YES * Step 1: 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 && A >= 101 && B = C && D = E && F = G && H = A] 1. 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 && G >= 1 + E && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [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 && E >= G && 100 >= A && B = C && D = E && F = G && H = A] 3. lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 (?,1) && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && A + E + G >= 102 + B + D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] 4. lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 (?,1) && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && B >= D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] 5. lbl71(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [E + -1*H >= 0 (?,1) && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && D >= 1 + B && 101 + B + D >= A + E + G && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] 6. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl71,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{},2->{3,4,5},3->{},4->{},5->{3,4,5},6->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 2: 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 && A >= 101 && B = C && D = E && F = G && H = A] 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 && G >= 1 + E && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [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 && E >= G && 100 >= A && B = C && D = E && F = G && H = A] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && A + E + G >= 102 + B + D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && B >= D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && D >= 1 + B && 101 + B + D >= A + E + G && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lbl71,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{},2->{3,4,5},3->{},4->{},5->{3,4,5},6->{0,1,2}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[5] c: [5] * Step 3: 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 && A >= 101 && B = C && D = E && F = G && H = A] 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 && G >= 1 + E && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [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 && E >= G && 100 >= A && B = C && D = E && F = G && H = A] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && A + E + G >= 102 + B + D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && B >= D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && D >= 1 + B && 101 + B + D >= A + E + G && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lbl71,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{},2->{3,4,5},3->{},4->{},5->{3,4,5},6->{0,1,2}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[5] c: [5]) + Applied Processor: CloseWith True + Details: () YES