YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatRules WORST_CASE(?,POLY) + 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) 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] (1,1) 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] (1,1) 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] (1,1) 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] (1,1) 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] (1,1) 15. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (1,1) && 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 (1,1) && 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] (1,1) 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] * Step 3: UnsatPaths WORST_CASE(?,POLY) + 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) 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] (1,1) 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] (1,1) 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] (1,1) 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] (1,1) 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] (1,1) 15. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (1,1) && 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 (1,1) && 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] (1,1) 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->{},7->{},8->{2},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},15->{7,8,9,10,11},16->{7,8,9,10,11},17->{7,8,9,10,11},18->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,13) ,(1,15) ,(1,17) ,(9,7) ,(9,8) ,(10,7) ,(11,7) ,(11,8) ,(11,11) ,(12,13) ,(12,14) ,(14,2) ,(15,7) ,(15,8) ,(16,7) ,(16,8) ,(17,7) ,(17,8) ,(17,11)] * Step 4: UnreachableRules WORST_CASE(?,POLY) + 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) 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] (1,1) 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] (1,1) 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] (1,1) 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] (1,1) 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] (1,1) 15. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (1,1) && 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 (1,1) && 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] (1,1) 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->{},7->{},8->{2},9->{9,10,11},10->{8,9,10,11},11->{9,10},12->{12,15,16,17},13->{} ,14->{},15->{9,10,11},16->{9,10,11},17->{9,10},18->{0,1}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [7,13] * Step 5: AddSinks WORST_CASE(?,POLY) + 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) 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] (1,1) 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] (1,1) 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] (1,1) 15. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [A + 11*D >= 112 (1,1) && 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 (1,1) && 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] (1,1) 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: AddSinks + Details: () * Step 6: UnsatPaths WORST_CASE(?,POLY) + 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) 19. lbl111(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 20. lbl161(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 21. start(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(lbl111,8);(lbl161,8);(lbl221,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{12,14,15,16,17,19},2->{},8->{2,20},9->{8,9,10,11},10->{8,9,10,11},11->{8,9,10,11},12->{12,14,15 ,16,17,19},14->{2,20},15->{8,9,10,11},16->{8,9,10,11},17->{8,9,10,11},18->{0,1,21},19->{},20->{},21->{}] + 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 7: LooptreeTransformer WORST_CASE(?,POLY) + 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) 19. lbl111(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 20. lbl161(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 21. start(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(lbl111,8);(lbl161,8);(lbl221,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{12,14,16,19},2->{},8->{2,20},9->{9,10,11},10->{8,9,10,11},11->{9,10},12->{12,15,16,17,19} ,14->{20},15->{9,10,11},16->{9,10,11},17->{9,10},18->{0,1,21},19->{},20->{},21->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,8,9,10,11,12,14,15,16,17,18,19,20,21] | +- p:[12] c: [12] | `- p:[9,10,11] c: [11] | `- p:[9,10] c: [10] | `- p:[9] c: [9] * Step 8: SizeAbstraction WORST_CASE(?,POLY) + 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) 19. lbl111(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 20. lbl161(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 21. start(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(lbl111,8);(lbl161,8);(lbl221,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{12,14,16,19},2->{},8->{2,20},9->{9,10,11},10->{8,9,10,11},11->{9,10},12->{12,15,16,17,19} ,14->{20},15->{9,10,11},16->{9,10,11},17->{9,10},18->{0,1,21},19->{},20->{},21->{}] ,We construct a looptree: P: [0,1,2,8,9,10,11,12,14,15,16,17,18,19,20,21] | +- p:[12] c: [12] | `- p:[9,10,11] c: [11] | `- p:[9,10] c: [10] | `- p:[9] c: [9]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 9: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,0.0,0.1,0.1.0,0.1.0.0] start ~> stop [A <= A, B <= H, C <= C, D <= K, E <= E, F <= H, G <= G, H <= H] start ~> lbl111 [A <= A, B <= B, C <= C, D <= 2*K, E <= E, F <= 11*K + H, G <= G, H <= H] lbl161 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl221 ~> lbl161 [A <= A, B <= 91*K, C <= C, D <= K, E <= E, F <= 101*K, G <= G, H <= H] lbl221 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 111*K, G <= G, H <= H] lbl221 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 111*K, G <= G, H <= H] lbl221 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 102*K, G <= G, H <= H] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= 11*K + F, G <= G, H <= H] lbl111 ~> lbl161 [A <= A, B <= 91*K, C <= C, D <= K, E <= E, F <= 101*K, G <= G, H <= H] lbl111 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 111*K, G <= G, H <= H] lbl111 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 111*K, G <= G, H <= H] lbl111 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 102*K, G <= G, H <= H] start0 ~> start [A <= A, B <= C, C <= C, D <= E, E <= E, F <= G, G <= G, H <= A] lbl111 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl161 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] start ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Loop: [0.0 <= 123*K + A + 11*D] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= K + D, E <= E, F <= 11*K + F, G <= G, H <= H] + Loop: [0.1 <= D] lbl221 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 111*K, G <= G, H <= H] lbl221 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 111*K, G <= G, H <= H] lbl221 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 102*K, G <= G, H <= H] + Loop: [0.1.0 <= 111*K + F] lbl221 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 111*K, G <= G, H <= H] lbl221 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 111*K, G <= G, H <= H] + Loop: [0.1.0.0 <= 112*K + F] lbl221 ~> lbl221 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 111*K, G <= G, H <= H] + Applied Processor: FlowAbstraction + Details: () * Step 10: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,0.0,0.1,0.1.0,0.1.0.0] start ~> stop [H ~=> B,H ~=> F,K ~=> D] start ~> lbl111 [K ~=> D,H ~+> F,K ~*> F] lbl161 ~> stop [] lbl221 ~> lbl161 [K ~=> B,K ~=> D,K ~=> F] lbl221 ~> lbl221 [K ~=> F] lbl221 ~> lbl221 [K ~=> F] lbl221 ~> lbl221 [K ~=> F] lbl111 ~> lbl111 [D ~+> D,F ~+> F,K ~+> D,K ~*> F] lbl111 ~> lbl161 [K ~=> B,K ~=> D,K ~=> F] lbl111 ~> lbl221 [K ~=> F] lbl111 ~> lbl221 [K ~=> F] lbl111 ~> lbl221 [K ~=> F] start0 ~> start [A ~=> H,C ~=> B,E ~=> D,G ~=> F] lbl111 ~> exitus616 [] lbl161 ~> exitus616 [] start ~> exitus616 [] + Loop: [A ~+> 0.0,D ~*> 0.0,K ~*> 0.0] lbl111 ~> lbl111 [D ~+> D,F ~+> F,K ~+> D,K ~*> F] + Loop: [D ~=> 0.1] lbl221 ~> lbl221 [K ~=> F] lbl221 ~> lbl221 [K ~=> F] lbl221 ~> lbl221 [K ~=> F] + Loop: [F ~+> 0.1.0,K ~*> 0.1.0] lbl221 ~> lbl221 [K ~=> F] lbl221 ~> lbl221 [K ~=> F] + Loop: [F ~+> 0.1.0.0,K ~*> 0.1.0.0] lbl221 ~> lbl221 [K ~=> F] + Applied Processor: LareProcessor + Details: start0 ~> stop [A ~=> B ,A ~=> F ,A ~=> H ,K ~=> B ,K ~=> D ,K ~=> F ,K ~=> 0.1 ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,A ~*> 0.1 ,A ~*> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick] start0 ~> exitus616 [A ~=> H ,C ~=> B ,E ~=> D ,G ~=> F ,K ~=> B ,K ~=> D ,K ~=> F ,K ~=> 0.1 ,A ~+> F ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,A ~*> D ,A ~*> F ,A ~*> 0.1 ,A ~*> tick ,K ~*> D ,K ~*> F ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick] + lbl111> [A ~+> 0.0 ,A ~+> tick ,D ~+> D ,F ~+> F ,tick ~+> tick ,K ~+> D ,A ~*> D ,A ~*> F ,D ~*> D ,D ~*> F ,D ~*> 0.0 ,D ~*> tick ,K ~*> D ,K ~*> F ,K ~*> 0.0 ,K ~*> tick] + lbl221> [D ~=> 0.1 ,K ~=> F ,D ~+> tick ,F ~+> 0.1.0 ,F ~+> 0.1.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,D ~*> tick ,F ~*> tick ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick] + lbl221> [K ~=> F ,F ~+> 0.1.0 ,F ~+> 0.1.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.1.0.0 ,K ~+> tick ,F ~*> tick ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick] + lbl221> [K ~=> F,F ~+> 0.1.0.0,F ~+> tick,tick ~+> tick,K ~*> 0.1.0.0,K ~*> tick] YES(?,POLY)