YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [A >= 0 && 0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) [A >= 0] (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 0 && A >= 3] (?,1) 4. f4(A) -> f11(A) [A >= 0] (?,1) 5. f5(A) -> f4(1 + A) [A >= 0 && 2 >= A] (?,1) 6. f11(A) -> f14(A) [A >= 0 && 1 >= A] (?,1) 7. f11(A) -> f14(A) [A >= 0 && A >= 2] (?,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{6,7},4->{6,7},5->{0,1,4},6->{},7->{}] + 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. f4(A) -> f5(A) [A >= 0 && 0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) [A >= 0] (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 0 && A >= 3] (1,1) 4. f4(A) -> f11(A) [A >= 0] (1,1) 5. f5(A) -> f4(1 + A) [A >= 0 && 2 >= A] (?,1) 6. f11(A) -> f14(A) [A >= 0 && 1 >= A] (1,1) 7. f11(A) -> f14(A) [A >= 0 && A >= 2] (1,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{6,7},4->{6,7},5->{0,1,4},6->{},7->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,6)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [A >= 0 && 0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) [A >= 0] (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 0 && A >= 3] (1,1) 4. f4(A) -> f11(A) [A >= 0] (1,1) 5. f5(A) -> f4(1 + A) [A >= 0 && 2 >= A] (?,1) 6. f11(A) -> f14(A) [A >= 0 && 1 >= A] (1,1) 7. f11(A) -> f14(A) [A >= 0 && A >= 2] (1,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{7},4->{6,7},5->{0,1,4},6->{},7->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [A >= 0 && 0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) [A >= 0] (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 0 && A >= 3] (?,1) 4. f4(A) -> f11(A) [A >= 0] (?,1) 5. f5(A) -> f4(1 + A) [A >= 0 && 2 >= A] (?,1) 6. f11(A) -> f14(A) [A >= 0 && 1 >= A] (?,1) 7. f11(A) -> f14(A) [A >= 0 && A >= 2] (?,1) 8. f11(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{6,7,8},4->{6,7,8},5->{0,1,4},6->{},7->{},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,6)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [A >= 0 && 0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) [A >= 0] (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 0 && A >= 3] (?,1) 4. f4(A) -> f11(A) [A >= 0] (?,1) 5. f5(A) -> f4(1 + A) [A >= 0 && 2 >= A] (?,1) 6. f11(A) -> f14(A) [A >= 0 && 1 >= A] (?,1) 7. f11(A) -> f14(A) [A >= 0 && A >= 2] (?,1) 8. f11(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{7,8},4->{6,7,8},5->{0,1,4},6->{},7->{},8->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[0,5,1] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f4(A) -> f5(A) [A >= 0 && 0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) [A >= 0] (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 0 && A >= 3] (?,1) 4. f4(A) -> f11(A) [A >= 0] (?,1) 5. f5(A) -> f4(1 + A) [A >= 0 && 2 >= A] (?,1) 6. f11(A) -> f14(A) [A >= 0 && 1 >= A] (?,1) 7. f11(A) -> f14(A) [A >= 0 && A >= 2] (?,1) 8. f11(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{7,8},4->{6,7,8},5->{0,1,4},6->{},7->{},8->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[0,5,1] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,0.0] f4 ~> f5 [A <= A] f4 ~> f5 [A <= A] f0 ~> f4 [A <= 0*K] f5 ~> f11 [A <= A] f4 ~> f11 [A <= A] f5 ~> f4 [A <= 3*K] f11 ~> f14 [A <= A] f11 ~> f14 [A <= A] f11 ~> exitus616 [A <= A] + Loop: [0.0 <= 3*K + A] f4 ~> f5 [A <= A] f5 ~> f4 [A <= 3*K] f4 ~> f5 [A <= A] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] f4 ~> f5 [] f4 ~> f5 [] f0 ~> f4 [K ~=> A] f5 ~> f11 [] f4 ~> f11 [] f5 ~> f4 [K ~=> A] f11 ~> f14 [] f11 ~> f14 [] f11 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f4 ~> f5 [] f5 ~> f4 [K ~=> A] f4 ~> f5 [] + Applied Processor: LareProcessor + Details: f0 ~> f14 [K ~=> A,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick] f0 ~> exitus616 [K ~=> A,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick] + f5> [K ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] f4> [K ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] YES(?,O(1))