YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 2. f17(A,B,C,D,E,F,G) -> f17(A,B,C,D,E,F,G) True (?,1) 3. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) [0 >= 1 + H] (?,1) 4. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) True (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,E,F,G) True (?,1) 6. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) [0 >= 1 + H] (?,1) 7. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) True (?,1) 8. f32(A,B,C,D,E,F,G) -> f13(A,B,C,C,C,F,G) True (?,1) 9. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) [0 >= 1 + I] (?,1) 10. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) True (?,1) 11. f17(A,B,C,D,E,F,G) -> f13(A,B,C,B,E,B,H) True (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (?,1) 13. f5(A,B,C,D,E,F,G) -> f17(A,-2 + A,C,-2 + A,E,F,G) [0 >= 1 + A && A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1,12,13},1->{1,12,13},2->{2,3,4,9,10,11},3->{2,3,4,9,10,11},4->{2,3,4,9,10,11},5->{5,6,7,8},6->{5,6,7 ,8},7->{5,6,7,8},8->{},9->{5,6,7,8},10->{5,6,7,8},11->{},12->{},13->{2,3,4,9,10,11}] + 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) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 2. f17(A,B,C,D,E,F,G) -> f17(A,B,C,D,E,F,G) True (?,1) 3. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) [0 >= 1 + H] (?,1) 4. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) True (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,E,F,G) True (?,1) 6. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) [0 >= 1 + H] (?,1) 7. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) True (?,1) 8. f32(A,B,C,D,E,F,G) -> f13(A,B,C,C,C,F,G) True (1,1) 9. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) [0 >= 1 + I] (1,1) 10. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) True (1,1) 11. f17(A,B,C,D,E,F,G) -> f13(A,B,C,B,E,B,H) True (1,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (1,1) 13. f5(A,B,C,D,E,F,G) -> f17(A,-2 + A,C,-2 + A,E,F,G) [0 >= 1 + A && A >= 100] (1,1) Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1,12,13},1->{1,12,13},2->{2,3,4,9,10,11},3->{2,3,4,9,10,11},4->{2,3,4,9,10,11},5->{5,6,7,8},6->{5,6,7 ,8},7->{5,6,7,8},8->{},9->{5,6,7,8},10->{5,6,7,8},11->{},12->{},13->{2,3,4,9,10,11}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12) ,(0,13) ,(1,13) ,(13,2) ,(13,3) ,(13,4) ,(13,9) ,(13,10) ,(13,11)] * Step 3: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 2. f17(A,B,C,D,E,F,G) -> f17(A,B,C,D,E,F,G) True (?,1) 3. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) [0 >= 1 + H] (?,1) 4. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) True (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,E,F,G) True (?,1) 6. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) [0 >= 1 + H] (?,1) 7. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) True (?,1) 8. f32(A,B,C,D,E,F,G) -> f13(A,B,C,C,C,F,G) True (1,1) 9. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) [0 >= 1 + I] (1,1) 10. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) True (1,1) 11. f17(A,B,C,D,E,F,G) -> f13(A,B,C,B,E,B,H) True (1,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (1,1) 13. f5(A,B,C,D,E,F,G) -> f17(A,-2 + A,C,-2 + A,E,F,G) [0 >= 1 + A && A >= 100] (1,1) Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1},1->{1,12},2->{2,3,4,9,10,11},3->{2,3,4,9,10,11},4->{2,3,4,9,10,11},5->{5,6,7,8},6->{5,6,7,8},7->{5 ,6,7,8},8->{},9->{5,6,7,8},10->{5,6,7,8},11->{},12->{},13->{}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [2,3,4,5,6,7,8,9,10,11,13] * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (1,1) Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1},1->{1,12},12->{}] + Applied Processor: AddSinks + Details: () * Step 5: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (?,1) 13. f5(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1,12,13},1->{1,12,13},12->{},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12)] * Step 6: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (?,1) 13. f5(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1,13},1->{1,12,13},12->{},13->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,12,13] | `- p:[1] c: [1] * Step 7: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (?,1) 13. f5(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1,13},1->{1,12,13},12->{},13->{}] ,We construct a looptree: P: [0,1,12,13] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 8: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,0.0] f0 ~> f5 [A <= 0*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f5 ~> f5 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f5 ~> f13 [A <= A, B <= B, C <= C, D <= A, E <= E, F <= F, G <= G] f5 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= 100*K + A] f5 ~> f5 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Applied Processor: FlowAbstraction + Details: () * Step 9: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,0.0] f0 ~> f5 [K ~=> A] f5 ~> f5 [A ~+> A,K ~+> A] f5 ~> f13 [A ~=> D] f5 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f5 ~> f5 [A ~+> A,K ~+> A] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> A,tick ~+> tick,K ~+> A,K ~+> 0.0,K ~+> tick,K ~*> A,K ~*> 0.0,K ~*> tick] f0 ~> f13 [K ~=> A ,K ~=> D ,tick ~+> tick ,K ~+> A ,K ~+> D ,K ~+> 0.0 ,K ~+> tick ,K ~*> A ,K ~*> D ,K ~*> 0.0 ,K ~*> tick] + f5> [A ~+> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> A,A ~*> A,K ~*> A,K ~*> 0.0,K ~*> tick] YES(?,O(1))