YES * Step 1: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [0 >= A && B = C && D = A] (?,1) 1. start(A,B,C,D) -> lbl6(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] (?,1) 2. start(A,B,C,D) -> cut(A,B,C,D) [A >= 1 && D = A && B = A && C = A] (?,1) 3. start(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] (?,1) 4. start(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [A >= 1 + C && C >= 1 && B = C && D = A] (?,1) 5. lbl6(A,B,C,D) -> stop(A,B,C,D) [A >= 1 && 0 >= C && D = A && B = C] (?,1) 6. lbl101(A,B,C,D) -> cut(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] (?,1) 7. lbl101(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 8. lbl101(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 9. lbl111(A,B,C,D) -> cut(A,B,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] (?,1) 10. lbl111(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] (?,1) 11. lbl111(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] (?,1) 12. cut(A,B,C,D) -> stop(A,B,C,D) [A >= B && B >= 1 && C >= B && D = B] (?,1) 13. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(cut,4);(lbl101,4);(lbl111,4);(lbl6,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{5},2->{12},3->{6,7,8},4->{9,10,11},5->{},6->{12},7->{6,7,8},8->{9,10,11},9->{12},10->{6,7,8} ,11->{9,10,11},12->{},13->{0,1,2,3,4}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: start(A,B,C,D) -> stop(A,B,C,D) [0 >= A && B = C && D = A] start(A,B,C,D) -> lbl6(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] start(A,B,C,D) -> cut(A,B,C,D) [A >= 1 && D = A && B = A && C = A] start(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] start(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [A >= 1 + C && C >= 1 && B = C && D = A] lbl6(A,B,C,D) -> stop(A,B,C,D) [A >= 1 && 0 >= C && D = A && B = C] lbl101(A,B,C,D) -> cut(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] lbl101(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] lbl101(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] lbl111(A,B,C,D) -> cut(A,B,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] lbl111(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] lbl111(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] cut(A,B,C,D) -> stop(A,B,C,D) [A >= B && B >= 1 && C >= B && D = B] start0(A,B,C,D) -> start(A,C,C,A) True Signature: {(cut,4);(lbl101,4);(lbl111,4);(lbl6,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{},1->{5},2->{12},3->{6,7,8},4->{9,10,11},5->{},6->{12},7->{6,7,8},8->{9,10,11},9->{12},10->{6,7,8} ,11->{9,10,11},12->{},13->{0,1,2,3,4}] + 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:[7,10,8,11] c: [11] | `- p:[7,10,8] c: [8,10] | `- p:[7] c: [7] * Step 3: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D) -> stop(A,B,C,D) [0 >= A && B = C && D = A] start(A,B,C,D) -> lbl6(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] start(A,B,C,D) -> cut(A,B,C,D) [A >= 1 && D = A && B = A && C = A] start(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] start(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [A >= 1 + C && C >= 1 && B = C && D = A] lbl6(A,B,C,D) -> stop(A,B,C,D) [A >= 1 && 0 >= C && D = A && B = C] lbl101(A,B,C,D) -> cut(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] lbl101(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] lbl101(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] lbl111(A,B,C,D) -> cut(A,B,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] lbl111(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] lbl111(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] cut(A,B,C,D) -> stop(A,B,C,D) [A >= B && B >= 1 && C >= B && D = B] start0(A,B,C,D) -> start(A,C,C,A) True Signature: {(cut,4);(lbl101,4);(lbl111,4);(lbl6,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{},1->{5},2->{12},3->{6,7,8},4->{9,10,11},5->{},6->{12},7->{6,7,8},8->{9,10,11},9->{12},10->{6,7,8} ,11->{9,10,11},12->{},13->{0,1,2,3,4}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[7,10,8,11] c: [11] | `- p:[7,10,8] c: [8,10] | `- p:[7] c: [7]) + Applied Processor: CloseWith True + Details: () YES