YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f15(0,H,I,0,E,F,G) True (1,1) 1. f15(A,B,C,D,E,F,G) -> f15(A,B,C,1 + D,E,F,G) [49 >= D] (?,1) 2. f25(A,B,C,D,E,F,G) -> f25(A,B,C,D,1 + E,F,G) [49 >= E] (?,1) 3. f33(A,B,C,D,E,F,G) -> f33(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 4. f42(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,1 + F,G) [49 >= F] (?,1) 5. f52(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1 + G) [49 >= G] (?,1) 6. f60(A,B,C,D,E,F,G) -> f60(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 7. f60(A,B,C,D,E,F,G) -> f69(A,B,C,D,E,F,G) [A >= 50] (?,1) 8. f52(A,B,C,D,E,F,G) -> f60(0,B,C,D,E,F,G) [G >= 50] (?,1) 9. f42(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [F >= 50] (?,1) 10. f33(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,0,G) [A >= 50] (?,1) 11. f25(A,B,C,D,E,F,G) -> f33(0,B,C,D,E,F,G) [E >= 50] (?,1) 12. f15(A,B,C,D,E,F,G) -> f25(A,B,C,D,0,F,G) [D >= 50] (?,1) Signature: {(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Flow Graph: [0->{1,12},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7},7->{},8->{6,7},9->{5,8},10->{4,9} ,11->{3,10},12->{2,11}] + 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) -> f15(0,H,I,0,E,F,G) True (1,1) 1. f15(A,B,C,D,E,F,G) -> f15(A,B,C,1 + D,E,F,G) [49 >= D] (?,1) 2. f25(A,B,C,D,E,F,G) -> f25(A,B,C,D,1 + E,F,G) [49 >= E] (?,1) 3. f33(A,B,C,D,E,F,G) -> f33(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 4. f42(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,1 + F,G) [49 >= F] (?,1) 5. f52(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1 + G) [49 >= G] (?,1) 6. f60(A,B,C,D,E,F,G) -> f60(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 7. f60(A,B,C,D,E,F,G) -> f69(A,B,C,D,E,F,G) [A >= 50] (1,1) 8. f52(A,B,C,D,E,F,G) -> f60(0,B,C,D,E,F,G) [G >= 50] (1,1) 9. f42(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [F >= 50] (1,1) 10. f33(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,0,G) [A >= 50] (1,1) 11. f25(A,B,C,D,E,F,G) -> f33(0,B,C,D,E,F,G) [E >= 50] (1,1) 12. f15(A,B,C,D,E,F,G) -> f25(A,B,C,D,0,F,G) [D >= 50] (1,1) Signature: {(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Flow Graph: [0->{1,12},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7},7->{},8->{6,7},9->{5,8},10->{4,9} ,11->{3,10},12->{2,11}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12),(8,7),(9,8),(10,9),(11,10),(12,11)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f15(0,H,I,0,E,F,G) True (1,1) 1. f15(A,B,C,D,E,F,G) -> f15(A,B,C,1 + D,E,F,G) [49 >= D] (?,1) 2. f25(A,B,C,D,E,F,G) -> f25(A,B,C,D,1 + E,F,G) [49 >= E] (?,1) 3. f33(A,B,C,D,E,F,G) -> f33(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 4. f42(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,1 + F,G) [49 >= F] (?,1) 5. f52(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1 + G) [49 >= G] (?,1) 6. f60(A,B,C,D,E,F,G) -> f60(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 7. f60(A,B,C,D,E,F,G) -> f69(A,B,C,D,E,F,G) [A >= 50] (1,1) 8. f52(A,B,C,D,E,F,G) -> f60(0,B,C,D,E,F,G) [G >= 50] (1,1) 9. f42(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [F >= 50] (1,1) 10. f33(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,0,G) [A >= 50] (1,1) 11. f25(A,B,C,D,E,F,G) -> f33(0,B,C,D,E,F,G) [E >= 50] (1,1) 12. f15(A,B,C,D,E,F,G) -> f25(A,B,C,D,0,F,G) [D >= 50] (1,1) Signature: {(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Flow Graph: [0->{1},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7},7->{},8->{6},9->{5},10->{4},11->{3} ,12->{2}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f15(0,H,I,0,E,F,G) True (1,1) 1. f15(A,B,C,D,E,F,G) -> f15(A,B,C,1 + D,E,F,G) [49 >= D] (?,1) 2. f25(A,B,C,D,E,F,G) -> f25(A,B,C,D,1 + E,F,G) [49 >= E] (?,1) 3. f33(A,B,C,D,E,F,G) -> f33(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 4. f42(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,1 + F,G) [49 >= F] (?,1) 5. f52(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1 + G) [49 >= G] (?,1) 6. f60(A,B,C,D,E,F,G) -> f60(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 7. f60(A,B,C,D,E,F,G) -> f69(A,B,C,D,E,F,G) [A >= 50] (?,1) 8. f52(A,B,C,D,E,F,G) -> f60(0,B,C,D,E,F,G) [G >= 50] (?,1) 9. f42(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [F >= 50] (?,1) 10. f33(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,0,G) [A >= 50] (?,1) 11. f25(A,B,C,D,E,F,G) -> f33(0,B,C,D,E,F,G) [E >= 50] (?,1) 12. f15(A,B,C,D,E,F,G) -> f25(A,B,C,D,0,F,G) [D >= 50] (?,1) 13. f60(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Flow Graph: [0->{1,12},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7,13},7->{},8->{6,7,13},9->{5,8},10->{4 ,9},11->{3,10},12->{2,11},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12),(8,7),(9,8),(10,9),(11,10),(12,11)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f15(0,H,I,0,E,F,G) True (1,1) 1. f15(A,B,C,D,E,F,G) -> f15(A,B,C,1 + D,E,F,G) [49 >= D] (?,1) 2. f25(A,B,C,D,E,F,G) -> f25(A,B,C,D,1 + E,F,G) [49 >= E] (?,1) 3. f33(A,B,C,D,E,F,G) -> f33(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 4. f42(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,1 + F,G) [49 >= F] (?,1) 5. f52(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1 + G) [49 >= G] (?,1) 6. f60(A,B,C,D,E,F,G) -> f60(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 7. f60(A,B,C,D,E,F,G) -> f69(A,B,C,D,E,F,G) [A >= 50] (?,1) 8. f52(A,B,C,D,E,F,G) -> f60(0,B,C,D,E,F,G) [G >= 50] (?,1) 9. f42(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [F >= 50] (?,1) 10. f33(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,0,G) [A >= 50] (?,1) 11. f25(A,B,C,D,E,F,G) -> f33(0,B,C,D,E,F,G) [E >= 50] (?,1) 12. f15(A,B,C,D,E,F,G) -> f25(A,B,C,D,0,F,G) [D >= 50] (?,1) 13. f60(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Flow Graph: [0->{1},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7,13},7->{},8->{6,13},9->{5},10->{4},11->{3} ,12->{2},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] c: [2] | +- p:[3] c: [3] | +- p:[4] c: [4] | +- p:[5] c: [5] | `- p:[6] c: [6] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G) -> f15(0,H,I,0,E,F,G) True (1,1) 1. f15(A,B,C,D,E,F,G) -> f15(A,B,C,1 + D,E,F,G) [49 >= D] (?,1) 2. f25(A,B,C,D,E,F,G) -> f25(A,B,C,D,1 + E,F,G) [49 >= E] (?,1) 3. f33(A,B,C,D,E,F,G) -> f33(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 4. f42(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,1 + F,G) [49 >= F] (?,1) 5. f52(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1 + G) [49 >= G] (?,1) 6. f60(A,B,C,D,E,F,G) -> f60(1 + A,B,C,D,E,F,G) [49 >= A] (?,1) 7. f60(A,B,C,D,E,F,G) -> f69(A,B,C,D,E,F,G) [A >= 50] (?,1) 8. f52(A,B,C,D,E,F,G) -> f60(0,B,C,D,E,F,G) [G >= 50] (?,1) 9. f42(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [F >= 50] (?,1) 10. f33(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,0,G) [A >= 50] (?,1) 11. f25(A,B,C,D,E,F,G) -> f33(0,B,C,D,E,F,G) [E >= 50] (?,1) 12. f15(A,B,C,D,E,F,G) -> f25(A,B,C,D,0,F,G) [D >= 50] (?,1) 13. f60(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Flow Graph: [0->{1},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7,13},7->{},8->{6,13},9->{5},10->{4},11->{3} ,12->{2},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] c: [2] | +- p:[3] c: [3] | +- p:[4] c: [4] | +- p:[5] c: [5] | `- p:[6] c: [6]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,0.0,0.1,0.2,0.3,0.4,0.5] f0 ~> f15 [A <= 0*K, B <= unknown, C <= unknown, D <= 0*K, E <= E, F <= F, G <= G] f15 ~> f15 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f25 ~> f25 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f33 ~> f33 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f42 ~> f42 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] f52 ~> f52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K + G] f60 ~> f60 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f60 ~> f69 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52 ~> f60 [A <= 0*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f42 ~> f52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= 0*K] f33 ~> f42 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f25 ~> f33 [A <= 0*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f15 ~> f25 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f60 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= 50*K + D] f15 ~> f15 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] + Loop: [0.1 <= 50*K + E] f25 ~> f25 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] + Loop: [0.2 <= 50*K + A] f33 ~> f33 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.3 <= 50*K + F] f42 ~> f42 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] + Loop: [0.4 <= 50*K + G] f52 ~> f52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K + G] + Loop: [0.5 <= 50*K + A] f60 ~> f60 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= 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,0.0,0.1,0.2,0.3,0.4,0.5] f0 ~> f15 [K ~=> A,K ~=> D,huge ~=> B,huge ~=> C] f15 ~> f15 [D ~+> D,K ~+> D] f25 ~> f25 [E ~+> E,K ~+> E] f33 ~> f33 [A ~+> A,K ~+> A] f42 ~> f42 [F ~+> F,K ~+> F] f52 ~> f52 [G ~+> G,K ~+> G] f60 ~> f60 [A ~+> A,K ~+> A] f60 ~> f69 [] f52 ~> f60 [K ~=> A] f42 ~> f52 [K ~=> G] f33 ~> f42 [K ~=> F] f25 ~> f33 [K ~=> A] f15 ~> f25 [K ~=> E] f60 ~> exitus616 [] + Loop: [D ~+> 0.0,K ~*> 0.0] f15 ~> f15 [D ~+> D,K ~+> D] + Loop: [E ~+> 0.1,K ~*> 0.1] f25 ~> f25 [E ~+> E,K ~+> E] + Loop: [A ~+> 0.2,K ~*> 0.2] f33 ~> f33 [A ~+> A,K ~+> A] + Loop: [F ~+> 0.3,K ~*> 0.3] f42 ~> f42 [F ~+> F,K ~+> F] + Loop: [G ~+> 0.4,K ~*> 0.4] f52 ~> f52 [G ~+> G,K ~+> G] + Loop: [A ~+> 0.5,K ~*> 0.5] f60 ~> f60 [A ~+> A,K ~+> A] + Applied Processor: LareProcessor + Details: f0 ~> f69 [K ~=> A ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,huge ~=> B ,huge ~=> C ,tick ~+> tick ,K ~+> A ,K ~+> D ,K ~+> E ,K ~+> F ,K ~+> G ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> 0.3 ,K ~+> 0.4 ,K ~+> 0.5 ,K ~+> tick ,K ~*> A ,K ~*> D ,K ~*> E ,K ~*> F ,K ~*> G ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> 0.3 ,K ~*> 0.4 ,K ~*> 0.5 ,K ~*> tick] f0 ~> exitus616 [K ~=> A ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,huge ~=> B ,huge ~=> C ,tick ~+> tick ,K ~+> A ,K ~+> D ,K ~+> E ,K ~+> F ,K ~+> G ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> 0.3 ,K ~+> 0.4 ,K ~+> 0.5 ,K ~+> tick ,K ~*> A ,K ~*> D ,K ~*> E ,K ~*> F ,K ~*> G ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> 0.3 ,K ~*> 0.4 ,K ~*> 0.5 ,K ~*> tick] + f15> [D ~+> D,D ~+> 0.0,D ~+> tick,tick ~+> tick,K ~+> D,D ~*> D,K ~*> D,K ~*> 0.0,K ~*> tick] + f25> [E ~+> E,E ~+> 0.1,E ~+> tick,tick ~+> tick,K ~+> E,E ~*> E,K ~*> E,K ~*> 0.1,K ~*> tick] + f33> [A ~+> A,A ~+> 0.2,A ~+> tick,tick ~+> tick,K ~+> A,A ~*> A,K ~*> A,K ~*> 0.2,K ~*> tick] + f42> [F ~+> F,F ~+> 0.3,F ~+> tick,tick ~+> tick,K ~+> F,F ~*> F,K ~*> F,K ~*> 0.3,K ~*> tick] + f52> [G ~+> G,G ~+> 0.4,G ~+> tick,tick ~+> tick,K ~+> G,G ~*> G,K ~*> G,K ~*> 0.4,K ~*> tick] + f60> [A ~+> A,A ~+> 0.5,A ~+> tick,tick ~+> tick,K ~+> A,A ~*> A,K ~*> A,K ~*> 0.5,K ~*> tick] YES(?,O(1))