YES(?,O(1)) * Step 1: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f12(2,H,I,0,E,F,G) True (1,1) 1. f12(A,B,C,D,E,F,G) -> f15(A,B,C,D,0,F,G) [A >= 1 + D] (?,1) 2. f15(A,B,C,D,E,F,G) -> f15(A,B,C,D,1 + E,F,G) [A >= 1 + E] (?,1) 3. f23(A,B,C,D,E,F,G) -> f26(A,B,C,D,0,F,G) [A >= 1 + D] (?,1) 4. f26(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,0,G) [A >= 1 + E] (?,1) 5. f30(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,1 + F,G) [A >= 1 + F] (?,1) 6. f30(A,B,C,D,E,F,G) -> f26(A,B,C,D,1 + E,F,G) [F >= A] (?,1) 7. f26(A,B,C,D,E,F,G) -> f23(A,B,C,1 + D,E,F,G) [E >= A] (?,1) 8. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [D >= A] (?,1) 9. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 49 >= H] (?,1) 10. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A] (?,1) 11. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 42 >= H] (?,1) 12. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 21 >= H] (?,1) 13. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 18 >= H] (?,1) 14. f15(A,B,C,D,E,F,G) -> f12(A,B,C,1 + D,E,F,G) [E >= A] (?,1) 15. f12(A,B,C,D,E,F,G) -> f23(A,B,C,0,E,F,G) [D >= A] (?,1) Signature: {(f0,7);(f12,7);(f15,7);(f23,7);(f26,7);(f30,7);(f52,7)} Flow Graph: [0->{1,15},1->{2,14},2->{2,14},3->{4,7},4->{5,6},5->{5,6},6->{4,7},7->{3,8,9,10,11,12,13},8->{},9->{} ,10->{},11->{},12->{},13->{},14->{1,15},15->{3,8,9,10,11,12,13}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,15)] * Step 2: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f12(2,H,I,0,E,F,G) True (1,1) 1. f12(A,B,C,D,E,F,G) -> f15(A,B,C,D,0,F,G) [A >= 1 + D] (?,1) 2. f15(A,B,C,D,E,F,G) -> f15(A,B,C,D,1 + E,F,G) [A >= 1 + E] (?,1) 3. f23(A,B,C,D,E,F,G) -> f26(A,B,C,D,0,F,G) [A >= 1 + D] (?,1) 4. f26(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,0,G) [A >= 1 + E] (?,1) 5. f30(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,1 + F,G) [A >= 1 + F] (?,1) 6. f30(A,B,C,D,E,F,G) -> f26(A,B,C,D,1 + E,F,G) [F >= A] (?,1) 7. f26(A,B,C,D,E,F,G) -> f23(A,B,C,1 + D,E,F,G) [E >= A] (?,1) 8. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [D >= A] (?,1) 9. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 49 >= H] (?,1) 10. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A] (?,1) 11. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 42 >= H] (?,1) 12. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 21 >= H] (?,1) 13. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 18 >= H] (?,1) 14. f15(A,B,C,D,E,F,G) -> f12(A,B,C,1 + D,E,F,G) [E >= A] (?,1) 15. f12(A,B,C,D,E,F,G) -> f23(A,B,C,0,E,F,G) [D >= A] (?,1) Signature: {(f0,7);(f12,7);(f15,7);(f23,7);(f26,7);(f30,7);(f52,7)} Flow Graph: [0->{1},1->{2,14},2->{2,14},3->{4,7},4->{5,6},5->{5,6},6->{4,7},7->{3,8,9,10,11,12,13},8->{},9->{},10->{} ,11->{},12->{},13->{},14->{1,15},15->{3,8,9,10,11,12,13}] + Applied Processor: FromIts + Details: () * Step 3: Unfold WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,B,C,D,E,F,G) -> f12(2,H,I,0,E,F,G) True f12(A,B,C,D,E,F,G) -> f15(A,B,C,D,0,F,G) [A >= 1 + D] f15(A,B,C,D,E,F,G) -> f15(A,B,C,D,1 + E,F,G) [A >= 1 + E] f23(A,B,C,D,E,F,G) -> f26(A,B,C,D,0,F,G) [A >= 1 + D] f26(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,0,G) [A >= 1 + E] f30(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,1 + F,G) [A >= 1 + F] f30(A,B,C,D,E,F,G) -> f26(A,B,C,D,1 + E,F,G) [F >= A] f26(A,B,C,D,E,F,G) -> f23(A,B,C,1 + D,E,F,G) [E >= A] f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [D >= A] f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 49 >= H] f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A] f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 42 >= H] f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 21 >= H] f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= A && 18 >= H] f15(A,B,C,D,E,F,G) -> f12(A,B,C,1 + D,E,F,G) [E >= A] f12(A,B,C,D,E,F,G) -> f23(A,B,C,0,E,F,G) [D >= A] Signature: {(f0,7);(f12,7);(f15,7);(f23,7);(f26,7);(f30,7);(f52,7)} Rule Graph: [0->{1},1->{2,14},2->{2,14},3->{4,7},4->{5,6},5->{5,6},6->{4,7},7->{3,8,9,10,11,12,13},8->{},9->{},10->{} ,11->{},12->{},13->{},14->{1,15},15->{3,8,9,10,11,12,13}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0.0(A,B,C,D,E,F,G) -> f12.1(2,H,I,0,E,F,G) True f12.1(A,B,C,D,E,F,G) -> f15.2(A,B,C,D,0,F,G) [A >= 1 + D] f12.1(A,B,C,D,E,F,G) -> f15.14(A,B,C,D,0,F,G) [A >= 1 + D] f15.2(A,B,C,D,E,F,G) -> f15.2(A,B,C,D,1 + E,F,G) [A >= 1 + E] f15.2(A,B,C,D,E,F,G) -> f15.14(A,B,C,D,1 + E,F,G) [A >= 1 + E] f23.3(A,B,C,D,E,F,G) -> f26.4(A,B,C,D,0,F,G) [A >= 1 + D] f23.3(A,B,C,D,E,F,G) -> f26.7(A,B,C,D,0,F,G) [A >= 1 + D] f26.4(A,B,C,D,E,F,G) -> f30.5(A,B,C,D,E,0,G) [A >= 1 + E] f26.4(A,B,C,D,E,F,G) -> f30.6(A,B,C,D,E,0,G) [A >= 1 + E] f30.5(A,B,C,D,E,F,G) -> f30.5(A,B,C,D,E,1 + F,G) [A >= 1 + F] f30.5(A,B,C,D,E,F,G) -> f30.6(A,B,C,D,E,1 + F,G) [A >= 1 + F] f30.6(A,B,C,D,E,F,G) -> f26.4(A,B,C,D,1 + E,F,G) [F >= A] f30.6(A,B,C,D,E,F,G) -> f26.7(A,B,C,D,1 + E,F,G) [F >= A] f26.7(A,B,C,D,E,F,G) -> f23.3(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.8(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.9(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.10(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.11(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.12(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.13(A,B,C,1 + D,E,F,G) [E >= A] f23.8(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,0) [D >= A] f23.9(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 49 >= H] f23.10(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A] f23.11(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 42 >= H] f23.12(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 21 >= H] f23.13(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 18 >= H] f15.14(A,B,C,D,E,F,G) -> f12.1(A,B,C,1 + D,E,F,G) [E >= A] f15.14(A,B,C,D,E,F,G) -> f12.15(A,B,C,1 + D,E,F,G) [E >= A] f12.15(A,B,C,D,E,F,G) -> f23.3(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.8(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.9(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.10(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.11(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.12(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.13(A,B,C,0,E,F,G) [D >= A] Signature: {(f0.0,7) ;(f12.1,7) ;(f12.15,7) ;(f15.14,7) ;(f15.2,7) ;(f23.10,7) ;(f23.11,7) ;(f23.12,7) ;(f23.13,7) ;(f23.3,7) ;(f23.8,7) ;(f23.9,7) ;(f26.4,7) ;(f26.7,7) ;(f30.5,7) ;(f30.6,7) ;(f52.16,7)} Rule Graph: [0->{1,2},1->{3,4},2->{26,27},3->{3,4},4->{26,27},5->{7,8},6->{13,14,15,16,17,18,19},7->{9,10},8->{11,12} ,9->{9,10},10->{11,12},11->{7,8},12->{13,14,15,16,17,18,19},13->{5,6},14->{20},15->{21},16->{22},17->{23} ,18->{24},19->{25},20->{},21->{},22->{},23->{},24->{},25->{},26->{1,2},27->{28,29,30,31,32,33,34},28->{5,6} ,29->{20},30->{21},31->{22},32->{23},33->{24},34->{25}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0.0(A,B,C,D,E,F,G) -> f12.1(2,H,I,0,E,F,G) True f12.1(A,B,C,D,E,F,G) -> f15.2(A,B,C,D,0,F,G) [A >= 1 + D] f12.1(A,B,C,D,E,F,G) -> f15.14(A,B,C,D,0,F,G) [A >= 1 + D] f15.2(A,B,C,D,E,F,G) -> f15.2(A,B,C,D,1 + E,F,G) [A >= 1 + E] f15.2(A,B,C,D,E,F,G) -> f15.14(A,B,C,D,1 + E,F,G) [A >= 1 + E] f23.3(A,B,C,D,E,F,G) -> f26.4(A,B,C,D,0,F,G) [A >= 1 + D] f23.3(A,B,C,D,E,F,G) -> f26.7(A,B,C,D,0,F,G) [A >= 1 + D] f26.4(A,B,C,D,E,F,G) -> f30.5(A,B,C,D,E,0,G) [A >= 1 + E] f26.4(A,B,C,D,E,F,G) -> f30.6(A,B,C,D,E,0,G) [A >= 1 + E] f30.5(A,B,C,D,E,F,G) -> f30.5(A,B,C,D,E,1 + F,G) [A >= 1 + F] f30.5(A,B,C,D,E,F,G) -> f30.6(A,B,C,D,E,1 + F,G) [A >= 1 + F] f30.6(A,B,C,D,E,F,G) -> f26.4(A,B,C,D,1 + E,F,G) [F >= A] f30.6(A,B,C,D,E,F,G) -> f26.7(A,B,C,D,1 + E,F,G) [F >= A] f26.7(A,B,C,D,E,F,G) -> f23.3(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.8(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.9(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.10(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.11(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.12(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.13(A,B,C,1 + D,E,F,G) [E >= A] f23.8(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,0) [D >= A] f23.9(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 49 >= H] f23.10(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A] f23.11(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 42 >= H] f23.12(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 21 >= H] f23.13(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 18 >= H] f15.14(A,B,C,D,E,F,G) -> f12.1(A,B,C,1 + D,E,F,G) [E >= A] f15.14(A,B,C,D,E,F,G) -> f12.15(A,B,C,1 + D,E,F,G) [E >= A] f12.15(A,B,C,D,E,F,G) -> f23.3(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.8(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.9(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.10(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.11(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.12(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.13(A,B,C,0,E,F,G) [D >= A] f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True Signature: {(exitus616,7) ;(f0.0,7) ;(f12.1,7) ;(f12.15,7) ;(f15.14,7) ;(f15.2,7) ;(f23.10,7) ;(f23.11,7) ;(f23.12,7) ;(f23.13,7) ;(f23.3,7) ;(f23.8,7) ;(f23.9,7) ;(f26.4,7) ;(f26.7,7) ;(f30.5,7) ;(f30.6,7) ;(f52.16,7)} Rule Graph: [0->{1,2},1->{3,4},2->{26,27},3->{3,4},4->{26,27},5->{7,8},6->{13,14,15,16,17,18,19},7->{9,10},8->{11,12} ,9->{9,10},10->{11,12},11->{7,8},12->{13,14,15,16,17,18,19},13->{5,6},14->{20},15->{21},16->{22},17->{23} ,18->{24},19->{25},20->{40,46},21->{39,45},22->{38,44},23->{37,43},24->{36,42},25->{35,41},26->{1,2},27->{28 ,29,30,31,32,33,34},28->{5,6},29->{20},30->{21},31->{22},32->{23},33->{24},34->{25}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46] | +- p:[1,26,2,4,3] c: [1,2,4,26] | | | `- p:[3] c: [3] | `- p:[5,13,6,12,8,11,10,7,9] c: [5,6,12,13] | `- p:[7,11,8,10,9] c: [7,8,10,11] | `- p:[9] c: [9] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0.0(A,B,C,D,E,F,G) -> f12.1(2,H,I,0,E,F,G) True f12.1(A,B,C,D,E,F,G) -> f15.2(A,B,C,D,0,F,G) [A >= 1 + D] f12.1(A,B,C,D,E,F,G) -> f15.14(A,B,C,D,0,F,G) [A >= 1 + D] f15.2(A,B,C,D,E,F,G) -> f15.2(A,B,C,D,1 + E,F,G) [A >= 1 + E] f15.2(A,B,C,D,E,F,G) -> f15.14(A,B,C,D,1 + E,F,G) [A >= 1 + E] f23.3(A,B,C,D,E,F,G) -> f26.4(A,B,C,D,0,F,G) [A >= 1 + D] f23.3(A,B,C,D,E,F,G) -> f26.7(A,B,C,D,0,F,G) [A >= 1 + D] f26.4(A,B,C,D,E,F,G) -> f30.5(A,B,C,D,E,0,G) [A >= 1 + E] f26.4(A,B,C,D,E,F,G) -> f30.6(A,B,C,D,E,0,G) [A >= 1 + E] f30.5(A,B,C,D,E,F,G) -> f30.5(A,B,C,D,E,1 + F,G) [A >= 1 + F] f30.5(A,B,C,D,E,F,G) -> f30.6(A,B,C,D,E,1 + F,G) [A >= 1 + F] f30.6(A,B,C,D,E,F,G) -> f26.4(A,B,C,D,1 + E,F,G) [F >= A] f30.6(A,B,C,D,E,F,G) -> f26.7(A,B,C,D,1 + E,F,G) [F >= A] f26.7(A,B,C,D,E,F,G) -> f23.3(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.8(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.9(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.10(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.11(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.12(A,B,C,1 + D,E,F,G) [E >= A] f26.7(A,B,C,D,E,F,G) -> f23.13(A,B,C,1 + D,E,F,G) [E >= A] f23.8(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,0) [D >= A] f23.9(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 49 >= H] f23.10(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A] f23.11(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 42 >= H] f23.12(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 21 >= H] f23.13(A,B,C,D,E,F,G) -> f52.16(A,B,C,D,E,F,1) [D >= A && 18 >= H] f15.14(A,B,C,D,E,F,G) -> f12.1(A,B,C,1 + D,E,F,G) [E >= A] f15.14(A,B,C,D,E,F,G) -> f12.15(A,B,C,1 + D,E,F,G) [E >= A] f12.15(A,B,C,D,E,F,G) -> f23.3(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.8(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.9(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.10(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.11(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.12(A,B,C,0,E,F,G) [D >= A] f12.15(A,B,C,D,E,F,G) -> f23.13(A,B,C,0,E,F,G) [D >= A] f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True f52.16(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True Signature: {(exitus616,7) ;(f0.0,7) ;(f12.1,7) ;(f12.15,7) ;(f15.14,7) ;(f15.2,7) ;(f23.10,7) ;(f23.11,7) ;(f23.12,7) ;(f23.13,7) ;(f23.3,7) ;(f23.8,7) ;(f23.9,7) ;(f26.4,7) ;(f26.7,7) ;(f30.5,7) ;(f30.6,7) ;(f52.16,7)} Rule Graph: [0->{1,2},1->{3,4},2->{26,27},3->{3,4},4->{26,27},5->{7,8},6->{13,14,15,16,17,18,19},7->{9,10},8->{11,12} ,9->{9,10},10->{11,12},11->{7,8},12->{13,14,15,16,17,18,19},13->{5,6},14->{20},15->{21},16->{22},17->{23} ,18->{24},19->{25},20->{40,46},21->{39,45},22->{38,44},23->{37,43},24->{36,42},25->{35,41},26->{1,2},27->{28 ,29,30,31,32,33,34},28->{5,6},29->{20},30->{21},31->{22},32->{23},33->{24},34->{25}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46] | +- p:[1,26,2,4,3] c: [1,2,4,26] | | | `- p:[3] c: [3] | `- p:[5,13,6,12,8,11,10,7,9] c: [5,6,12,13] | `- p:[7,11,8,10,9] c: [7,8,10,11] | `- p:[9] c: [9]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,0.0,0.0.0,0.1,0.1.0,0.1.0.0] f0.0 ~> f12.1 [A <= 2*K, B <= unknown, C <= unknown, D <= 0*K, E <= E, F <= F, G <= G] f12.1 ~> f15.2 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f12.1 ~> f15.14 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f15.2 ~> f15.2 [A <= A, B <= B, C <= C, D <= D, E <= A + E, F <= F, G <= G] f15.2 ~> f15.14 [A <= A, B <= B, C <= C, D <= D, E <= A + E, F <= F, G <= G] f23.3 ~> f26.4 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f23.3 ~> f26.7 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f26.4 ~> f30.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f26.4 ~> f30.6 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f30.5 ~> f30.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= A + F, G <= G] f30.5 ~> f30.6 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= A + F, G <= G] f30.6 ~> f26.4 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f30.6 ~> f26.7 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f26.7 ~> f23.3 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f26.7 ~> f23.8 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f26.7 ~> f23.9 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f26.7 ~> f23.10 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f26.7 ~> f23.11 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f26.7 ~> f23.12 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f26.7 ~> f23.13 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f23.8 ~> f52.16 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= 0*K] f23.9 ~> f52.16 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f23.10 ~> f52.16 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f23.11 ~> f52.16 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f23.12 ~> f52.16 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f23.13 ~> f52.16 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f15.14 ~> f12.1 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f15.14 ~> f12.15 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f12.15 ~> f23.3 [A <= A, B <= B, C <= C, D <= 0*K, E <= E, F <= F, G <= G] f12.15 ~> f23.8 [A <= A, B <= B, C <= C, D <= 0*K, E <= E, F <= F, G <= G] f12.15 ~> f23.9 [A <= A, B <= B, C <= C, D <= 0*K, E <= E, F <= F, G <= G] f12.15 ~> f23.10 [A <= A, B <= B, C <= C, D <= 0*K, E <= E, F <= F, G <= G] f12.15 ~> f23.11 [A <= A, B <= B, C <= C, D <= 0*K, E <= E, F <= F, G <= G] f12.15 ~> f23.12 [A <= A, B <= B, C <= C, D <= 0*K, E <= E, F <= F, G <= G] f12.15 ~> f23.13 [A <= A, B <= B, C <= C, D <= 0*K, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f52.16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= K + A + D] f12.1 ~> f15.2 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f15.14 ~> f12.1 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f12.1 ~> f15.14 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f15.2 ~> f15.14 [A <= A, B <= B, C <= C, D <= D, E <= A + E, F <= F, G <= G] f15.2 ~> f15.2 [A <= A, B <= B, C <= C, D <= D, E <= A + E, F <= F, G <= G] + Loop: [0.0.0 <= K + A + E] f15.2 ~> f15.2 [A <= A, B <= B, C <= C, D <= D, E <= A + E, F <= F, G <= G] + Loop: [0.1 <= K + A + D] f23.3 ~> f26.4 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f26.7 ~> f23.3 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= F, G <= G] f23.3 ~> f26.7 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f30.6 ~> f26.7 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f26.4 ~> f30.6 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f30.6 ~> f26.4 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f30.5 ~> f30.6 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= A + F, G <= G] f26.4 ~> f30.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f30.5 ~> f30.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= A + F, G <= G] + Loop: [0.1.0 <= K + A + E] f26.4 ~> f30.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f30.6 ~> f26.4 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f26.4 ~> f30.6 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f30.5 ~> f30.6 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= A + F, G <= G] f30.5 ~> f30.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= A + F, G <= G] + Loop: [0.1.0.0 <= K + A + F] f30.5 ~> f30.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= A + 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,0.0,0.0.0,0.1,0.1.0,0.1.0.0] f0.0 ~> f12.1 [K ~=> A,K ~=> D,huge ~=> B,huge ~=> C] f12.1 ~> f15.2 [K ~=> E] f12.1 ~> f15.14 [K ~=> E] f15.2 ~> f15.2 [A ~+> E,E ~+> E] f15.2 ~> f15.14 [A ~+> E,E ~+> E] f23.3 ~> f26.4 [K ~=> E] f23.3 ~> f26.7 [K ~=> E] f26.4 ~> f30.5 [K ~=> F] f26.4 ~> f30.6 [K ~=> F] f30.5 ~> f30.5 [A ~+> F,F ~+> F] f30.5 ~> f30.6 [A ~+> F,F ~+> F] f30.6 ~> f26.4 [E ~+> E,K ~+> E] f30.6 ~> f26.7 [E ~+> E,K ~+> E] f26.7 ~> f23.3 [D ~+> D,K ~+> D] f26.7 ~> f23.8 [D ~+> D,K ~+> D] f26.7 ~> f23.9 [D ~+> D,K ~+> D] f26.7 ~> f23.10 [D ~+> D,K ~+> D] f26.7 ~> f23.11 [D ~+> D,K ~+> D] f26.7 ~> f23.12 [D ~+> D,K ~+> D] f26.7 ~> f23.13 [D ~+> D,K ~+> D] f23.8 ~> f52.16 [K ~=> G] f23.9 ~> f52.16 [K ~=> G] f23.10 ~> f52.16 [K ~=> G] f23.11 ~> f52.16 [K ~=> G] f23.12 ~> f52.16 [K ~=> G] f23.13 ~> f52.16 [K ~=> G] f15.14 ~> f12.1 [D ~+> D,K ~+> D] f15.14 ~> f12.15 [D ~+> D,K ~+> D] f12.15 ~> f23.3 [K ~=> D] f12.15 ~> f23.8 [K ~=> D] f12.15 ~> f23.9 [K ~=> D] f12.15 ~> f23.10 [K ~=> D] f12.15 ~> f23.11 [K ~=> D] f12.15 ~> f23.12 [K ~=> D] f12.15 ~> f23.13 [K ~=> D] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] f52.16 ~> exitus616 [] + Loop: [A ~+> 0.0,D ~+> 0.0,K ~+> 0.0] f12.1 ~> f15.2 [K ~=> E] f15.14 ~> f12.1 [D ~+> D,K ~+> D] f12.1 ~> f15.14 [K ~=> E] f15.2 ~> f15.14 [A ~+> E,E ~+> E] f15.2 ~> f15.2 [A ~+> E,E ~+> E] + Loop: [A ~+> 0.0.0,E ~+> 0.0.0,K ~+> 0.0.0] f15.2 ~> f15.2 [A ~+> E,E ~+> E] + Loop: [A ~+> 0.1,D ~+> 0.1,K ~+> 0.1] f23.3 ~> f26.4 [K ~=> E] f26.7 ~> f23.3 [D ~+> D,K ~+> D] f23.3 ~> f26.7 [K ~=> E] f30.6 ~> f26.7 [E ~+> E,K ~+> E] f26.4 ~> f30.6 [K ~=> F] f30.6 ~> f26.4 [E ~+> E,K ~+> E] f30.5 ~> f30.6 [A ~+> F,F ~+> F] f26.4 ~> f30.5 [K ~=> F] f30.5 ~> f30.5 [A ~+> F,F ~+> F] + Loop: [A ~+> 0.1.0,E ~+> 0.1.0,K ~+> 0.1.0] f26.4 ~> f30.5 [K ~=> F] f30.6 ~> f26.4 [E ~+> E,K ~+> E] f26.4 ~> f30.6 [K ~=> F] f30.5 ~> f30.6 [A ~+> F,F ~+> F] f30.5 ~> f30.5 [A ~+> F,F ~+> F] + Loop: [A ~+> 0.1.0.0,F ~+> 0.1.0.0,K ~+> 0.1.0.0] f30.5 ~> f30.5 [A ~+> F,F ~+> F] + Applied Processor: Lare + Details: f0.0 ~> exitus616 [K ~=> A ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,huge ~=> B ,huge ~=> C ,tick ~+> tick ,K ~+> D ,K ~+> E ,K ~+> F ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,K ~*> D ,K ~*> E ,K ~*> F ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,K ~^> E ,K ~^> F] + f15.14> [K ~=> E ,A ~+> E ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,D ~+> D ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> E ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> D ,A ~*> E ,A ~*> 0.0.0 ,A ~*> tick ,D ~*> D ,D ~*> E ,D ~*> tick ,K ~*> D ,K ~*> E ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> E ,D ~^> E ,K ~^> E] + f15.2> [A ~+> E ,A ~+> 0.0.0 ,A ~+> tick ,E ~+> E ,E ~+> 0.0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> E ,E ~*> E ,K ~*> E] + f26.7> [K ~=> E ,K ~=> F ,A ~+> F ,A ~+> 0.1 ,A ~+> 0.1.0 ,A ~+> 0.1.0.0 ,A ~+> tick ,D ~+> D ,D ~+> 0.1 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> E ,K ~+> F ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,A ~*> D ,A ~*> E ,A ~*> F ,A ~*> 0.1.0.0 ,A ~*> tick ,D ~*> D ,D ~*> tick ,K ~*> D ,K ~*> E ,K ~*> F ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,A ~^> F ,K ~^> F] + f30.6> [K ~=> F ,A ~+> F ,A ~+> 0.1.0 ,A ~+> 0.1.0.0 ,A ~+> tick ,E ~+> E ,E ~+> 0.1.0 ,E ~+> tick ,tick ~+> tick ,K ~+> E ,K ~+> F ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,A ~*> E ,A ~*> F ,A ~*> 0.1.0.0 ,A ~*> tick ,E ~*> E ,E ~*> F ,E ~*> tick ,K ~*> E ,K ~*> F ,K ~*> 0.1.0.0 ,K ~*> tick ,A ~^> F ,E ~^> F ,K ~^> F] + f30.5> [A ~+> F ,A ~+> 0.1.0.0 ,A ~+> tick ,F ~+> F ,F ~+> 0.1.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.1.0.0 ,K ~+> tick ,A ~*> F ,F ~*> F ,K ~*> F] YES(?,O(1))