YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = A] 1. start(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = E && F = A] 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && B = 0 && F = A] 3. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && A >= 1 + D && B = 0 && F = A] 4. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && A >= 1 && D >= 1 && B = 0 && F = A] 5. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 && A >= D && A >= 1 + B && D >= 1 && F = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{},3->{4,5},4->{2,3},5->{4,5},6->{0,1}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 (1,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = A] 1. start(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,F,E,F) [A + -1*F >= 0 (1,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = E && F = A] 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 (1,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && B = 0 && F = A] 3. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && A >= 1 + D && B = 0 && F = A] 4. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && A >= 1 && D >= 1 && B = 0 && F = A] 5. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 && A >= D && A >= 1 + B && D >= 1 && F = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{},3->{4,5},4->{2,3},5->{4,5},6->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,4)] * Step 3: Looptree YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 (1,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = A] 1. start(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,F,E,F) [A + -1*F >= 0 (1,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = E && F = A] 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 (1,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && B = 0 && F = A] 3. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && A >= 1 + D && B = 0 && F = A] 4. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && A >= 1 && D >= 1 && B = 0 && F = A] 5. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 && A >= D && A >= 1 + B && D >= 1 && F = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{},3->{5},4->{2,3},5->{4,5},6->{0,1}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[4,5,3] c: [4] | `- p:[5] c: [5] YES