YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 0 && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] 3. start(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && H >= C && A >= 0 && B = C && D = A && E = F && G = H] 4. lbl72(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1*E + H >= 0 && 1 + -1*B + H >= 0 && -1*E + G >= 0 && 1 + -1*B + G >= 0 && -1 + B + -1*E >= 0 && 1 + -1*B + E >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && A >= 1 + D && 1 + H >= B && 1 + E = B && G = H] 5. lbl72(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,D,B,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1*E + H >= 0 && 1 + -1*B + H >= 0 && -1*E + G >= 0 && 1 + -1*B + G >= 0 && -1 + B + -1*E >= 0 && 1 + -1*B + E >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && H >= B && A >= 1 + D && 1 + H >= B && 1 + E = B && G = H] 6. lbl42(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && A + -1*D >= 0 && D >= 0 && 1 + B + D >= 0 && A + D >= 0 && 1 + B >= 0 && 1 + A + B >= 0 && A >= 0 && B >= 0 && A >= D && G = H] 7. lbl42(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && A + -1*D >= 0 && D >= 0 && 1 + B + D >= 0 && A + D >= 0 && 1 + B >= 0 && 1 + A + B >= 0 && A >= 0 && A >= D && G = H] 8. lbl42(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && A + -1*D >= 0 && D >= 0 && 1 + B + D >= 0 && A + D >= 0 && 1 + B >= 0 && 1 + A + B >= 0 && A >= 0 && H >= B && A >= D && G = H] 9. cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && 1 + D = 0 && G = H] 10. cut(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && D >= 0 && B >= 0 && A >= 1 + D && G = H] 11. cut(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && D >= 0 && A >= 1 + D && G = H] 12. cut(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && H >= B && D >= 0 && A >= 1 + D && G = H] 13. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(cut,8);(lbl42,8);(lbl72,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{6,7,8},2->{9,10,11,12},3->{4,5},4->{9,10,11,12},5->{4,5},6->{6,7,8},7->{9,10,11,12},8->{4,5} ,9->{},10->{6,7,8},11->{9,10,11,12},12->{4,5},13->{0,1,2,3}] + 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) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (1,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [G + -1*H >= 0 (1,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 0 && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [G + -1*H >= 0 (1,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] 3. start(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [G + -1*H >= 0 (1,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && H >= C && A >= 0 && B = C && D = A && E = F && G = H] 4. lbl72(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1*E + H >= 0 && 1 + -1*B + H >= 0 && -1*E + G >= 0 && 1 + -1*B + G >= 0 && -1 + B + -1*E >= 0 && 1 + -1*B + E >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && A >= 1 + D && 1 + H >= B && 1 + E = B && G = H] 5. lbl72(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,D,B,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1*E + H >= 0 && 1 + -1*B + H >= 0 && -1*E + G >= 0 && 1 + -1*B + G >= 0 && -1 + B + -1*E >= 0 && 1 + -1*B + E >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && H >= B && A >= 1 + D && 1 + H >= B && 1 + E = B && G = H] 6. lbl42(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && A + -1*D >= 0 && D >= 0 && 1 + B + D >= 0 && A + D >= 0 && 1 + B >= 0 && 1 + A + B >= 0 && A >= 0 && B >= 0 && A >= D && G = H] 7. lbl42(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && A + -1*D >= 0 && D >= 0 && 1 + B + D >= 0 && A + D >= 0 && 1 + B >= 0 && 1 + A + B >= 0 && A >= 0 && A >= D && G = H] 8. lbl42(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && A + -1*D >= 0 && D >= 0 && 1 + B + D >= 0 && A + D >= 0 && 1 + B >= 0 && 1 + A + B >= 0 && A >= 0 && H >= B && A >= D && G = H] 9. cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (1,1) && -1*G + H >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && 1 + D = 0 && G = H] 10. cut(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && D >= 0 && B >= 0 && A >= 1 + D && G = H] 11. cut(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && D >= 0 && A >= 1 + D && G = H] 12. cut(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && 1 + A + D >= 0 && A >= 0 && H >= B && D >= 0 && A >= 1 + D && G = H] 13. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(cut,8);(lbl42,8);(lbl72,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{6,7,8},2->{9,10,11,12},3->{4,5},4->{9,10,11,12},5->{4,5},6->{6,7,8},7->{9,10,11,12},8->{4,5} ,9->{},10->{6,7,8},11->{9,10,11,12},12->{4,5},13->{0,1,2,3}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[6,10,4,5,8,12,7,11] c: [12] | `- p:[4,5,8,6,10,7,11] c: [11] | `- p:[4,5,8,6,10,7] c: [10] | +- p:[6] c: [6] | `- p:[5] c: [5] YES