YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= 1 + A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] (?,1) 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] (?,1) 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{6,7},3->{},4->{3,4,5},5->{6,7},6->{6,7},7->{3,4,5},8->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(4,5),(7,3)] * Step 2: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= 1 + A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] (?,1) 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] (?,1) 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] (?,1) 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] (?,1) 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4},2->{6,7},3->{},4->{3,4},5->{6,7},6->{6,7},7->{4,5},8->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= 1 + A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{3,4},2->{6,7},3->{},4->{3,4},5->{6,7},6->{6,7},7->{4,5},8->{0,1,2}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[6,5,7] c: [5,7] | | | `- p:[6] c: [6] | `- p:[4] c: [4] * Step 4: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= 1 + A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A >= 0 && 1 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A >= 2 && B = C && D = E && F = A] lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && 1 + D >= 0 && F = A] lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{3,4},2->{6,7},3->{},4->{3,4},5->{6,7},6->{6,7},7->{4,5},8->{0,1,2}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[6,5,7] c: [5,7] | | | `- p:[6] c: [6] | `- p:[4] c: [4]) + Applied Processor: CloseWith True + Details: () YES