YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] 1. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 3. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] 4. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 5. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) Signature: {(lbl101,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{3,4,5},3->{},4->{3,4,5},5->{3,4,5},6->{0,1,2}] + 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) -> stop(A,B,C,D,E,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] 1. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 3. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 (1,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] 4. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 5. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) Signature: {(lbl101,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{3,4,5},3->{},4->{3,4,5},5->{3,4,5},6->{0,1,2}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[4,5] c: [5] | `- p:[4] c: [4] YES