YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = G && H = A] 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 4. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{},3->{3,4,5},4->{6,7},5->{6,7},6->{2},7->{3,4,5},8->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(4,6),(7,5)] * Step 2: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = G && H = A] 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 4. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4},2->{},3->{3,4,5},4->{7},5->{6,7},6->{2},7->{3,4},8->{0,1}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = G && H = A] lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{3,4},2->{},3->{3,4,5},4->{7},5->{6,7},6->{2},7->{3,4},8->{0,1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[3,7,4,5] c: [4,5,7] | `- p:[3] c: [3] * Step 4: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = G && H = A] lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{3,4},2->{},3->{3,4,5},4->{7},5->{6,7},6->{2},7->{3,4},8->{0,1}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[3,7,4,5] c: [4,5,7] | `- p:[3] c: [3]) + Applied Processor: CloseWith True + Details: () YES