YES * Step 1: 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*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) -> lbl52(A,-1 + 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 && A >= 1 && C >= 1 && B = C && D = E && F = A] 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + 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 && 0 >= C && B = C && D = E && F = A] 3. lbl52(A,B,C,D,E,F) -> lbl52(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 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && B >= 1 && A >= D && F = A] 4. lbl52(A,B,C,D,E,F) -> lbl72(A,F,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 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= D && B = 0 && F = A] 5. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B + -1*F >= 0 (?,1) && A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && F = A && B = A] 6. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [B + -1*F >= 0 (?,1) && A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= 1 && A >= 1 + D && F = A && B = A] 7. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4},2->{5,6},3->{3,4},4->{5,6},5->{},6->{3,4},7->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(6,4)] * Step 2: FromIts 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) -> lbl52(A,-1 + 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 && A >= 1 && C >= 1 && B = C && D = E && F = A] 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + 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 && 0 >= C && B = C && D = E && F = A] 3. lbl52(A,B,C,D,E,F) -> lbl52(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 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && B >= 1 && A >= D && F = A] 4. lbl52(A,B,C,D,E,F) -> lbl72(A,F,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 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= D && B = 0 && F = A] 5. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B + -1*F >= 0 (?,1) && A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && F = A && B = A] 6. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [B + -1*F >= 0 (?,1) && A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= 1 && A >= 1 + D && F = A && B = A] 7. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4},2->{5,6},3->{3,4},4->{5,6},5->{},6->{3},7->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 && -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] start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [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 >= 1 && C >= 1 && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [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 >= 1 && 0 >= C && B = C && D = E && F = A] lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -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 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && B >= 1 && A >= D && F = A] lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -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 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= D && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B + -1*F >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && F = A && B = A] lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [B + -1*F >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= 1 && A >= 1 + D && F = A && B = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{3,4},2->{5,6},3->{3,4},4->{5,6},5->{},6->{3},7->{0,1,2}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[3,6,4] c: [4,6] | `- p:[3] c: [3] * Step 4: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 && -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] start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [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 >= 1 && C >= 1 && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [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 >= 1 && 0 >= C && B = C && D = E && F = A] lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -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 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && B >= 1 && A >= D && F = A] lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -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 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= D && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B + -1*F >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && F = A && B = A] lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [B + -1*F >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= 1 && A >= 1 + D && F = A && B = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{3,4},2->{5,6},3->{3,4},4->{5,6},5->{},6->{3},7->{0,1,2}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[3,6,4] c: [4,6] | `- p:[3] c: [3]) + Applied Processor: CloseWith True + Details: () YES