D,C,1 + E,C,G,H,I) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && B >= E] 2. f7(A,B,C,D,E,F,G,H,I) -> f19(A,B,C,D,E,F,C,C,C) [-2 + E >= 0 (?,1) && -2 + D + E >= 0 && -3 + C + E >= 0 && -32 + B + E >= 0 && 28 + -1*B + E >= 0 && -32 + A + E >= 0 && 28 + -1*A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -30 + B + D >= 0 && 30 + -1*B + D >= 0 && -30 + A + D >= 0 && 30 + -1*A + D >= 0 && -1 + C >= 0 && -31 + B + C >= 0 && 29 + -1*B + C >= 0 && -31 + A + C >= 0 && 29 + -1*A + C >= 0 && 30 + -1*B >= 0 && A + -1*B >= 0 && 60 + -1*A + -1*B >= 0 && -30 + B >= 0 && -60 + A + B >= 0 && -1*A + B >= 0 && 30 + -1*A >= 0 && -30 + A >= 0 && E >= 1 + B] 3. f7(A,B,C,D,E,F,G,H,I) -> exitus616(A,B,C,D,E,F,G,H,I) True (?,1) Signature: {(exitus616,9);(f0,9);(f19,9);(f7,9)} Flow Graph: [0->{1,3},1->{1,2,3},2->{},3->{}] ,We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,I,0.0] f0 ~> f7 [A <= 30*K, B <= 30*K, C <= K, D <= 0*K, E <= 2*K, F <= F, G <= G, H <= H, I <= I] f7 ~> f7 [A <= A, B <= B, C <= C + D, D <= C, E <= 31*K, F <= C, G <= G, H <= H, I <= I] f7 ~> f19 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= C, H <= C, I <= C] f7 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I] + Loop: [0.0 <= K + B + E] f7 ~> f7 [A <= A, B <= B, C <= C + D, D <= C, E <= 31*K, F <= C, G <= G, H <= H, I <= I] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,I,0.0] f0 ~> f7 [K ~=> A,K ~=> B,K ~=> C,K ~=> D,K ~=> E] f7 ~> f7 [C ~=> D,C ~=> F,K ~=> E,C ~+> C,D ~+> C] f7 ~> f19 [C ~=> G,C ~=> H,C ~=> I] f7 ~> exitus616 [] + Loop: [B ~+> 0.0,E ~+> 0.0,K ~+> 0.0] f7 ~> f7 [C ~=> D,C ~=> F,K ~=> E,C ~+> C,D ~+> C] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,K ~=> F ,tick ~+> tick ,K ~+> C ,K ~+> D ,K ~+> F ,K ~+> 0.0 ,K ~+> tick ,K ~*> C ,K ~*> D ,K ~*> F ,K ~*> 0.0 ,K ~*> tick ,K ~^> C] f0 ~> f19 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,K ~=> H ,K ~=> I ,tick ~+> tick ,K ~+> C ,K ~+> D ,K ~+> F ,K ~+> G ,K ~+> H ,K ~+> I ,K ~+> 0.0 ,K ~+> tick ,K ~*> C ,K ~*> D ,K ~*> F ,K ~*> G ,K ~*> H ,K ~*> I ,K ~*> 0.0 ,K ~*> tick ,K ~^> C ,K ~^> G ,K ~^> H ,K ~^> I] + f7> [C ~=> D ,C ~=> F ,K ~=> E ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> D ,C ~+> F ,D ~+> C ,D ~+> D ,D ~+> F ,E ~+> 0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,B ~*> C ,B ~*> D ,C ~*> C ,C ~*> D ,C ~*> F ,D ~*> C ,E ~*> C ,E ~*> D ,K ~*> C ,K ~*> D ,B ~^> C ,E ~^> C ,K ~^> C] YES(?,O(1))