YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f8(-1,-1,1,D,E,F,G) True (1,1) 1. f8(A,B,C,D,E,F,G) -> f8(A,B,1 + C,D,E,F,G) [100 >= C] (?,1) 2. f18(A,B,C,D,E,F,G) -> f22(A,B,C,D,1,1,G) [99 >= D] (?,1) 3. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [F >= 100] (?,1) 4. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [99 >= F && D + F >= 101] (?,1) 5. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,E,1 + F,G) [99 >= F && 100 >= D + F] (?,1) 6. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,0,1 + F,H) [99 >= F && 100 >= D + F] (?,1) 7. f33(A,B,C,D,E,F,G) -> f18(A,B,C,1 + D,0,F,G) [E = 0] (?,1) 8. f18(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [D >= 100] (?,1) 9. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [0 >= 1 + E] (?,1) 10. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [E >= 1] (?,1) 11. f8(A,B,C,D,E,F,G) -> f18(A,B,C,1,0,F,G) [C >= 101] (?,1) Signature: {(f0,7);(f18,7);(f22,7);(f33,7);(f40,7);(f8,7)} Flow Graph: [0->{1,11},1->{1,11},2->{3,4,5,6},3->{7,9,10},4->{7,9,10},5->{3,4,5,6},6->{3,4,5,6},7->{2,8},8->{},9->{} ,10->{},11->{2,8}] + 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) -> f8(-1,-1,1,D,E,F,G) True (1,1) 1. f8(A,B,C,D,E,F,G) -> f8(A,B,1 + C,D,E,F,G) [100 >= C] (?,1) 2. f18(A,B,C,D,E,F,G) -> f22(A,B,C,D,1,1,G) [99 >= D] (?,1) 3. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [F >= 100] (?,1) 4. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [99 >= F && D + F >= 101] (?,1) 5. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,E,1 + F,G) [99 >= F && 100 >= D + F] (?,1) 6. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,0,1 + F,H) [99 >= F && 100 >= D + F] (?,1) 7. f33(A,B,C,D,E,F,G) -> f18(A,B,C,1 + D,0,F,G) [E = 0] (?,1) 8. f18(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [D >= 100] (1,1) 9. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [0 >= 1 + E] (1,1) 10. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [E >= 1] (1,1) 11. f8(A,B,C,D,E,F,G) -> f18(A,B,C,1,0,F,G) [C >= 101] (1,1) Signature: {(f0,7);(f18,7);(f22,7);(f33,7);(f40,7);(f8,7)} Flow Graph: [0->{1,11},1->{1,11},2->{3,4,5,6},3->{7,9,10},4->{7,9,10},5->{3,4,5,6},6->{3,4,5,6},7->{2,8},8->{},9->{} ,10->{},11->{2,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,11),(2,3),(2,4),(11,8)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f8(-1,-1,1,D,E,F,G) True (1,1) 1. f8(A,B,C,D,E,F,G) -> f8(A,B,1 + C,D,E,F,G) [100 >= C] (?,1) 2. f18(A,B,C,D,E,F,G) -> f22(A,B,C,D,1,1,G) [99 >= D] (?,1) 3. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [F >= 100] (?,1) 4. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [99 >= F && D + F >= 101] (?,1) 5. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,E,1 + F,G) [99 >= F && 100 >= D + F] (?,1) 6. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,0,1 + F,H) [99 >= F && 100 >= D + F] (?,1) 7. f33(A,B,C,D,E,F,G) -> f18(A,B,C,1 + D,0,F,G) [E = 0] (?,1) 8. f18(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [D >= 100] (1,1) 9. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [0 >= 1 + E] (1,1) 10. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [E >= 1] (1,1) 11. f8(A,B,C,D,E,F,G) -> f18(A,B,C,1,0,F,G) [C >= 101] (1,1) Signature: {(f0,7);(f18,7);(f22,7);(f33,7);(f40,7);(f8,7)} Flow Graph: [0->{1},1->{1,11},2->{5,6},3->{7,9,10},4->{7,9,10},5->{3,4,5,6},6->{3,4,5,6},7->{2,8},8->{},9->{},10->{} ,11->{2}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f8(-1,-1,1,D,E,F,G) True (1,1) 1. f8(A,B,C,D,E,F,G) -> f8(A,B,1 + C,D,E,F,G) [100 >= C] (?,1) 2. f18(A,B,C,D,E,F,G) -> f22(A,B,C,D,1,1,G) [99 >= D] (?,1) 3. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [F >= 100] (?,1) 4. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [99 >= F && D + F >= 101] (?,1) 5. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,E,1 + F,G) [99 >= F && 100 >= D + F] (?,1) 6. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,0,1 + F,H) [99 >= F && 100 >= D + F] (?,1) 7. f33(A,B,C,D,E,F,G) -> f18(A,B,C,1 + D,0,F,G) [E = 0] (?,1) 8. f18(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [D >= 100] (?,1) 9. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [0 >= 1 + E] (?,1) 10. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [E >= 1] (?,1) 11. f8(A,B,C,D,E,F,G) -> f18(A,B,C,1,0,F,G) [C >= 101] (?,1) 12. f33(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) 13. f18(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f18,7);(f22,7);(f33,7);(f40,7);(f8,7)} Flow Graph: [0->{1,11},1->{1,11},2->{3,4,5,6},3->{7,9,10,12},4->{7,9,10,12},5->{3,4,5,6},6->{3,4,5,6},7->{2,8,13} ,8->{},9->{},10->{},11->{2,8,13},12->{},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,11),(2,3),(2,4),(11,8)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f8(-1,-1,1,D,E,F,G) True (1,1) 1. f8(A,B,C,D,E,F,G) -> f8(A,B,1 + C,D,E,F,G) [100 >= C] (?,1) 2. f18(A,B,C,D,E,F,G) -> f22(A,B,C,D,1,1,G) [99 >= D] (?,1) 3. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [F >= 100] (?,1) 4. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [99 >= F && D + F >= 101] (?,1) 5. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,E,1 + F,G) [99 >= F && 100 >= D + F] (?,1) 6. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,0,1 + F,H) [99 >= F && 100 >= D + F] (?,1) 7. f33(A,B,C,D,E,F,G) -> f18(A,B,C,1 + D,0,F,G) [E = 0] (?,1) 8. f18(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [D >= 100] (?,1) 9. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [0 >= 1 + E] (?,1) 10. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [E >= 1] (?,1) 11. f8(A,B,C,D,E,F,G) -> f18(A,B,C,1,0,F,G) [C >= 101] (?,1) 12. f33(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) 13. f18(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f18,7);(f22,7);(f33,7);(f40,7);(f8,7)} Flow Graph: [0->{1},1->{1,11},2->{5,6},3->{7,9,10,12},4->{7,9,10,12},5->{3,4,5,6},6->{3,4,5,6},7->{2,8,13},8->{},9->{} ,10->{},11->{2,13},12->{},13->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | +- p:[1] c: [1] | `- p:[2,7,3,5,6,4] c: [2] | `- p:[5,6] c: [6] | `- p:[5] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G) -> f8(-1,-1,1,D,E,F,G) True (1,1) 1. f8(A,B,C,D,E,F,G) -> f8(A,B,1 + C,D,E,F,G) [100 >= C] (?,1) 2. f18(A,B,C,D,E,F,G) -> f22(A,B,C,D,1,1,G) [99 >= D] (?,1) 3. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [F >= 100] (?,1) 4. f22(A,B,C,D,E,F,G) -> f33(A,B,C,D,E,F,G) [99 >= F && D + F >= 101] (?,1) 5. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,E,1 + F,G) [99 >= F && 100 >= D + F] (?,1) 6. f22(A,B,C,D,E,F,G) -> f22(A,B,C,D,0,1 + F,H) [99 >= F && 100 >= D + F] (?,1) 7. f33(A,B,C,D,E,F,G) -> f18(A,B,C,1 + D,0,F,G) [E = 0] (?,1) 8. f18(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [D >= 100] (?,1) 9. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [0 >= 1 + E] (?,1) 10. f33(A,B,C,D,E,F,G) -> f40(A,B,C,D,E,F,G) [E >= 1] (?,1) 11. f8(A,B,C,D,E,F,G) -> f18(A,B,C,1,0,F,G) [C >= 101] (?,1) 12. f33(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) 13. f18(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f18,7);(f22,7);(f33,7);(f40,7);(f8,7)} Flow Graph: [0->{1},1->{1,11},2->{5,6},3->{7,9,10,12},4->{7,9,10,12},5->{3,4,5,6},6->{3,4,5,6},7->{2,8,13},8->{},9->{} ,10->{},11->{2,13},12->{},13->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | +- p:[1] c: [1] | `- p:[2,7,3,5,6,4] c: [2] | `- p:[5,6] c: [6] | `- p:[5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,0.0,0.1,0.1.0,0.1.0.0] f0 ~> f8 [A <= K, B <= K, C <= K, D <= D, E <= E, F <= F, G <= G] f8 ~> f8 [A <= A, B <= B, C <= K + C, D <= D, E <= E, F <= F, G <= G] f18 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= K, F <= K, G <= G] f22 ~> f33 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f22 ~> f33 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= K + F, G <= unknown] f33 ~> f18 [A <= A, B <= B, C <= C, D <= K + D, E <= 0*K, F <= F, G <= G] f18 ~> f40 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f33 ~> f40 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f33 ~> f40 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f8 ~> f18 [A <= A, B <= B, C <= C, D <= K, E <= 0*K, F <= F, G <= G] f33 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f18 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= 101*K + C] f8 ~> f8 [A <= A, B <= B, C <= K + C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.1 <= 100*K + D] f18 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= K, F <= K, G <= G] f33 ~> f18 [A <= A, B <= B, C <= C, D <= K + D, E <= 0*K, F <= F, G <= G] f22 ~> f33 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= K + F, G <= unknown] f22 ~> f33 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.1.0 <= 100*K + F] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= K + F, G <= unknown] + Loop: [0.1.0.0 <= 101*K + D + F] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,0.0,0.1,0.1.0,0.1.0.0] f0 ~> f8 [K ~=> A,K ~=> B,K ~=> C] f8 ~> f8 [C ~+> C,K ~+> C] f18 ~> f22 [K ~=> E,K ~=> F] f22 ~> f33 [] f22 ~> f33 [] f22 ~> f22 [F ~+> F,K ~+> F] f22 ~> f22 [K ~=> E,huge ~=> G,F ~+> F,K ~+> F] f33 ~> f18 [K ~=> E,D ~+> D,K ~+> D] f18 ~> f40 [] f33 ~> f40 [] f33 ~> f40 [] f8 ~> f18 [K ~=> D,K ~=> E] f33 ~> exitus616 [] f18 ~> exitus616 [] + Loop: [C ~+> 0.0,K ~*> 0.0] f8 ~> f8 [C ~+> C,K ~+> C] + Loop: [D ~+> 0.1,K ~*> 0.1] f18 ~> f22 [K ~=> E,K ~=> F] f33 ~> f18 [K ~=> E,D ~+> D,K ~+> D] f22 ~> f33 [] f22 ~> f22 [F ~+> F,K ~+> F] f22 ~> f22 [K ~=> E,huge ~=> G,F ~+> F,K ~+> F] f22 ~> f33 [] + Loop: [F ~+> 0.1.0,K ~*> 0.1.0] f22 ~> f22 [F ~+> F,K ~+> F] f22 ~> f22 [K ~=> E,huge ~=> G,F ~+> F,K ~+> F] + Loop: [D ~+> 0.1.0.0,F ~+> 0.1.0.0,K ~*> 0.1.0.0] f22 ~> f22 [F ~+> F,K ~+> F] + Applied Processor: LareProcessor + Details: f0 ~> f40 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,K ~=> F ,huge ~=> G ,tick ~+> tick ,K ~+> C ,K ~+> D ,K ~+> F ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,K ~*> C ,K ~*> D ,K ~*> F ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,K ~^> F ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,K ~=> F ,huge ~=> G ,tick ~+> tick ,K ~+> C ,K ~+> D ,K ~+> F ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,K ~*> C ,K ~*> D ,K ~*> F ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,K ~^> F ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] + f8> [C ~+> C,C ~+> 0.0,C ~+> tick,tick ~+> tick,K ~+> C,C ~*> C,K ~*> C,K ~*> 0.0,K ~*> tick] + f18> [K ~=> E ,K ~=> F ,huge ~=> G ,D ~+> D ,D ~+> 0.1 ,D ~+> 0.1.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> F ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,D ~*> D ,D ~*> F ,D ~*> 0.1.0 ,D ~*> 0.1.0.0 ,D ~*> tick ,K ~*> D ,K ~*> F ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,D ~^> F ,K ~^> F ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] f33> [K ~=> E ,K ~=> F ,huge ~=> G ,D ~+> D ,D ~+> 0.1 ,D ~+> 0.1.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> F ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,D ~*> D ,D ~*> F ,D ~*> 0.1.0 ,D ~*> 0.1.0.0 ,D ~*> tick ,K ~*> D ,K ~*> F ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,D ~^> F ,K ~^> F ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] + f22> [K ~=> E ,huge ~=> G ,D ~+> 0.1.0.0 ,D ~+> tick ,F ~+> F ,F ~+> 0.1.0 ,F ~+> 0.1.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> F ,K ~+> 0.1.0.0 ,K ~+> tick ,D ~*> F ,D ~*> 0.1.0.0 ,D ~*> tick ,F ~*> F ,F ~*> 0.1.0.0 ,F ~*> tick ,K ~*> F ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,F ~^> F ,K ~^> F] + f22> [D ~+> 0.1.0.0 ,D ~+> tick ,F ~+> F ,F ~+> 0.1.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> F ,D ~*> F ,F ~*> F ,K ~*> F ,K ~*> 0.1.0.0 ,K ~*> tick] YES(?,O(1))