YES * Step 1: UnsatPaths YES + 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 YES + 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: Decompose YES + 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: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | +- p:[1,14,2] c: [1,14] | | | `- p:[2] c: [2] | `- p:[3,7,6,4,5] c: [3,7] | `- p:[4,6,5] c: [4,6] | `- p:[5] c: [5] * Step 4: CloseWith YES + 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}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | +- p:[1,14,2] c: [1,14] | | | `- p:[2] c: [2] | `- p:[3,7,6,4,5] c: [3,7] | `- p:[4,6,5] c: [4,6] | `- p:[5] c: [5]) + Applied Processor: CloseWith True + Details: () YES