YES(?,O(1)) * Step 1: 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) 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 2: FromIts 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},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: FromIts + Details: () * Step 3: Unfold WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,B,C,D,E,F,G) -> f15(0,H,I,0,E,F,G) True f15(A,B,C,D,E,F,G) -> f15(A,B,C,1 + D,E,F,G) [49 >= D] f25(A,B,C,D,E,F,G) -> f25(A,B,C,D,1 + E,F,G) [49 >= E] f33(A,B,C,D,E,F,G) -> f33(1 + A,B,C,D,E,F,G) [49 >= A] f42(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,1 + F,G) [49 >= F] f52(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1 + G) [49 >= G] f60(A,B,C,D,E,F,G) -> f60(1 + A,B,C,D,E,F,G) [49 >= A] f60(A,B,C,D,E,F,G) -> f69(A,B,C,D,E,F,G) [A >= 50] f52(A,B,C,D,E,F,G) -> f60(0,B,C,D,E,F,G) [G >= 50] f42(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [F >= 50] f33(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,0,G) [A >= 50] f25(A,B,C,D,E,F,G) -> f33(0,B,C,D,E,F,G) [E >= 50] f15(A,B,C,D,E,F,G) -> f25(A,B,C,D,0,F,G) [D >= 50] Signature: {(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Rule 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: Unfold + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0.0(A,B,C,D,E,F,G) -> f15.1(0,H,I,0,E,F,G) True f15.1(A,B,C,D,E,F,G) -> f15.1(A,B,C,1 + D,E,F,G) [49 >= D] f15.1(A,B,C,D,E,F,G) -> f15.12(A,B,C,1 + D,E,F,G) [49 >= D] f25.2(A,B,C,D,E,F,G) -> f25.2(A,B,C,D,1 + E,F,G) [49 >= E] f25.2(A,B,C,D,E,F,G) -> f25.11(A,B,C,D,1 + E,F,G) [49 >= E] f33.3(A,B,C,D,E,F,G) -> f33.3(1 + A,B,C,D,E,F,G) [49 >= A] f33.3(A,B,C,D,E,F,G) -> f33.10(1 + A,B,C,D,E,F,G) [49 >= A] f42.4(A,B,C,D,E,F,G) -> f42.4(A,B,C,D,E,1 + F,G) [49 >= F] f42.4(A,B,C,D,E,F,G) -> f42.9(A,B,C,D,E,1 + F,G) [49 >= F] f52.5(A,B,C,D,E,F,G) -> f52.5(A,B,C,D,E,F,1 + G) [49 >= G] f52.5(A,B,C,D,E,F,G) -> f52.8(A,B,C,D,E,F,1 + G) [49 >= G] f60.6(A,B,C,D,E,F,G) -> f60.6(1 + A,B,C,D,E,F,G) [49 >= A] f60.6(A,B,C,D,E,F,G) -> f60.7(1 + A,B,C,D,E,F,G) [49 >= A] f60.7(A,B,C,D,E,F,G) -> f69.13(A,B,C,D,E,F,G) [A >= 50] f52.8(A,B,C,D,E,F,G) -> f60.6(0,B,C,D,E,F,G) [G >= 50] f42.9(A,B,C,D,E,F,G) -> f52.5(A,B,C,D,E,F,0) [F >= 50] f33.10(A,B,C,D,E,F,G) -> f42.4(A,B,C,D,E,0,G) [A >= 50] f25.11(A,B,C,D,E,F,G) -> f33.3(0,B,C,D,E,F,G) [E >= 50] f15.12(A,B,C,D,E,F,G) -> f25.2(A,B,C,D,0,F,G) [D >= 50] Signature: {(f0.0,7) ;(f15.1,7) ;(f15.12,7) ;(f25.11,7) ;(f25.2,7) ;(f33.10,7) ;(f33.3,7) ;(f42.4,7) ;(f42.9,7) ;(f52.5,7) ;(f52.8,7) ;(f60.6,7) ;(f60.7,7) ;(f69.13,7)} Rule Graph: [0->{1,2},1->{1,2},2->{18},3->{3,4},4->{17},5->{5,6},6->{16},7->{7,8},8->{15},9->{9,10},10->{14},11->{11 ,12},12->{13},13->{},14->{11,12},15->{9,10},16->{7,8},17->{5,6},18->{3,4}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0.0(A,B,C,D,E,F,G) -> f15.1(0,H,I,0,E,F,G) True f15.1(A,B,C,D,E,F,G) -> f15.1(A,B,C,1 + D,E,F,G) [49 >= D] f15.1(A,B,C,D,E,F,G) -> f15.12(A,B,C,1 + D,E,F,G) [49 >= D] f25.2(A,B,C,D,E,F,G) -> f25.2(A,B,C,D,1 + E,F,G) [49 >= E] f25.2(A,B,C,D,E,F,G) -> f25.11(A,B,C,D,1 + E,F,G) [49 >= E] f33.3(A,B,C,D,E,F,G) -> f33.3(1 + A,B,C,D,E,F,G) [49 >= A] f33.3(A,B,C,D,E,F,G) -> f33.10(1 + A,B,C,D,E,F,G) [49 >= A] f42.4(A,B,C,D,E,F,G) -> f42.4(A,B,C,D,E,1 + F,G) [49 >= F] f42.4(A,B,C,D,E,F,G) -> f42.9(A,B,C,D,E,1 + F,G) [49 >= F] f52.5(A,B,C,D,E,F,G) -> f52.5(A,B,C,D,E,F,1 + G) [49 >= G] f52.5(A,B,C,D,E,F,G) -> f52.8(A,B,C,D,E,F,1 + G) [49 >= G] f60.6(A,B,C,D,E,F,G) -> f60.6(1 + A,B,C,D,E,F,G) [49 >= A] f60.6(A,B,C,D,E,F,G) -> f60.7(1 + A,B,C,D,E,F,G) [49 >= A] f60.7(A,B,C,D,E,F,G) -> f69.13(A,B,C,D,E,F,G) [A >= 50] f52.8(A,B,C,D,E,F,G) -> f60.6(0,B,C,D,E,F,G) [G >= 50] f42.9(A,B,C,D,E,F,G) -> f52.5(A,B,C,D,E,F,0) [F >= 50] f33.10(A,B,C,D,E,F,G) -> f42.4(A,B,C,D,E,0,G) [A >= 50] f25.11(A,B,C,D,E,F,G) -> f33.3(0,B,C,D,E,F,G) [E >= 50] f15.12(A,B,C,D,E,F,G) -> f25.2(A,B,C,D,0,F,G) [D >= 50] f69.13(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True Signature: {(exitus616,7) ;(f0.0,7) ;(f15.1,7) ;(f15.12,7) ;(f25.11,7) ;(f25.2,7) ;(f33.10,7) ;(f33.3,7) ;(f42.4,7) ;(f42.9,7) ;(f52.5,7) ;(f52.8,7) ;(f60.6,7) ;(f60.7,7) ;(f69.13,7)} Rule Graph: [0->{1,2},1->{1,2},2->{18},3->{3,4},4->{17},5->{5,6},6->{16},7->{7,8},8->{15},9->{9,10},10->{14},11->{11 ,12},12->{13},13->{19},14->{11,12},15->{9,10},16->{7,8},17->{5,6},18->{3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | +- p:[1] c: [1] | +- p:[3] c: [3] | +- p:[5] c: [5] | +- p:[7] c: [7] | +- p:[9] c: [9] | `- p:[11] c: [11] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0.0(A,B,C,D,E,F,G) -> f15.1(0,H,I,0,E,F,G) True f15.1(A,B,C,D,E,F,G) -> f15.1(A,B,C,1 + D,E,F,G) [49 >= D] f15.1(A,B,C,D,E,F,G) -> f15.12(A,B,C,1 + D,E,F,G) [49 >= D] f25.2(A,B,C,D,E,F,G) -> f25.2(A,B,C,D,1 + E,F,G) [49 >= E] f25.2(A,B,C,D,E,F,G) -> f25.11(A,B,C,D,1 + E,F,G) [49 >= E] f33.3(A,B,C,D,E,F,G) -> f33.3(1 + A,B,C,D,E,F,G) [49 >= A] f33.3(A,B,C,D,E,F,G) -> f33.10(1 + A,B,C,D,E,F,G) [49 >= A] f42.4(A,B,C,D,E,F,G) -> f42.4(A,B,C,D,E,1 + F,G) [49 >= F] f42.4(A,B,C,D,E,F,G) -> f42.9(A,B,C,D,E,1 + F,G) [49 >= F] f52.5(A,B,C,D,E,F,G) -> f52.5(A,B,C,D,E,F,1 + G) [49 >= G] f52.5(A,B,C,D,E,F,G) -> f52.8(A,B,C,D,E,F,1 + G) [49 >= G] f60.6(A,B,C,D,E,F,G) -> f60.6(1 + A,B,C,D,E,F,G) [49 >= A] f60.6(A,B,C,D,E,F,G) -> f60.7(1 + A,B,C,D,E,F,G) [49 >= A] f60.7(A,B,C,D,E,F,G) -> f69.13(A,B,C,D,E,F,G) [A >= 50] f52.8(A,B,C,D,E,F,G) -> f60.6(0,B,C,D,E,F,G) [G >= 50] f42.9(A,B,C,D,E,F,G) -> f52.5(A,B,C,D,E,F,0) [F >= 50] f33.10(A,B,C,D,E,F,G) -> f42.4(A,B,C,D,E,0,G) [A >= 50] f25.11(A,B,C,D,E,F,G) -> f33.3(0,B,C,D,E,F,G) [E >= 50] f15.12(A,B,C,D,E,F,G) -> f25.2(A,B,C,D,0,F,G) [D >= 50] f69.13(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True Signature: {(exitus616,7) ;(f0.0,7) ;(f15.1,7) ;(f15.12,7) ;(f25.11,7) ;(f25.2,7) ;(f33.10,7) ;(f33.3,7) ;(f42.4,7) ;(f42.9,7) ;(f52.5,7) ;(f52.8,7) ;(f60.6,7) ;(f60.7,7) ;(f69.13,7)} Rule Graph: [0->{1,2},1->{1,2},2->{18},3->{3,4},4->{17},5->{5,6},6->{16},7->{7,8},8->{15},9->{9,10},10->{14},11->{11 ,12},12->{13},13->{19},14->{11,12},15->{9,10},16->{7,8},17->{5,6},18->{3,4}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | +- p:[1] c: [1] | +- p:[3] c: [3] | +- p:[5] c: [5] | +- p:[7] c: [7] | +- p:[9] c: [9] | `- p:[11] c: [11]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow 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] f0.0 ~> f15.1 [A <= 0*K, B <= unknown, C <= unknown, D <= 0*K, E <= E, F <= F, G <= G] f15.1 ~> f15.1 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f15.1 ~> f15.12 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f25.2 ~> f25.2 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f25.2 ~> f25.11 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f33.3 ~> f33.3 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f33.3 ~> f33.10 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f42.4 ~> f42.4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] f42.4 ~> f42.9 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] f52.5 ~> f52.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K + G] f52.5 ~> f52.8 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K + G] f60.6 ~> f60.6 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f60.6 ~> f60.7 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f60.7 ~> f69.13 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.8 ~> f60.6 [A <= 0*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f42.9 ~> f52.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= 0*K] f33.10 ~> f42.4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f25.11 ~> f33.3 [A <= 0*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f15.12 ~> f25.2 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f69.13 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= 49*K + D] f15.1 ~> f15.1 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] + Loop: [0.1 <= 49*K + E] f25.2 ~> f25.2 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] + Loop: [0.2 <= 49*K + A] f33.3 ~> f33.3 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.3 <= 49*K + F] f42.4 ~> f42.4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] + Loop: [0.4 <= 49*K + G] f52.5 ~> f52.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K + G] + Loop: [0.5 <= 49*K + A] f60.6 ~> f60.6 [A <= K + A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare 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] f0.0 ~> f15.1 [K ~=> A,K ~=> D,huge ~=> B,huge ~=> C] f15.1 ~> f15.1 [D ~+> D,K ~+> D] f15.1 ~> f15.12 [D ~+> D,K ~+> D] f25.2 ~> f25.2 [E ~+> E,K ~+> E] f25.2 ~> f25.11 [E ~+> E,K ~+> E] f33.3 ~> f33.3 [A ~+> A,K ~+> A] f33.3 ~> f33.10 [A ~+> A,K ~+> A] f42.4 ~> f42.4 [F ~+> F,K ~+> F] f42.4 ~> f42.9 [F ~+> F,K ~+> F] f52.5 ~> f52.5 [G ~+> G,K ~+> G] f52.5 ~> f52.8 [G ~+> G,K ~+> G] f60.6 ~> f60.6 [A ~+> A,K ~+> A] f60.6 ~> f60.7 [A ~+> A,K ~+> A] f60.7 ~> f69.13 [] f52.8 ~> f60.6 [K ~=> A] f42.9 ~> f52.5 [K ~=> G] f33.10 ~> f42.4 [K ~=> F] f25.11 ~> f33.3 [K ~=> A] f15.12 ~> f25.2 [K ~=> E] f69.13 ~> exitus616 [] + Loop: [D ~+> 0.0,K ~*> 0.0] f15.1 ~> f15.1 [D ~+> D,K ~+> D] + Loop: [E ~+> 0.1,K ~*> 0.1] f25.2 ~> f25.2 [E ~+> E,K ~+> E] + Loop: [A ~+> 0.2,K ~*> 0.2] f33.3 ~> f33.3 [A ~+> A,K ~+> A] + Loop: [F ~+> 0.3,K ~*> 0.3] f42.4 ~> f42.4 [F ~+> F,K ~+> F] + Loop: [G ~+> 0.4,K ~*> 0.4] f52.5 ~> f52.5 [G ~+> G,K ~+> G] + Loop: [A ~+> 0.5,K ~*> 0.5] f60.6 ~> f60.6 [A ~+> A,K ~+> A] + Applied Processor: Lare + Details: f0.0 ~> exitus616 [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] + f15.1> [D ~+> D ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,D ~*> D ,K ~*> D ,K ~*> 0.0 ,K ~*> tick] + f25.2> [E ~+> E ,E ~+> 0.1 ,E ~+> tick ,tick ~+> tick ,K ~+> E ,E ~*> E ,K ~*> E ,K ~*> 0.1 ,K ~*> tick] + f33.3> [A ~+> A ,A ~+> 0.2 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,A ~*> A ,K ~*> A ,K ~*> 0.2 ,K ~*> tick] + f42.4> [F ~+> F ,F ~+> 0.3 ,F ~+> tick ,tick ~+> tick ,K ~+> F ,F ~*> F ,K ~*> F ,K ~*> 0.3 ,K ~*> tick] + f52.5> [G ~+> G ,G ~+> 0.4 ,G ~+> tick ,tick ~+> tick ,K ~+> G ,G ~*> G ,K ~*> G ,K ~*> 0.4 ,K ~*> tick] + f60.6> [A ~+> A ,A ~+> 0.5 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,A ~*> A ,K ~*> A ,K ~*> 0.5 ,K ~*> tick] YES(?,O(1))