YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E) -> f1(A,F,C,D,E) [1 >= A] (1,1) 1. f2(A,B,C,D,E) -> f300(A,B,C,D,E) [A >= 2 && C >= 2] (1,1) 2. f300(A,B,C,D,E) -> f1(A,F,C,D,E) [1 + D >= 0] (?,1) 3. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [E >= 0 && 0 >= 2 + D] (?,1) 4. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [0 >= 2 + E && 0 >= 2 + D] (?,1) Signature: {(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{},1->{2,3,4},2->{},3->{2,3,4},4->{2,3,4}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E) -> f1(A,F,C,D,E) [1 >= A] (1,1) 1. f2(A,B,C,D,E) -> f300(A,B,C,D,E) [A >= 2 && C >= 2] (1,1) 2. f300(A,B,C,D,E) -> f1(A,F,C,D,E) [1 + D >= 0] (1,1) 3. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [E >= 0 && 0 >= 2 + D] (?,1) 4. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [0 >= 2 + E && 0 >= 2 + D] (?,1) Signature: {(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{},1->{2,3,4},2->{},3->{2,3,4},4->{2,3,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,4),(4,3)] * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E) -> f1(A,F,C,D,E) [1 >= A] (1,1) 1. f2(A,B,C,D,E) -> f300(A,B,C,D,E) [A >= 2 && C >= 2] (1,1) 2. f300(A,B,C,D,E) -> f1(A,F,C,D,E) [1 + D >= 0] (1,1) 3. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [E >= 0 && 0 >= 2 + D] (?,1) 4. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [0 >= 2 + E && 0 >= 2 + D] (?,1) Signature: {(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{},1->{2,3,4},2->{},3->{2,3},4->{2,4}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E) -> f1(A,F,C,D,E) [1 >= A] (1,1) 1. f2(A,B,C,D,E) -> f300(A,B,C,D,E) [A >= 2 && C >= 2] (1,1) 2. f300(A,B,C,D,E) -> f1(A,F,C,D,E) [1 + D >= 0] (?,1) 3. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [E >= 0 && 0 >= 2 + D] (?,1) 4. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [0 >= 2 + E && 0 >= 2 + D] (?,1) 5. f300(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) 6. f2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (1,1) Signature: {(exitus616,5);(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{},1->{2,3,4,5},2->{},3->{2,3,4,5},4->{2,3,4,5},5->{},6->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,4),(4,3)] * Step 5: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E) -> f1(A,F,C,D,E) [1 >= A] (1,1) 1. f2(A,B,C,D,E) -> f300(A,B,C,D,E) [A >= 2 && C >= 2] (1,1) 2. f300(A,B,C,D,E) -> f1(A,F,C,D,E) [1 + D >= 0] (?,1) 3. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [E >= 0 && 0 >= 2 + D] (?,1) 4. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [0 >= 2 + E && 0 >= 2 + D] (?,1) 5. f300(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) 6. f2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (1,1) Signature: {(exitus616,5);(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{},1->{2,3,4,5},2->{},3->{2,3,5},4->{2,4,5},5->{},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | +- p:[4] c: [4] | `- p:[3] c: [3] * Step 6: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f2(A,B,C,D,E) -> f1(A,F,C,D,E) [1 >= A] (1,1) 1. f2(A,B,C,D,E) -> f300(A,B,C,D,E) [A >= 2 && C >= 2] (1,1) 2. f300(A,B,C,D,E) -> f1(A,F,C,D,E) [1 + D >= 0] (?,1) 3. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [E >= 0 && 0 >= 2 + D] (?,1) 4. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [0 >= 2 + E && 0 >= 2 + D] (?,1) 5. f300(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) 6. f2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (1,1) Signature: {(exitus616,5);(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{},1->{2,3,4,5},2->{},3->{2,3,5},4->{2,4,5},5->{},6->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | +- p:[4] c: [4] | `- p:[3] c: [3]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,0.0,0.1] f2 ~> f1 [A <= A, B <= unknown, C <= C, D <= D, E <= E] f2 ~> f300 [A <= A, B <= B, C <= C, D <= D, E <= E] f300 ~> f1 [A <= A, B <= unknown, C <= C, D <= D, E <= E] f300 ~> f300 [A <= A, B <= B, C <= C, D <= D, E <= K + E] f300 ~> f300 [A <= A, B <= B, C <= C, D <= D, E <= E] f300 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] f2 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= E] f300 ~> f300 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.1 <= K + D] f300 ~> f300 [A <= A, B <= B, C <= C, D <= D, E <= K + E] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,0.0,0.1] f2 ~> f1 [huge ~=> B] f2 ~> f300 [] f300 ~> f1 [huge ~=> B] f300 ~> f300 [E ~+> E,K ~+> E] f300 ~> f300 [] f300 ~> exitus616 [] f2 ~> exitus616 [] + Loop: [E ~=> 0.0] f300 ~> f300 [] + Loop: [D ~+> 0.1,K ~+> 0.1] f300 ~> f300 [E ~+> E,K ~+> E] + Applied Processor: LareProcessor + Details: f2 ~> exitus616 [E ~=> 0.0 ,D ~+> 0.1 ,D ~+> tick ,E ~+> E ,E ~+> tick ,tick ~+> tick ,K ~+> E ,K ~+> 0.1 ,K ~+> tick ,D ~*> E ,K ~*> E] f2 ~> f1 [E ~=> 0.0 ,huge ~=> B ,D ~+> 0.1 ,D ~+> tick ,E ~+> E ,E ~+> tick ,tick ~+> tick ,K ~+> E ,K ~+> 0.1 ,K ~+> tick ,D ~*> E ,K ~*> E] + f300> [E ~=> 0.0,E ~+> tick,tick ~+> tick] + f300> [D ~+> 0.1 ,D ~+> tick ,E ~+> E ,tick ~+> tick ,K ~+> E ,K ~+> 0.1 ,K ~+> tick ,D ~*> E ,K ~*> E] YES(?,O(n^1))