YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 30 && B = C && D = A] (?,1) 1. start(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && C >= A && 29 >= A && B = C && D = A] (?,1) 2. start(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [A + -1*D >= 0 (?,1) && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 + C && C >= 6 && 29 >= A && B = C && D = A] 3. start(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [A + -1*D >= 0 (?,1) && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 + C && 5 >= C && 29 >= A && B = C && D = A] 4. lbl171(A,B,C,D) -> stop(A,B,C,D) [12 + B + -1*D >= 0 (?,1) && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 30 && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] 5. lbl171(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [12 + B + -1*D >= 0 (?,1) && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && B >= D && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] 6. lbl171(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [12 + B + -1*D >= 0 (?,1) && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 1 + B && B >= 6 && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] 7. lbl171(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [12 + B + -1*D >= 0 (?,1) && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 1 + B && 5 >= B && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] 8. lbl151(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [5 + -1*B + D >= 0 (?,1) && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && B >= D && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] 9. lbl151(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [5 + -1*B + D >= 0 (?,1) && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && D >= 1 + B && B >= 6 && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] 10. lbl151(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [5 + -1*B + D >= 0 (?,1) && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && D >= 1 + B && 5 >= B && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] 11. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl151,4);(lbl171,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{4,5,6,7},2->{8,9,10},3->{8,9,10},4->{},5->{4,5,6,7},6->{8,9,10},7->{8,9,10},8->{4,5,6,7},9->{8 ,9,10},10->{8,9,10},11->{0,1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,10),(6,10),(8,5),(9,10)] * Step 2: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 30 && B = C && D = A] (?,1) 1. start(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && C >= A && 29 >= A && B = C && D = A] (?,1) 2. start(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [A + -1*D >= 0 (?,1) && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 + C && C >= 6 && 29 >= A && B = C && D = A] 3. start(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [A + -1*D >= 0 (?,1) && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 + C && 5 >= C && 29 >= A && B = C && D = A] 4. lbl171(A,B,C,D) -> stop(A,B,C,D) [12 + B + -1*D >= 0 (?,1) && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 30 && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] 5. lbl171(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [12 + B + -1*D >= 0 (?,1) && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && B >= D && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] 6. lbl171(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [12 + B + -1*D >= 0 (?,1) && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 1 + B && B >= 6 && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] 7. lbl171(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [12 + B + -1*D >= 0 (?,1) && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 1 + B && 5 >= B && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] 8. lbl151(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [5 + -1*B + D >= 0 (?,1) && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && B >= D && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] 9. lbl151(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [5 + -1*B + D >= 0 (?,1) && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && D >= 1 + B && B >= 6 && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] 10. lbl151(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [5 + -1*B + D >= 0 (?,1) && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && D >= 1 + B && 5 >= B && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] 11. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl151,4);(lbl171,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{4,5,6,7},2->{8,9},3->{8,9,10},4->{},5->{4,5,6,7},6->{8,9},7->{8,9,10},8->{4,6,7},9->{8,9} ,10->{8,9,10},11->{0,1,2,3}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 30 && B = C && D = A] start(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && C >= A && 29 >= A && B = C && D = A] start(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 + C && C >= 6 && 29 >= A && B = C && D = A] start(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 + C && 5 >= C && 29 >= A && B = C && D = A] lbl171(A,B,C,D) -> stop(A,B,C,D) [12 + B + -1*D >= 0 && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 30 && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] lbl171(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [12 + B + -1*D >= 0 && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && B >= D && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] lbl171(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [12 + B + -1*D >= 0 && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 1 + B && B >= 6 && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] lbl171(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [12 + B + -1*D >= 0 && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 1 + B && 5 >= B && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] lbl151(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [5 + -1*B + D >= 0 && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && B >= D && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] lbl151(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [5 + -1*B + D >= 0 && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && D >= 1 + B && B >= 6 && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] lbl151(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [5 + -1*B + D >= 0 && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && D >= 1 + B && 5 >= B && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] start0(A,B,C,D) -> start(A,C,C,A) True Signature: {(lbl151,4);(lbl171,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{},1->{4,5,6,7},2->{8,9},3->{8,9,10},4->{},5->{4,5,6,7},6->{8,9},7->{8,9,10},8->{4,6,7},9->{8,9} ,10->{8,9,10},11->{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] | +- p:[5] c: [5] | `- p:[6,8,7,9,10] c: [10] | `- p:[6,8,7,9] c: [9] | `- p:[6,8,7] c: [6,7,8] * Step 4: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 30 && B = C && D = A] start(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && C >= A && 29 >= A && B = C && D = A] start(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 + C && C >= 6 && 29 >= A && B = C && D = A] start(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 + C && 5 >= C && 29 >= A && B = C && D = A] lbl171(A,B,C,D) -> stop(A,B,C,D) [12 + B + -1*D >= 0 && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 30 && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] lbl171(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [12 + B + -1*D >= 0 && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && B >= D && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] lbl171(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [12 + B + -1*D >= 0 && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 1 + B && B >= 6 && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] lbl171(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [12 + B + -1*D >= 0 && -2 + -1*A + D >= 0 && 10 + -1*A + B >= 0 && 29 + -1*A >= 0 && D >= 1 + B && 5 >= B && 29 >= D && 29 >= A && B + 5*D >= 5*A + C && C + 7*D >= 24 + 7*A + B && 1674 + 7*B >= 35*A + 7*C + 19*D && 12 + B >= D] lbl151(A,B,C,D) -> lbl171(A,-10 + B,C,2 + D) [5 + -1*B + D >= 0 && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && B >= D && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] lbl151(A,B,C,D) -> lbl151(A,7 + B,C,1 + D) [5 + -1*B + D >= 0 && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && D >= 1 + B && B >= 6 && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] lbl151(A,B,C,D) -> lbl151(A,2 + B,C,1 + D) [5 + -1*B + D >= 0 && -1 + -1*A + D >= 0 && 29 + -1*A >= 0 && D >= 1 + B && 5 >= B && 6*D >= 7 + 5*A + C && B + 5*D >= 7 + 5*A + C && D >= 1 + A && 29 >= A && 203 + B >= 5*A + C + 2*D && 1561 + 2*B >= 35*A + 7*C + 14*D && 23*B + 140*D >= 161 + 140*A + 28*C && 5719 + 23*B >= 140*A + 28*C + 56*D && 5 + D >= B && C + 7*D >= 7*A + B] start0(A,B,C,D) -> start(A,C,C,A) True Signature: {(lbl151,4);(lbl171,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{},1->{4,5,6,7},2->{8,9},3->{8,9,10},4->{},5->{4,5,6,7},6->{8,9},7->{8,9,10},8->{4,6,7},9->{8,9} ,10->{8,9,10},11->{0,1,2,3}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | +- p:[5] c: [5] | `- p:[6,8,7,9,10] c: [10] | `- p:[6,8,7,9] c: [9] | `- p:[6,8,7] c: [6,7,8]) + Applied Processor: CloseWith True + Details: () YES