YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] (?,1) Signature: {(f0,5);(f19,5);(f7,5)} 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) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] (1,1) Signature: {(f0,5);(f19,5);(f7,5)} 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) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] (1,1) Signature: {(f0,5);(f19,5);(f7,5)} 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) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] (?,1) 3. f7(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f19,5);(f7,5)} 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) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] (?,1) 3. f7(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f19,5);(f7,5)} 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) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] (?,1) 3. f7(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f19,5);(f7,5)} 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,0.0] f0 ~> f7 [A <= unknown, B <= unknown, C <= 10*K, D <= 0*K, E <= E] f7 ~> f7 [A <= A, B <= B, C <= C, D <= 10*K, E <= unknown] f7 ~> f19 [A <= A, B <= B, C <= C, D <= D, E <= E] f7 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= C + D] f7 ~> f7 [A <= A, B <= B, C <= C, D <= 10*K, E <= unknown] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,0.0] f0 ~> f7 [K ~=> C,K ~=> D,huge ~=> A,huge ~=> B] f7 ~> f7 [K ~=> D,huge ~=> E] f7 ~> f19 [] f7 ~> exitus616 [] + Loop: [C ~+> 0.0,D ~+> 0.0] f7 ~> f7 [K ~=> D,huge ~=> E] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> C ,K ~=> D ,huge ~=> A ,huge ~=> B ,huge ~=> E ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] f0 ~> f19 [K ~=> C ,K ~=> D ,huge ~=> A ,huge ~=> B ,huge ~=> E ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] + f7> [K ~=> D,huge ~=> E,C ~+> 0.0,C ~+> tick,D ~+> 0.0,D ~+> tick,tick ~+> tick] YES(?,O(1))