YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,1,J) [-1*I + J >= 0 (?,1) && I + -1*J >= 0 && G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = E && F = A && G = H && I = J] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,1,J) [-1*I + J >= 0 (?,1) && I + -1*J >= 0 && G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A && G = H && I = J] 2. lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-1 + G,H,I,J) [-1 + F + -1*I >= 0 (?,1) && -1 + A + -1*I >= 0 && -1 + I >= 0 && G + I >= 0 && -2 + -1*G + I >= 0 && -3 + F + I >= 0 && -3 + A + I >= 0 && -3 + F + -1*G >= 0 && -3 + A + -1*G >= 0 && 1 + G >= 0 && -1 + F + G >= 0 && -1 + A + G >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -2 + A >= 0 && G >= 0 && I >= 2 + G && A >= 1 + I && F = A] 3. lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,G,H,1 + I,J) [-1 + F + -1*I >= 0 (?,1) && -1 + A + -1*I >= 0 && -1 + I >= 0 && G + I >= 0 && -2 + -1*G + I >= 0 && -3 + F + I >= 0 && -3 + A + I >= 0 && -3 + F + -1*G >= 0 && -3 + A + -1*G >= 0 && 1 + G >= 0 && -1 + F + G >= 0 && -1 + A + G >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -2 + A >= 0 && I >= 2 + G && A >= 1 + I && F = A] 4. lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-2 + I,H,I,J) [-1 + F + -1*I >= 0 (?,1) && -1 + A + -1*I >= 0 && -1 + I >= 0 && -3 + F + I >= 0 && -3 + A + I >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -2 + A >= 0 && I >= 1 && A >= 1 + I && F = A] 5. lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,-1 + I,H,1 + I,J) [-1 + F + -1*I >= 0 (?,1) && -1 + A + -1*I >= 0 && -1 + I >= 0 && -3 + F + I >= 0 && -3 + A + I >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -2 + A >= 0 && I >= 1 && A >= 1 + I && F = A] 6. lbl13(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [F + -1*I >= 0 (?,1) && 1 + D + -1*I >= 0 && A + -1*I >= 0 && -2 + I >= 0 && -1 + G + I >= 0 && -2 + -1*G + I >= 0 && -4 + F + I >= 0 && -3 + D + I >= 0 && -1 + -1*D + I >= 0 && -4 + A + I >= 0 && -2 + F + -1*G >= 0 && -1 + D + -1*G >= 0 && -2 + A + -1*G >= 0 && 1 + G >= 0 && -1 + F + G >= 0 && D + G >= 0 && -1 + A + G >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -3 + D + F >= 0 && -1 + -1*D + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && -1 + D >= 0 && -3 + A + D >= 0 && -2 + A >= 0 && A + G >= 2 && A >= 2 + G && F = A && I = A && 1 + D = A] 7. lbl13(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,I,J) [F + -1*I >= 0 (?,1) && 1 + D + -1*I >= 0 && A + -1*I >= 0 && -2 + I >= 0 && -1 + G + I >= 0 && -2 + -1*G + I >= 0 && -4 + F + I >= 0 && -3 + D + I >= 0 && -1 + -1*D + I >= 0 && -4 + A + I >= 0 && -2 + F + -1*G >= 0 && -1 + D + -1*G >= 0 && -2 + A + -1*G >= 0 && 1 + G >= 0 && -1 + F + G >= 0 && D + G >= 0 && -1 + A + G >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -3 + D + F >= 0 && -1 + -1*D + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && -1 + D >= 0 && -3 + A + D >= 0 && -2 + A >= 0 && A >= 2 + D && D + G >= 1 && A >= 1 + D && D >= 1 + G && F = A && I = 1 + D] 8. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,A,H,H,J,J) True (1,1) Signature: {(lbl13,10);(lbl31,10);(lbl43,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5},2->{2,3},3->{6,7},4->{2,3},5->{6,7},6->{},7->{4,5},8->{0,1}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,1,J) [-1*I + J >= 0 (1,1) && I + -1*J >= 0 && G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = E && F = A && G = H && I = J] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,1,J) [-1*I + J >= 0 (1,1) && I + -1*J >= 0 && G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A && G = H && I = J] 2. lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-1 + G,H,I,J) [-1 + F + -1*I >= 0 (?,1) && -1 + A + -1*I >= 0 && -1 + I >= 0 && G + I >= 0 && -2 + -1*G + I >= 0 && -3 + F + I >= 0 && -3 + A + I >= 0 && -3 + F + -1*G >= 0 && -3 + A + -1*G >= 0 && 1 + G >= 0 && -1 + F + G >= 0 && -1 + A + G >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -2 + A >= 0 && G >= 0 && I >= 2 + G && A >= 1 + I && F = A] 3. lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,G,H,1 + I,J) [-1 + F + -1*I >= 0 (?,1) && -1 + A + -1*I >= 0 && -1 + I >= 0 && G + I >= 0 && -2 + -1*G + I >= 0 && -3 + F + I >= 0 && -3 + A + I >= 0 && -3 + F + -1*G >= 0 && -3 + A + -1*G >= 0 && 1 + G >= 0 && -1 + F + G >= 0 && -1 + A + G >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -2 + A >= 0 && I >= 2 + G && A >= 1 + I && F = A] 4. lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-2 + I,H,I,J) [-1 + F + -1*I >= 0 (?,1) && -1 + A + -1*I >= 0 && -1 + I >= 0 && -3 + F + I >= 0 && -3 + A + I >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -2 + A >= 0 && I >= 1 && A >= 1 + I && F = A] 5. lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,-1 + I,H,1 + I,J) [-1 + F + -1*I >= 0 (?,1) && -1 + A + -1*I >= 0 && -1 + I >= 0 && -3 + F + I >= 0 && -3 + A + I >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -2 + A >= 0 && I >= 1 && A >= 1 + I && F = A] 6. lbl13(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [F + -1*I >= 0 (1,1) && 1 + D + -1*I >= 0 && A + -1*I >= 0 && -2 + I >= 0 && -1 + G + I >= 0 && -2 + -1*G + I >= 0 && -4 + F + I >= 0 && -3 + D + I >= 0 && -1 + -1*D + I >= 0 && -4 + A + I >= 0 && -2 + F + -1*G >= 0 && -1 + D + -1*G >= 0 && -2 + A + -1*G >= 0 && 1 + G >= 0 && -1 + F + G >= 0 && D + G >= 0 && -1 + A + G >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -3 + D + F >= 0 && -1 + -1*D + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && -1 + D >= 0 && -3 + A + D >= 0 && -2 + A >= 0 && A + G >= 2 && A >= 2 + G && F = A && I = A && 1 + D = A] 7. lbl13(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,I,J) [F + -1*I >= 0 (?,1) && 1 + D + -1*I >= 0 && A + -1*I >= 0 && -2 + I >= 0 && -1 + G + I >= 0 && -2 + -1*G + I >= 0 && -4 + F + I >= 0 && -3 + D + I >= 0 && -1 + -1*D + I >= 0 && -4 + A + I >= 0 && -2 + F + -1*G >= 0 && -1 + D + -1*G >= 0 && -2 + A + -1*G >= 0 && 1 + G >= 0 && -1 + F + G >= 0 && D + G >= 0 && -1 + A + G >= 0 && A + -1*F >= 0 && -2 + F >= 0 && -3 + D + F >= 0 && -1 + -1*D + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && -1 + D >= 0 && -3 + A + D >= 0 && -2 + A >= 0 && A >= 2 + D && D + G >= 1 && A >= 1 + D && D >= 1 + G && F = A && I = 1 + D] 8. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,A,H,H,J,J) True (1,1) Signature: {(lbl13,10);(lbl31,10);(lbl43,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5},2->{2,3},3->{6,7},4->{2,3},5->{6,7},6->{},7->{4,5},8->{0,1}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[4,7,3,2,5] c: [7] | `- p:[2] c: [2] YES