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) [0 >= 1 + A && B = C && D = A && E = F && G = H] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [A >= 0 && C >= 0 && B = C && D = A && E = F && G = H] (?,1) 2. start(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [A >= 0 && B = C && D = A && E = F && G = H] (?,1) 3. start(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [H >= C && A >= 0 && B = C && D = A && E = F && G = H] (?,1) 4. lbl72(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [A >= 1 + D && 1 + D >= 0 && 1 + H >= B && 1 + E = B && G = H] (?,1) 5. lbl72(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,D,B,F,G,H) [H >= B && A >= 1 + D && 1 + D >= 0 && 1 + H >= B && 1 + E = B && G = H] (?,1) 6. lbl42(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [B >= 0 && 1 + B >= 0 && D >= 0 && A >= D && G = H] (?,1) 7. lbl42(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [1 + B >= 0 && D >= 0 && A >= D && G = H] (?,1) 8. lbl42(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [H >= B && 1 + B >= 0 && D >= 0 && A >= D && G = H] (?,1) 9. cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 0 && 1 + D = 0 && G = H] (?,1) 10. cut(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [D >= 0 && B >= 0 && 1 + D >= 0 && A >= 1 + D && G = H] (?,1) 11. cut(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [D >= 0 && 1 + D >= 0 && A >= 1 + D && G = H] (?,1) 12. cut(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [H >= B && D >= 0 && 1 + D >= 0 && A >= 1 + D && G = H] (?,1) 13. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(cut,8);(lbl42,8);(lbl72,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{6,7,8},2->{9,10,11,12},3->{4,5},4->{9,10,11,12},5->{4,5},6->{6,7,8},7->{9,10,11,12},8->{4,5} ,9->{},10->{6,7,8},11->{9,10,11,12},12->{4,5},13->{0,1,2,3}] + 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) [0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [A >= 0 && C >= 0 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [A >= 0 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [H >= C && A >= 0 && B = C && D = A && E = F && G = H] lbl72(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [A >= 1 + D && 1 + D >= 0 && 1 + H >= B && 1 + E = B && G = H] lbl72(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,D,B,F,G,H) [H >= B && A >= 1 + D && 1 + D >= 0 && 1 + H >= B && 1 + E = B && G = H] lbl42(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [B >= 0 && 1 + B >= 0 && D >= 0 && A >= D && G = H] lbl42(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [1 + B >= 0 && D >= 0 && A >= D && G = H] lbl42(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [H >= B && 1 + B >= 0 && D >= 0 && A >= D && G = H] cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 0 && 1 + D = 0 && G = H] cut(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [D >= 0 && B >= 0 && 1 + D >= 0 && A >= 1 + D && G = H] cut(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [D >= 0 && 1 + D >= 0 && A >= 1 + D && G = H] cut(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [H >= B && D >= 0 && 1 + D >= 0 && A >= 1 + D && G = H] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True Signature: {(cut,8);(lbl42,8);(lbl72,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{6,7,8},2->{9,10,11,12},3->{4,5},4->{9,10,11,12},5->{4,5},6->{6,7,8},7->{9,10,11,12},8->{4,5} ,9->{},10->{6,7,8},11->{9,10,11,12},12->{4,5},13->{0,1,2,3}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[6,10,4,5,8,12,7,11] c: [12] | `- p:[4,5,8,6,10,7,11] c: [11] | `- p:[4,5,8,6,10,7] c: [4,7,10] | +- p:[6] c: [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) [0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [A >= 0 && C >= 0 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [A >= 0 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [H >= C && A >= 0 && B = C && D = A && E = F && G = H] lbl72(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [A >= 1 + D && 1 + D >= 0 && 1 + H >= B && 1 + E = B && G = H] lbl72(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,D,B,F,G,H) [H >= B && A >= 1 + D && 1 + D >= 0 && 1 + H >= B && 1 + E = B && G = H] lbl42(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [B >= 0 && 1 + B >= 0 && D >= 0 && A >= D && G = H] lbl42(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [1 + B >= 0 && D >= 0 && A >= D && G = H] lbl42(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [H >= B && 1 + B >= 0 && D >= 0 && A >= D && G = H] cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 0 && 1 + D = 0 && G = H] cut(A,B,C,D,E,F,G,H) -> lbl42(A,-1 + B,C,D,E,F,G,H) [D >= 0 && B >= 0 && 1 + D >= 0 && A >= 1 + D && G = H] cut(A,B,C,D,E,F,G,H) -> cut(A,B,C,-1 + D,E,F,G,H) [D >= 0 && 1 + D >= 0 && A >= 1 + D && G = H] cut(A,B,C,D,E,F,G,H) -> lbl72(A,1 + B,C,-1 + D,B,F,G,H) [H >= B && D >= 0 && 1 + D >= 0 && A >= 1 + D && G = H] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True Signature: {(cut,8);(lbl42,8);(lbl72,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{6,7,8},2->{9,10,11,12},3->{4,5},4->{9,10,11,12},5->{4,5},6->{6,7,8},7->{9,10,11,12},8->{4,5} ,9->{},10->{6,7,8},11->{9,10,11,12},12->{4,5},13->{0,1,2,3}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[6,10,4,5,8,12,7,11] c: [12] | `- p:[4,5,8,6,10,7,11] c: [11] | `- p:[4,5,8,6,10,7] c: [4,7,10] | +- p:[6] c: [6] | `- p:[5] c: [5]) + Applied Processor: CloseWith True + Details: () YES