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,D,H) [0 >= 1 + A && B = C && D = A && E = F && G = H] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + D,H) [D = 0 && B = C && A = 0 && E = F && G = H] (?,1) 2. start(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,D,H) [A >= 1 && B = C && D = A && E = F && G = H] (?,1) 3. start(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,D,H) [A >= 1 && B = C && D = A && E = F && G = H] (?,1) 4. lbl142(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 0 && 1 + G = 0 && E = 0 && D = A] (?,1) 5. lbl142(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + G,H) [A >= 1 && G = 0 && E = 1 && D = A] (?,1) 6. lbl142(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,G,H) [E >= 2 && E >= 0 && A >= E && 1 + G = E && D = A] (?,1) 7. lbl142(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,G,H) [E >= 2 && E >= 0 && A >= E && 1 + G = E && D = A] (?,1) 8. lbl131(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,E,F,-1 + G,H) [G >= 1 && A >= G && E = G && D = A] (?,1) 9. lbl131(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,E,F,G,H) [G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] (?,1) 10. lbl131(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] (?,1) 11. lbl91(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [E >= 0 && G >= 1 + E && A >= G && D = A] (?,1) 12. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(lbl131,8);(lbl142,8);(lbl91,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{4,5,6,7},2->{11},3->{8,9,10},4->{},5->{4,5,6,7},6->{11},7->{8,9,10},8->{4,5,6,7},9->{11},10->{8 ,9,10},11->{8,9,10},12->{0,1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(1,6),(1,7),(5,5),(5,6),(5,7),(8,4)] * Step 2: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,D,H) [0 >= 1 + A && B = C && D = A && E = F && G = H] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + D,H) [D = 0 && B = C && A = 0 && E = F && G = H] (?,1) 2. start(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,D,H) [A >= 1 && B = C && D = A && E = F && G = H] (?,1) 3. start(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,D,H) [A >= 1 && B = C && D = A && E = F && G = H] (?,1) 4. lbl142(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 0 && 1 + G = 0 && E = 0 && D = A] (?,1) 5. lbl142(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + G,H) [A >= 1 && G = 0 && E = 1 && D = A] (?,1) 6. lbl142(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,G,H) [E >= 2 && E >= 0 && A >= E && 1 + G = E && D = A] (?,1) 7. lbl142(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,G,H) [E >= 2 && E >= 0 && A >= E && 1 + G = E && D = A] (?,1) 8. lbl131(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,E,F,-1 + G,H) [G >= 1 && A >= G && E = G && D = A] (?,1) 9. lbl131(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,E,F,G,H) [G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] (?,1) 10. lbl131(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] (?,1) 11. lbl91(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [E >= 0 && G >= 1 + E && A >= G && D = A] (?,1) 12. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(lbl131,8);(lbl142,8);(lbl91,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{4},2->{11},3->{8,9,10},4->{},5->{4},6->{11},7->{8,9,10},8->{5,6,7},9->{11},10->{8,9,10},11->{8 ,9,10},12->{0,1,2,3}] + 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,D,H) [0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + D,H) [D = 0 && B = C && A = 0 && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,D,H) [A >= 1 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,D,H) [A >= 1 && B = C && D = A && E = F && G = H] lbl142(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 0 && 1 + G = 0 && E = 0 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + G,H) [A >= 1 && G = 0 && E = 1 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,G,H) [E >= 2 && E >= 0 && A >= E && 1 + G = E && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,G,H) [E >= 2 && E >= 0 && A >= E && 1 + G = E && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,E,F,-1 + G,H) [G >= 1 && A >= G && E = G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,E,F,G,H) [G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl91(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [E >= 0 && G >= 1 + E && A >= G && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True Signature: {(lbl131,8);(lbl142,8);(lbl91,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{4},2->{11},3->{8,9,10},4->{},5->{4},6->{11},7->{8,9,10},8->{5,6,7},9->{11},10->{8,9,10},11->{8 ,9,10},12->{0,1,2,3}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[11,6,8,7,10,9] c: [6,7,8] | `- p:[9,10,11] c: [9,11] | `- p:[10] c: [10] * Step 4: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,D,H) [0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + D,H) [D = 0 && B = C && A = 0 && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,D,H) [A >= 1 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,D,H) [A >= 1 && B = C && D = A && E = F && G = H] lbl142(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 0 && 1 + G = 0 && E = 0 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + G,H) [A >= 1 && G = 0 && E = 1 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,G,H) [E >= 2 && E >= 0 && A >= E && 1 + G = E && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,G,H) [E >= 2 && E >= 0 && A >= E && 1 + G = E && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,E,F,-1 + G,H) [G >= 1 && A >= G && E = G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,E,F,G,H) [G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl91(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [E >= 0 && G >= 1 + E && A >= G && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True Signature: {(lbl131,8);(lbl142,8);(lbl91,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{4},2->{11},3->{8,9,10},4->{},5->{4},6->{11},7->{8,9,10},8->{5,6,7},9->{11},10->{8,9,10},11->{8 ,9,10},12->{0,1,2,3}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[11,6,8,7,10,9] c: [6,7,8] | `- p:[9,10,11] c: [9,11] | `- p:[10] c: [10]) + Applied Processor: CloseWith True + Details: () YES