YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] (1,1) 1. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] (1,1) 2. f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True (1,1) 3. f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [B >= C] (?,1) 4. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [E >= 0 && C >= 1 + B && 1022 >= E] (?,1) 5. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && E >= 1023] (?,1) 6. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && 0 >= 1 + E] (?,1) Signature: {(f0,5);(f21,5);(f7,5)} Flow Graph: [0->{3,4,5,6},1->{3,4,5,6},2->{3,4,5,6},3->{3,4,5,6},4->{},5->{},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. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] (1,1) 1. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] (1,1) 2. f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True (1,1) 3. f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [B >= C] (?,1) 4. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [E >= 0 && C >= 1 + B && 1022 >= E] (1,1) 5. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && E >= 1023] (1,1) 6. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && 0 >= 1 + E] (1,1) Signature: {(f0,5);(f21,5);(f7,5)} Flow Graph: [0->{3,4,5,6},1->{3,4,5,6},2->{3,4,5,6},3->{3,4,5,6},4->{},5->{},6->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] (1,1) 1. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] (1,1) 2. f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True (1,1) 3. f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [B >= C] (?,1) 4. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [E >= 0 && C >= 1 + B && 1022 >= E] (1,1) 5. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && E >= 1023] (1,1) 6. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && 0 >= 1 + E] (1,1) Signature: {(f0,5);(f21,5);(f7,5)} Flow Graph: [0->{3},1->{3},2->{3},3->{3,4,5,6},4->{},5->{},6->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] (1,1) 1. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] (1,1) 2. f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True (1,1) 3. f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [B >= C] (?,1) 4. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [E >= 0 && C >= 1 + B && 1022 >= E] (?,1) 5. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && E >= 1023] (?,1) 6. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && 0 >= 1 + E] (?,1) 7. f7(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f21,5);(f7,5)} Flow Graph: [0->{3,4,5,6,7},1->{3,4,5,6,7},2->{3,4,5,6,7},3->{3,4,5,6,7},4->{},5->{},6->{},7->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] (1,1) 1. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] (1,1) 2. f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True (1,1) 3. f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [B >= C] (?,1) 4. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [E >= 0 && C >= 1 + B && 1022 >= E] (?,1) 5. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && E >= 1023] (?,1) 6. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && 0 >= 1 + E] (?,1) 7. f7(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f21,5);(f7,5)} Flow Graph: [0->{3,7},1->{3,7},2->{3,7},3->{3,4,5,6,7},4->{},5->{},6->{},7->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[3] c: [3] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] (1,1) 1. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] (1,1) 2. f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True (1,1) 3. f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [B >= C] (?,1) 4. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [E >= 0 && C >= 1 + B && 1022 >= E] (?,1) 5. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && E >= 1023] (?,1) 6. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 1 + B && 0 >= 1 + E] (?,1) 7. f7(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f21,5);(f7,5)} Flow Graph: [0->{3,7},1->{3,7},2->{3,7},3->{3,4,5,6,7},4->{},5->{},6->{},7->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[3] c: [3]) + 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 <= 0*K, C <= 0*K, D <= D, E <= E] f0 ~> f7 [A <= unknown, B <= 0*K, C <= 0*K, D <= D, E <= E] f0 ~> f7 [A <= 0*K, B <= 1023*K, C <= 0*K, D <= D, E <= E] f7 ~> f7 [A <= A, B <= B, C <= K + C, D <= 2*K + D, E <= E] f7 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E] f7 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E] f7 ~> f21 [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 <= K + B + C] f7 ~> f7 [A <= A, B <= B, C <= K + C, D <= 2*K + D, E <= E] + 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 ~=> B,K ~=> C,huge ~=> A] f0 ~> f7 [K ~=> B,K ~=> C,huge ~=> A] f0 ~> f7 [K ~=> A,K ~=> B,K ~=> C] f7 ~> f7 [C ~+> C,D ~+> D,K ~+> C,K ~*> D] f7 ~> f21 [] f7 ~> f21 [] f7 ~> f21 [] f7 ~> exitus616 [] + Loop: [B ~+> 0.0,C ~+> 0.0,K ~+> 0.0] f7 ~> f7 [C ~+> C,D ~+> D,K ~+> C,K ~*> D] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,huge ~=> A ,D ~+> D ,tick ~+> tick ,K ~+> C ,K ~+> 0.0 ,K ~+> tick ,K ~*> C ,K ~*> D ,K ~*> 0.0 ,K ~*> tick] f0 ~> f21 [K ~=> A ,K ~=> B ,K ~=> C ,huge ~=> A ,D ~+> D ,tick ~+> tick ,K ~+> C ,K ~+> 0.0 ,K ~+> tick ,K ~*> C ,K ~*> D ,K ~*> 0.0 ,K ~*> tick] + f7> [B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,D ~+> D ,tick ~+> tick ,K ~+> C ,K ~+> 0.0 ,K ~+> tick ,B ~*> C ,B ~*> D ,C ~*> C ,C ~*> D ,K ~*> C ,K ~*> D] YES(?,O(1))