YES * Step 1: UnsatRules YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= 1 + A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && C >= 1 + E && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && E >= C && B = C && D = E && F = A] (?,1) 3. start(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && E >= C && B = C && D = E && F = A] (?,1) 4. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B >= 1 + D && B >= C && A >= 0 && 1 + A + D >= B && E >= 1 + A + D && F = A] (?,1) 5. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D >= B && 0 >= 1 + A && B >= C && A >= 0 && 1 + A + D >= B && E >= 1 + A + D && F = A] (?,1) 6. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && D >= B && B >= C && 1 + A + D >= B && E >= 1 + A + D && F = A] (?,1) 7. lbl91(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && D >= B && B >= C && 1 + A + D >= B && E >= 1 + A + D && F = A] (?,1) 8. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B >= 1 + D && E >= D && A >= 0 && B >= 1 + A + C && 1 + A + D >= B && F = A] (?,1) 9. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D >= B && 0 >= 1 + A && E >= D && A >= 0 && B >= 1 + A + C && 1 + A + D >= B && F = A] (?,1) 10. lbl101(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && D >= B && E >= D && B >= 1 + A + C && 1 + A + D >= B && F = A] (?,1) 11. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && D >= B && E >= D && B >= 1 + A + C && 1 + A + D >= B && F = A] (?,1) 12. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl101,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{},2->{4,5,6,7},3->{8,9,10,11},4->{},5->{},6->{4,5,6,7},7->{8,9,10,11},8->{},9->{},10->{4,5,6,7} ,11->{8,9,10,11},12->{0,1,2,3}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [5,9] * Step 2: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= 1 + A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && C >= 1 + E && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && E >= C && B = C && D = E && F = A] (?,1) 3. start(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && E >= C && B = C && D = E && F = A] (?,1) 4. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B >= 1 + D && B >= C && A >= 0 && 1 + A + D >= B && E >= 1 + A + D && F = A] (?,1) 6. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && D >= B && B >= C && 1 + A + D >= B && E >= 1 + A + D && F = A] (?,1) 7. lbl91(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && D >= B && B >= C && 1 + A + D >= B && E >= 1 + A + D && F = A] (?,1) 8. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B >= 1 + D && E >= D && A >= 0 && B >= 1 + A + C && 1 + A + D >= B && F = A] (?,1) 10. lbl101(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && D >= B && E >= D && B >= 1 + A + C && 1 + A + D >= B && F = A] (?,1) 11. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && D >= B && E >= D && B >= 1 + A + C && 1 + A + D >= B && F = A] (?,1) 12. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl101,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{},2->{4,6,7},3->{8,10,11},4->{},6->{4,6,7},7->{8,10,11},8->{},10->{4,6,7},11->{8,10,11},12->{0 ,1,2,3}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= 1 + A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && C >= 1 + E && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && E >= C && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && E >= C && B = C && D = E && F = A] lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B >= 1 + D && B >= C && A >= 0 && 1 + A + D >= B && E >= 1 + A + D && F = A] lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && D >= B && B >= C && 1 + A + D >= B && E >= 1 + A + D && F = A] lbl91(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && D >= B && B >= C && 1 + A + D >= B && E >= 1 + A + D && F = A] lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B >= 1 + D && E >= D && A >= 0 && B >= 1 + A + C && 1 + A + D >= B && F = A] lbl101(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && D >= B && E >= D && B >= 1 + A + C && 1 + A + D >= B && F = A] lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && D >= B && E >= D && B >= 1 + A + C && 1 + A + D >= B && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl101,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{},2->{4,6,7},3->{8,10,11},4->{},6->{4,6,7},7->{8,10,11},8->{},10->{4,6,7},11->{8,10,11},12->{0 ,1,2,3}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,6,7,8,10,11,12] | `- p:[6,10,7,11] c: [11] | `- p:[6,10,7] c: [7,10] | `- p:[6] c: [6] * Step 4: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= 1 + A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && C >= 1 + E && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && E >= C && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && E >= C && B = C && D = E && F = A] lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B >= 1 + D && B >= C && A >= 0 && 1 + A + D >= B && E >= 1 + A + D && F = A] lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && D >= B && B >= C && 1 + A + D >= B && E >= 1 + A + D && F = A] lbl91(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && D >= B && B >= C && 1 + A + D >= B && E >= 1 + A + D && F = A] lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [B >= 1 + D && E >= D && A >= 0 && B >= 1 + A + C && 1 + A + D >= B && F = A] lbl101(A,B,C,D,E,F) -> lbl91(A,B,C,-1 + D + -1*F,E,F) [A >= 0 && D >= B && E >= D && B >= 1 + A + C && 1 + A + D >= B && F = A] lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B + F,C,D,E,F) [A >= 0 && D >= B && E >= D && B >= 1 + A + C && 1 + A + D >= B && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl101,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{},2->{4,6,7},3->{8,10,11},4->{},6->{4,6,7},7->{8,10,11},8->{},10->{4,6,7},11->{8,10,11},12->{0 ,1,2,3}] ,We construct a looptree: P: [0,1,2,3,4,6,7,8,10,11,12] | `- p:[6,10,7,11] c: [11] | `- p:[6,10,7] c: [7,10] | `- p:[6] c: [6]) + Applied Processor: CloseWith True + Details: () YES