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) [0 >= 1 + A && B = C && D = A && E = F && G = H] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,2*D,F,-1 + 2*D,H) [A >= 0 && B = C && D = A && E = F && G = H] (?,1) 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,2*D,C,D,-1 + 2*D,F,-1 + 2*D,H) [A >= 0 && B = C && D = A && E = F && G = H] (?,1) 3. lbl82(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E >= A && 2*A >= E && D = A && 1 + G = A] (?,1) 4. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] (?,1) 5. lbl82(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] (?,1) 6. lbl121(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 1 + E && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] (?,1) 7. lbl121(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] (?,1) 8. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] (?,1) 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(lbl121,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{6,7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(5,6)] * 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) [0 >= 1 + A && B = C && D = A && E = F && G = H] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,2*D,F,-1 + 2*D,H) [A >= 0 && B = C && D = A && E = F && G = H] (?,1) 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,2*D,C,D,-1 + 2*D,F,-1 + 2*D,H) [A >= 0 && B = C && D = A && E = F && G = H] (?,1) 3. lbl82(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E >= A && 2*A >= E && D = A && 1 + G = A] (?,1) 4. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] (?,1) 5. lbl82(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] (?,1) 6. lbl121(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 1 + E && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] (?,1) 7. lbl121(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] (?,1) 8. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] (?,1) 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(lbl121,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + 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) [0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,2*D,F,-1 + 2*D,H) [A >= 0 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl121(A,2*D,C,D,-1 + 2*D,F,-1 + 2*D,H) [A >= 0 && B = C && D = A && E = F && G = H] lbl82(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E >= A && 2*A >= E && D = A && 1 + G = A] lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl82(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl121(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 1 + E && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True Signature: {(lbl121,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[4,7,5,8] c: [8] | `- p:[4,7,5] c: [5,7] | `- p:[4] c: [4] * 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) [0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,2*D,F,-1 + 2*D,H) [A >= 0 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl121(A,2*D,C,D,-1 + 2*D,F,-1 + 2*D,H) [A >= 0 && B = C && D = A && E = F && G = H] lbl82(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E >= A && 2*A >= E && D = A && 1 + G = A] lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl82(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl121(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 1 + E && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True Signature: {(lbl121,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[4,7,5,8] c: [8] | `- p:[4,7,5] c: [5,7] | `- p:[4] c: [4]) + Applied Processor: CloseWith True + Details: () YES