YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*H >= 0 (?,1) && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] 3. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] 4. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 5. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 6. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] 7. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 8. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] 9. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 10. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 11. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] 12. 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->{7,8,9,10,11},2->{},3->{2},4->{3,4,5,6},5->{3,4,5,6},6->{3,4,5,6},7->{7,8,9,10,11},8->{2},9->{3 ,4,5,6},10->{3,4,5,6},11->{3,4,5,6},12->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,9) ,(1,11) ,(4,3) ,(6,3) ,(6,6) ,(7,8) ,(8,2) ,(9,3) ,(10,3) ,(11,3) ,(11,6)] * Step 2: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*H >= 0 (?,1) && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] 3. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] 4. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 5. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 6. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] 7. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 8. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] 9. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 10. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 11. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] 12. 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->{7,8,10},2->{},3->{2},4->{4,5,6},5->{3,4,5,6},6->{4,5},7->{7,9,10,11},8->{},9->{4,5,6},10->{4,5 ,6},11->{4,5},12->{0,1}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*H >= 0 (1,1) && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] 3. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 (1,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] 4. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 5. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 6. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] 7. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 (?,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 8. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] 9. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 10. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 11. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] 12. 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->{7,8,10},2->{},3->{2},4->{4,5,6},5->{3,4,5,6},6->{4,5},7->{7,9,10,11},8->{},9->{4,5,6},10->{4,5 ,6},11->{4,5},12->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl111) = 5310 + -41*x1 + -1*x4 + -12*x8 p(lbl161) = 107 + -41*x1 + 81*x4 + 39*x8 p(lbl221) = 1035 + 6*x1 + 81*x4 + -9*x6 + -8*x8 p(start) = 5708 + x1 + -58*x8 p(start0) = 5708 + -57*x1 p(stop) = 5607 + x1 + -2*x2 + 81*x4 + -64*x6 + 8*x8 Following rules are strictly oriented: [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 5310 + -41*A + -1*D + -12*H > 5309 + -41*A + -1*D + -12*H = lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] lbl111(A,B,C,D,E,F,G,H) = 5310 + -41*A + -1*D + -12*H > 26 + -41*A + 81*D + 39*H = lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 5310 + -41*A + -1*D + -12*H > 1026 + 6*A + 81*D + -9*F + -8*H = lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 5310 + -41*A + -1*D + -12*H > 1026 + 6*A + 81*D + -9*F + -8*H = lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] lbl111(A,B,C,D,E,F,G,H) = 5310 + -41*A + -1*D + -12*H > 1035 + 6*A + 81*D + -9*F + -8*H = lbl221(A,B,C,-1 + D,E,-9 + F,G,H) Following rules are weakly oriented: [A + -1*H >= 0 ==> && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) = 5708 + A + -58*H >= 5708 + A + -58*H = stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 ==> && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) = 5708 + A + -58*H >= 5308 + -41*A + -12*H = lbl111(A,B,C,2,E,11 + H,G,H) [100 + -1*H >= 0 ==> && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] lbl161(A,B,C,D,E,F,G,H) = 107 + -41*A + 81*D + 39*H >= 5607 + A + -2*B + 81*D + -64*F + 8*H = stop(A,B,C,D,E,F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) = 1035 + 6*A + 81*D + -9*F + -8*H >= 26 + -41*A + 81*D + 39*H = lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 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) = 1035 + 6*A + 81*D + -9*F + -8*H >= 1026 + 6*A + 81*D + -9*F + -8*H = lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 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) = 1035 + 6*A + 81*D + -9*F + -8*H >= 1026 + 6*A + 81*D + -9*F + -8*H = lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) = 1035 + 6*A + 81*D + -9*F + -8*H >= 1035 + 6*A + 81*D + -9*F + -8*H = lbl221(A,B,C,-1 + D,E,-9 + F,G,H) True ==> start0(A,B,C,D,E,F,G,H) = 5708 + -57*A >= 5708 + -57*A = start(A,C,C,E,E,G,G,A) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*H >= 0 (1,1) && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] 3. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 (1,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] 4. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 5. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 6. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] 7. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 (5708 + 57*A,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 8. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] 9. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 10. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 11. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] 12. 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->{7,8,10},2->{},3->{2},4->{4,5,6},5->{3,4,5,6},6->{4,5},7->{7,9,10,11},8->{},9->{4,5,6},10->{4,5 ,6},11->{4,5},12->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl111) = 7899 + -68*x1 + -11*x8 p(lbl161) = 90 + -68*x1 + 9*x4 + 67*x8 p(lbl221) = 192 + -1*x1 + 9*x4 + -1*x6 p(start) = 8399 + x1 + -85*x8 p(start0) = 8399 + -84*x1 p(stop) = 7610 + x1 + -78*x2 + 9*x4 + -5*x6 + -2*x8 Following rules are strictly oriented: [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 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) = 192 + -1*A + 9*D + -1*F > 191 + -1*A + 9*D + -1*F = lbl221(A,B,C,D,E,1 + F,G,H) Following rules are weakly oriented: [A + -1*H >= 0 ==> && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) = 8399 + A + -85*H >= 8399 + A + -85*H = stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 ==> && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) = 8399 + A + -85*H >= 7899 + -68*A + -11*H = lbl111(A,B,C,2,E,11 + H,G,H) [100 + -1*H >= 0 ==> && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] lbl161(A,B,C,D,E,F,G,H) = 90 + -68*A + 9*D + 67*H >= 7610 + A + -78*B + 9*D + -5*F + -2*H = stop(A,B,C,D,E,F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) = 192 + -1*A + 9*D + -1*F >= 81 + -68*A + 9*D + 67*H = lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 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) = 192 + -1*A + 9*D + -1*F >= 191 + -1*A + 9*D + -1*F = lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) = 192 + -1*A + 9*D + -1*F >= 192 + -1*A + 9*D + -1*F = lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 7899 + -68*A + -11*H >= 7899 + -68*A + -11*H = lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] lbl111(A,B,C,D,E,F,G,H) = 7899 + -68*A + -11*H >= 81 + -68*A + 9*D + 67*H = lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 7899 + -68*A + -11*H >= 191 + -1*A + 9*D + -1*F = lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 7899 + -68*A + -11*H >= 191 + -1*A + 9*D + -1*F = lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] lbl111(A,B,C,D,E,F,G,H) = 7899 + -68*A + -11*H >= 192 + -1*A + 9*D + -1*F = lbl221(A,B,C,-1 + D,E,-9 + F,G,H) True ==> start0(A,B,C,D,E,F,G,H) = 8399 + -84*A >= 8399 + -84*A = start(A,C,C,E,E,G,G,A) * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*H >= 0 (1,1) && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] 3. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 (1,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] 4. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 5. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (8399 + 84*A,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 6. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] 7. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 (5708 + 57*A,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 8. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] 9. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 10. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 11. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] 12. 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->{7,8,10},2->{},3->{2},4->{4,5,6},5->{3,4,5,6},6->{4,5},7->{7,9,10,11},8->{},9->{4,5,6},10->{4,5 ,6},11->{4,5},12->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl111) = 1654 + -16*x1 + -27*x4 p(lbl161) = 870 + -16*x1 + x4 + 7*x8 p(lbl221) = 870 + -9*x1 + x4 p(start) = 1600 + x1 + -17*x8 p(start0) = 1600 + -16*x1 p(stop) = 1406 + x1 + -19*x2 + x4 + -7*x6 + 9*x8 Following rules are strictly oriented: [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) = 870 + -9*A + D > 869 + -9*A + D = lbl221(A,B,C,-1 + D,E,-9 + F,G,H) Following rules are weakly oriented: [A + -1*H >= 0 ==> && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) = 1600 + A + -17*H >= 1597 + A + -17*H = stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 ==> && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) = 1600 + A + -17*H >= 1600 + -16*A = lbl111(A,B,C,2,E,11 + H,G,H) [100 + -1*H >= 0 ==> && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] lbl161(A,B,C,D,E,F,G,H) = 870 + -16*A + D + 7*H >= 1406 + A + -19*B + D + -7*F + 9*H = stop(A,B,C,D,E,F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) = 870 + -9*A + D >= 869 + -16*A + D + 7*H = lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 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) = 870 + -9*A + D >= 870 + -9*A + D = lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 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) = 870 + -9*A + D >= 870 + -9*A + D = lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 1654 + -16*A + -27*D >= 1627 + -16*A + -27*D = lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] lbl111(A,B,C,D,E,F,G,H) = 1654 + -16*A + -27*D >= 869 + -16*A + D + 7*H = lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 1654 + -16*A + -27*D >= 870 + -9*A + D = lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 1654 + -16*A + -27*D >= 870 + -9*A + D = lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] lbl111(A,B,C,D,E,F,G,H) = 1654 + -16*A + -27*D >= 869 + -9*A + D = lbl221(A,B,C,-1 + D,E,-9 + F,G,H) True ==> start0(A,B,C,D,E,F,G,H) = 1600 + -16*A >= 1600 + -16*A = start(A,C,C,E,E,G,G,A) * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*H >= 0 (1,1) && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] 3. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 (1,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] 4. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (?,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 5. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (8399 + 84*A,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 6. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [99 + -1*H >= 0 (1600 + 16*A,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] 7. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 (5708 + 57*A,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 8. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] 9. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 10. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 11. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] 12. 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->{7,8,10},2->{},3->{2},4->{4,5,6},5->{3,4,5,6},6->{4,5},7->{7,9,10,11},8->{},9->{4,5,6},10->{4,5 ,6},11->{4,5},12->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl111) = 516 + -5*x1 + -4*x4 p(lbl161) = -9 + -5*x1 + 9*x4 + 5*x8 p(lbl221) = 93 + 9*x4 + -1*x6 p(start) = 909 + x1 + -10*x8 p(start0) = 909 + -9*x1 p(stop) = 909 + x1 + -9*x6 + -1*x8 Following rules are strictly oriented: [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 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) = 93 + 9*D + -1*F > 92 + 9*D + -1*F = lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 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) = 93 + 9*D + -1*F > 92 + 9*D + -1*F = lbl221(A,B,C,D,E,1 + F,G,H) Following rules are weakly oriented: [A + -1*H >= 0 ==> && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) = 909 + A + -10*H >= 909 + A + -10*H = stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 ==> && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) = 909 + A + -10*H >= 508 + -5*A = lbl111(A,B,C,2,E,11 + H,G,H) [100 + -1*H >= 0 ==> && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] lbl161(A,B,C,D,E,F,G,H) = -9 + -5*A + 9*D + 5*H >= 909 + A + -9*F + -1*H = stop(A,B,C,D,E,F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) = 93 + 9*D + -1*F >= -18 + -5*A + 9*D + 5*H = lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 ==> && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] lbl221(A,B,C,D,E,F,G,H) = 93 + 9*D + -1*F >= 93 + 9*D + -1*F = lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 516 + -5*A + -4*D >= 512 + -5*A + -4*D = lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] lbl111(A,B,C,D,E,F,G,H) = 516 + -5*A + -4*D >= -18 + -5*A + 9*D + 5*H = lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 516 + -5*A + -4*D >= 92 + 9*D + -1*F = lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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) = 516 + -5*A + -4*D >= 92 + 9*D + -1*F = lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 ==> && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] lbl111(A,B,C,D,E,F,G,H) = 516 + -5*A + -4*D >= 93 + 9*D + -1*F = lbl221(A,B,C,-1 + D,E,-9 + F,G,H) True ==> start0(A,B,C,D,E,F,G,H) = 909 + -9*A >= 909 + -9*A = start(A,C,C,E,E,G,G,A) * Step 7: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,-10 + H,C,1,E,H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,2,E,11 + H,G,H) [A + -1*H >= 0 (1,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 >= A && B = C && D = E && F = G && H = A] 2. lbl161(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*H >= 0 (1,1) && -1 + F + -1*H >= 0 && 201 + -1*F + -1*H >= 0 && 99 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && 9 + B + -1*H >= 0 && 191 + -1*B + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && 101 + -1*F >= 0 && 100 + D + -1*F >= 0 && 102 + -1*D + -1*F >= 0 && 10 + B + -1*F >= 0 && 192 + -1*B + -1*F >= 0 && 201 + -1*A + -1*F >= 0 && -101 + F >= 0 && -102 + D + F >= 0 && -100 + -1*D + F >= 0 && -192 + B + F >= 0 && -10 + -1*B + F >= 0 && -1 + -1*A + F >= 0 && 1 + -1*D >= 0 && -90 + B + -1*D >= 0 && 92 + -1*B + -1*D >= 0 && 101 + -1*A + -1*D >= 0 && -1 + D >= 0 && -92 + B + D >= 0 && 90 + -1*B + D >= 0 && 99 + -1*A + D >= 0 && 91 + -1*B >= 0 && 191 + -1*A + -1*B >= 0 && -91 + B >= 0 && 9 + -1*A + B >= 0 && 100 + -1*A >= 0 && 89 >= A && D = 1 && H = A && F = 101 && B = 91] 3. lbl221(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [99 + -1*H >= 0 (1,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && 99 >= A && 89 >= A && F = 111 && D = 2 && H = A && B = C] 4. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (909 + 9*A,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 5. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [99 + -1*H >= 0 (8399 + 84*A,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 2 && 110 >= F && F >= 102 && 111 >= F && 10 + F >= A + 11*D && 89 >= A && H = A && B = C] 6. lbl221(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [99 + -1*H >= 0 (1600 + 16*A,1) && -12 + F + -1*H >= 0 && 97 + D + -1*H >= 0 && 101 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 198 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -12 + -1*A + F >= 0 && 101 + -1*A + -1*D >= 0 && -2 + D >= 0 && 97 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 99 + -1*A >= 0 && D >= 3 && D >= 2 && 121 >= A + 11*D && 89 >= A && F = 111 && H = A && B = C] 7. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,1 + D,E,11 + F,G,H) [100 + -1*H >= 0 (5708 + 57*A,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 111 >= A + 11*D && 122 >= A + 11*D && 11*D >= 22 && H = A && B = C && 11 + F = A + 11*D] 8. lbl111(A,B,C,D,E,F,G,H) -> lbl161(A,-20 + F,C,-1 + D,E,-10 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && F = 111 && D = 2 && H = 100 && B = C && A = 100] 9. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 10. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,D,E,1 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && 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] 11. lbl111(A,B,C,D,E,F,G,H) -> lbl221(A,B,C,-1 + D,E,-9 + F,G,H) [100 + -1*H >= 0 (1,1) && -11 + F + -1*H >= 0 && 98 + D + -1*H >= 0 && 102 + -1*D + -1*H >= 0 && A + -1*H >= 0 && 200 + -1*A + -1*H >= 0 && -1*A + H >= 0 && -11 + -1*A + F >= 0 && 102 + -1*A + -1*D >= 0 && -2 + D >= 0 && 98 + -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 100 + -1*A >= 0 && D >= 3 && 11*D >= 22 && F = 111 && 11*D + H = 122 && B = C && A + 11*D = 122] 12. 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->{7,8,10},2->{},3->{2},4->{4,5,6},5->{3,4,5,6},6->{4,5},7->{7,9,10,11},8->{},9->{4,5,6},10->{4,5 ,6},11->{4,5},12->{0,1}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))