YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> f2(A,B,C,D,E,F,G,H) True (1,1) 1. f2(A,B,C,D,E,F,G,H) -> f1(A,B,C,D,E,F,G,H) [B >= A] (?,1) 2. f2(A,B,C,D,E,F,G,H) -> f8(A,B,0,B,E,F,G,H) [A >= 1 + B] (?,1) 3. f8(A,B,C,D,E,F,G,H) -> f34(A,B,C,B,E,F,G,H) [-1 + A + -1*B >= 0 && E >= 1 + A && B = D] (?,1) 4. f8(A,B,C,D,E,F,G,H) -> f8(A,B,J,E,1 + E,I,K,H) [-1 + A + -1*B >= 0 && A >= E && I >= 1 + K] (?,1) 5. f8(A,B,C,D,E,F,G,H) -> f8(A,B,C,D,1 + E,J,I,H) [-1 + A + -1*B >= 0 && A >= E && I >= J] (?,1) 6. f34(A,B,C,D,E,F,G,H) -> f2(A,1 + B,0,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && C = 0] (?,1) 7. f34(A,B,C,D,E,F,G,H) -> f36(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && C >= 1] (?,1) 8. f34(A,B,C,D,E,F,G,H) -> f36(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && 0 >= 1 + C] (?,1) 9. f8(A,B,C,D,E,F,G,H) -> f19(A,B,C,D,E,F,G,H) [-1 + A + -1*B >= 0 && D >= 1 + B && E >= 1 + A] (?,1) 10. f8(A,B,C,D,E,F,G,H) -> f19(A,B,C,D,E,F,G,H) [-1 + A + -1*B >= 0 && B >= 1 + D && E >= 1 + A] (?,1) 11. f19(A,B,C,D,E,F,G,H) -> f27(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] (?,1) 12. f36(A,B,C,D,E,F,G,H) -> f2(A,1 + B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && D >= 1 + A] (?,1) 13. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G,0) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D] (?,1) 14. f36(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,J) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D && I >= 1] (?,1) 15. f36(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,J) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D && 0 >= 1 + I] (?,1) 16. f27(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] (?,1) 17. f43(A,B,C,D,E,F,G,H) -> f49(A,B,C,D,E,F,G,H) [-1 + -1*D + E >= 0 (?,1) && -2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && A + -1*D >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] 18. f49(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G,H) [-1 + -1*D + E >= 0 (?,1) && -2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && A + -1*D >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] Signature: {(f1,8);(f19,8);(f2,8);(f27,8);(f34,8);(f36,8);(f43,8);(f49,8);(f8,8);(start,8)} Flow Graph: [0->{1,2},1->{},2->{3,4,5,9,10},3->{6,7,8},4->{3,4,5,9,10},5->{3,4,5,9,10},6->{1,2},7->{12,13,14,15} ,8->{12,13,14,15},9->{11},10->{11},11->{16},12->{1,2},13->{12,13,14,15},14->{17},15->{17},16->{6,7,8} ,17->{18},18->{12,13,14,15}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,9),(2,10),(4,3),(4,10)] * Step 2: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> f2(A,B,C,D,E,F,G,H) True (1,1) 1. f2(A,B,C,D,E,F,G,H) -> f1(A,B,C,D,E,F,G,H) [B >= A] (?,1) 2. f2(A,B,C,D,E,F,G,H) -> f8(A,B,0,B,E,F,G,H) [A >= 1 + B] (?,1) 3. f8(A,B,C,D,E,F,G,H) -> f34(A,B,C,B,E,F,G,H) [-1 + A + -1*B >= 0 && E >= 1 + A && B = D] (?,1) 4. f8(A,B,C,D,E,F,G,H) -> f8(A,B,J,E,1 + E,I,K,H) [-1 + A + -1*B >= 0 && A >= E && I >= 1 + K] (?,1) 5. f8(A,B,C,D,E,F,G,H) -> f8(A,B,C,D,1 + E,J,I,H) [-1 + A + -1*B >= 0 && A >= E && I >= J] (?,1) 6. f34(A,B,C,D,E,F,G,H) -> f2(A,1 + B,0,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && C = 0] (?,1) 7. f34(A,B,C,D,E,F,G,H) -> f36(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && C >= 1] (?,1) 8. f34(A,B,C,D,E,F,G,H) -> f36(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && 0 >= 1 + C] (?,1) 9. f8(A,B,C,D,E,F,G,H) -> f19(A,B,C,D,E,F,G,H) [-1 + A + -1*B >= 0 && D >= 1 + B && E >= 1 + A] (?,1) 10. f8(A,B,C,D,E,F,G,H) -> f19(A,B,C,D,E,F,G,H) [-1 + A + -1*B >= 0 && B >= 1 + D && E >= 1 + A] (?,1) 11. f19(A,B,C,D,E,F,G,H) -> f27(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] (?,1) 12. f36(A,B,C,D,E,F,G,H) -> f2(A,1 + B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && D >= 1 + A] (?,1) 13. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G,0) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D] (?,1) 14. f36(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,J) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D && I >= 1] (?,1) 15. f36(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,J) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D && 0 >= 1 + I] (?,1) 16. f27(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] (?,1) 17. f43(A,B,C,D,E,F,G,H) -> f49(A,B,C,D,E,F,G,H) [-1 + -1*D + E >= 0 (?,1) && -2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && A + -1*D >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] 18. f49(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G,H) [-1 + -1*D + E >= 0 (?,1) && -2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && A + -1*D >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] Signature: {(f1,8);(f19,8);(f2,8);(f27,8);(f34,8);(f36,8);(f43,8);(f49,8);(f8,8);(start,8)} Flow Graph: [0->{1,2},1->{},2->{3,4,5},3->{6,7,8},4->{4,5,9},5->{3,4,5,9,10},6->{1,2},7->{12,13,14,15},8->{12,13,14 ,15},9->{11},10->{11},11->{16},12->{1,2},13->{12,13,14,15},14->{17},15->{17},16->{6,7,8},17->{18},18->{12,13 ,14,15}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F,G,H) -> f2(A,B,C,D,E,F,G,H) True f2(A,B,C,D,E,F,G,H) -> f1(A,B,C,D,E,F,G,H) [B >= A] f2(A,B,C,D,E,F,G,H) -> f8(A,B,0,B,E,F,G,H) [A >= 1 + B] f8(A,B,C,D,E,F,G,H) -> f34(A,B,C,B,E,F,G,H) [-1 + A + -1*B >= 0 && E >= 1 + A && B = D] f8(A,B,C,D,E,F,G,H) -> f8(A,B,J,E,1 + E,I,K,H) [-1 + A + -1*B >= 0 && A >= E && I >= 1 + K] f8(A,B,C,D,E,F,G,H) -> f8(A,B,C,D,1 + E,J,I,H) [-1 + A + -1*B >= 0 && A >= E && I >= J] f34(A,B,C,D,E,F,G,H) -> f2(A,1 + B,0,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && C = 0] f34(A,B,C,D,E,F,G,H) -> f36(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && C >= 1] f34(A,B,C,D,E,F,G,H) -> f36(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && 0 >= 1 + C] f8(A,B,C,D,E,F,G,H) -> f19(A,B,C,D,E,F,G,H) [-1 + A + -1*B >= 0 && D >= 1 + B && E >= 1 + A] f8(A,B,C,D,E,F,G,H) -> f19(A,B,C,D,E,F,G,H) [-1 + A + -1*B >= 0 && B >= 1 + D && E >= 1 + A] f19(A,B,C,D,E,F,G,H) -> f27(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] f36(A,B,C,D,E,F,G,H) -> f2(A,1 + B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && D >= 1 + A] f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G,0) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D] f36(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,J) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D && I >= 1] f36(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,J) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D && 0 >= 1 + I] f27(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] f43(A,B,C,D,E,F,G,H) -> f49(A,B,C,D,E,F,G,H) [-1 + -1*D + E >= 0 && -2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && A + -1*D >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] f49(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G,H) [-1 + -1*D + E >= 0 && -2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && A + -1*D >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] Signature: {(f1,8);(f19,8);(f2,8);(f27,8);(f34,8);(f36,8);(f43,8);(f49,8);(f8,8);(start,8)} Rule Graph: [0->{1,2},1->{},2->{3,4,5},3->{6,7,8},4->{4,5,9},5->{3,4,5,9,10},6->{1,2},7->{12,13,14,15},8->{12,13,14 ,15},9->{11},10->{11},11->{16},12->{1,2},13->{12,13,14,15},14->{17},15->{17},16->{6,7,8},17->{18},18->{12,13 ,14,15}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[2,6,3,5,4,16,11,9,10,12,7,8,13,18,17,14,15] c: [9,10,11,16] | `- p:[2,6,3,5,4,12,7,8,13,18,17,14,15] c: [12] | +- p:[2,6,3,5,4] c: [2,3,6] | | | `- p:[4,5] c: [5] | | | `- p:[4] c: [4] | `- p:[13,18,17,14,15] c: [14,15,17,18] | `- p:[13] c: [13] * Step 4: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H) -> f2(A,B,C,D,E,F,G,H) True f2(A,B,C,D,E,F,G,H) -> f1(A,B,C,D,E,F,G,H) [B >= A] f2(A,B,C,D,E,F,G,H) -> f8(A,B,0,B,E,F,G,H) [A >= 1 + B] f8(A,B,C,D,E,F,G,H) -> f34(A,B,C,B,E,F,G,H) [-1 + A + -1*B >= 0 && E >= 1 + A && B = D] f8(A,B,C,D,E,F,G,H) -> f8(A,B,J,E,1 + E,I,K,H) [-1 + A + -1*B >= 0 && A >= E && I >= 1 + K] f8(A,B,C,D,E,F,G,H) -> f8(A,B,C,D,1 + E,J,I,H) [-1 + A + -1*B >= 0 && A >= E && I >= J] f34(A,B,C,D,E,F,G,H) -> f2(A,1 + B,0,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && C = 0] f34(A,B,C,D,E,F,G,H) -> f36(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && C >= 1] f34(A,B,C,D,E,F,G,H) -> f36(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && 0 >= 1 + C] f8(A,B,C,D,E,F,G,H) -> f19(A,B,C,D,E,F,G,H) [-1 + A + -1*B >= 0 && D >= 1 + B && E >= 1 + A] f8(A,B,C,D,E,F,G,H) -> f19(A,B,C,D,E,F,G,H) [-1 + A + -1*B >= 0 && B >= 1 + D && E >= 1 + A] f19(A,B,C,D,E,F,G,H) -> f27(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] f36(A,B,C,D,E,F,G,H) -> f2(A,1 + B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && D >= 1 + A] f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G,0) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D] f36(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,J) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D && I >= 1] f36(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,J) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && A >= D && 0 >= 1 + I] f27(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,E,F,G,H) [-2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] f43(A,B,C,D,E,F,G,H) -> f49(A,B,C,D,E,F,G,H) [-1 + -1*D + E >= 0 && -2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && A + -1*D >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] f49(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G,H) [-1 + -1*D + E >= 0 && -2 + -1*B + E >= 0 && -1 + -1*A + E >= 0 && A + -1*D >= 0 && -1 + A + -1*B >= 0 && E >= 1 + A] Signature: {(f1,8);(f19,8);(f2,8);(f27,8);(f34,8);(f36,8);(f43,8);(f49,8);(f8,8);(start,8)} Rule Graph: [0->{1,2},1->{},2->{3,4,5},3->{6,7,8},4->{4,5,9},5->{3,4,5,9,10},6->{1,2},7->{12,13,14,15},8->{12,13,14 ,15},9->{11},10->{11},11->{16},12->{1,2},13->{12,13,14,15},14->{17},15->{17},16->{6,7,8},17->{18},18->{12,13 ,14,15}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[2,6,3,5,4,16,11,9,10,12,7,8,13,18,17,14,15] c: [9,10,11,16] | `- p:[2,6,3,5,4,12,7,8,13,18,17,14,15] c: [12] | +- p:[2,6,3,5,4] c: [2,3,6] | | | `- p:[4,5] c: [5] | | | `- p:[4] c: [4] | `- p:[13,18,17,14,15] c: [14,15,17,18] | `- p:[13] c: [13]) + Applied Processor: CloseWith True + Details: () YES