YES * Step 1: UnsatRules YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A >= 101 && B = C && D = E && F = G && H = A] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [100 >= A && B = C && D = E && F = G && H = A] (?,1) 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [89 >= A && D = 1 && H = A && F = 101 && B = 91] (?,1) 3. lbl161(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [0 >= 10 && 89 >= A && 0 >= 1 && D = 2 && H = A && F = 101 && B = 91] (?,1) 4. lbl161(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [0 >= 2 && 89 >= A && H = A && F = 101 && D = 1 && B = 91] (?,1) 5. lbl161(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [0 >= 1 && 89 >= A && H = A && F = 101 && D = 1 && B = 91] (?,1) 6. lbl161(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [0 >= 10 && 0 >= 2 && 89 >= A && H = A && F = 101 && D = 1 && B = 91] (?,1) 7. lbl221(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 >= D && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] (?,1) 8. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] (?,1) 9. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] (?,1) 10. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] (?,1) 11. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] (?,1) 12. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] (?,1) 13. lbl111(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + 11*D >= 112 && 1 >= D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] (?,1) 14. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [F = 111 && D = 2 && H = 100 && B = C && A = 100] (?,1) 15. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (?,1) && D >= 3 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 16. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (?,1) && D >= 2 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 17. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] (?,1) 18. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl161,8);(lbl221,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{2,3,4,5,6},4->{7,8,9,10,11},5->{7,8,9,10,11},6->{7,8,9,10,11} ,7->{},8->{2,3,4,5,6},9->{7,8,9,10,11},10->{7,8,9,10,11},11->{7,8,9,10,11},12->{12,13,14,15,16,17},13->{} ,14->{2,3,4,5,6},15->{7,8,9,10,11},16->{7,8,9,10,11},17->{7,8,9,10,11},18->{0,1}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [3,4,5,6,7,13] * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A >= 101 && B = C && D = E && F = G && H = A] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [100 >= A && B = C && D = E && F = G && H = A] (?,1) 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [89 >= A && D = 1 && H = A && F = 101 && B = 91] (?,1) 8. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] (?,1) 9. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] (?,1) 10. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] (?,1) 11. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] (?,1) 12. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] (?,1) 14. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [F = 111 && D = 2 && H = 100 && B = C && A = 100] (?,1) 15. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (?,1) && D >= 3 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 16. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (?,1) && D >= 2 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 17. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] (?,1) 18. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl161,8);(lbl221,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{12,14,15,16,17},2->{},8->{2},9->{8,9,10,11},10->{8,9,10,11},11->{8,9,10,11},12->{12,14,15,16 ,17},14->{2},15->{8,9,10,11},16->{8,9,10,11},17->{8,9,10,11},18->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,15) ,(1,17) ,(9,8) ,(11,8) ,(11,11) ,(12,14) ,(14,2) ,(15,8) ,(16,8) ,(17,8) ,(17,11)] * Step 3: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A >= 101 && B = C && D = E && F = G && H = A] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [100 >= A && B = C && D = E && F = G && H = A] (?,1) 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [89 >= A && D = 1 && H = A && F = 101 && B = 91] (?,1) 8. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] (?,1) 9. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] (?,1) 10. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] (?,1) 11. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] (?,1) 12. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] (?,1) 14. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [F = 111 && D = 2 && H = 100 && B = C && A = 100] (?,1) 15. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (?,1) && D >= 3 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 16. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (?,1) && D >= 2 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 17. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] (?,1) 18. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl161,8);(lbl221,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{12,14,16},2->{},8->{2},9->{9,10,11},10->{8,9,10,11},11->{9,10},12->{12,15,16,17},14->{},15->{9 ,10,11},16->{9,10,11},17->{9,10},18->{0,1}] + Applied Processor: FromIts + Details: () * Step 4: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A >= 101 && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [100 >= A && B = C && D = E && F = G && H = A] lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [89 >= A && D = 1 && H = A && F = 101 && B = 91] lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [F = 111 && D = 2 && H = 100 && B = C && A = 100] lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 && D >= 3 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 && D >= 2 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lbl111,8);(lbl161,8);(lbl221,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{12,14,16},2->{},8->{2},9->{9,10,11},10->{8,9,10,11},11->{9,10},12->{12,15,16,17},14->{},15->{9 ,10,11},16->{9,10,11},17->{9,10},18->{0,1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,8,9,10,11,12,14,15,16,17,18] | +- p:[12] c: [12] | `- p:[9,10,11] c: [11] | `- p:[9,10] c: [10] | `- p:[9] c: [9] * Step 5: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A >= 101 && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [100 >= A && B = C && D = E && F = G && H = A] lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [89 >= A && D = 1 && H = A && F = 101 && B = 91] lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [F = 111 && D = 2 && H = 100 && B = C && A = 100] lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 && D >= 3 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 && D >= 2 && 121 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lbl111,8);(lbl161,8);(lbl221,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{12,14,16},2->{},8->{2},9->{9,10,11},10->{8,9,10,11},11->{9,10},12->{12,15,16,17},14->{},15->{9 ,10,11},16->{9,10,11},17->{9,10},18->{0,1}] ,We construct a looptree: P: [0,1,2,8,9,10,11,12,14,15,16,17,18] | +- p:[12] c: [12] | `- p:[9,10,11] c: [11] | `- p:[9,10] c: [10] | `- p:[9] c: [9]) + Applied Processor: CloseWith True + Details: () YES