YES * Step 1: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,1,J) [1 >= A && B = C && D = E && F = A && G = H && I = J] (?,1) 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,1,J) [A >= 2 && B = C && D = E && F = A && G = H && I = J] (?,1) 2. lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-1 + G,H,I,J) [G >= 0 && I >= 2 + G && 1 + G >= 0 && A >= 1 + I && F = A] (?,1) 3. lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,G,H,1 + I,J) [I >= 2 + G && 1 + G >= 0 && A >= 1 + I && F = A] (?,1) 4. lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-2 + I,H,I,J) [I >= 1 && A >= 1 + I && F = A] (?,1) 5. lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,-1 + I,H,1 + I,J) [I >= 1 && A >= 1 + I && F = A] (?,1) 6. lbl13(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [A + G >= 2 && 1 + G >= 0 && A >= 2 + G && F = A && I = A && 1 + D = A] (?,1) 7. lbl13(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,I,J) [A >= 2 + D && D + G >= 1 && 1 + G >= 0 && A >= 1 + D && D >= 1 + G && F = A && I = 1 + D] (?,1) 8. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,A,H,H,J,J) True (1,1) Signature: {(lbl13,10);(lbl31,10);(lbl43,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5},2->{2,3},3->{6,7},4->{2,3},5->{6,7},6->{},7->{4,5},8->{0,1}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,1,J) [1 >= A && B = C && D = E && F = A && G = H && I = J] start(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,1,J) [A >= 2 && B = C && D = E && F = A && G = H && I = J] lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-1 + G,H,I,J) [G >= 0 && I >= 2 + G && 1 + G >= 0 && A >= 1 + I && F = A] lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,G,H,1 + I,J) [I >= 2 + G && 1 + G >= 0 && A >= 1 + I && F = A] lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-2 + I,H,I,J) [I >= 1 && A >= 1 + I && F = A] lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,-1 + I,H,1 + I,J) [I >= 1 && A >= 1 + I && F = A] lbl13(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [A + G >= 2 && 1 + G >= 0 && A >= 2 + G && F = A && I = A && 1 + D = A] lbl13(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,I,J) [A >= 2 + D && D + G >= 1 && 1 + G >= 0 && A >= 1 + D && D >= 1 + G && F = A && I = 1 + D] start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,A,H,H,J,J) True Signature: {(lbl13,10);(lbl31,10);(lbl43,10);(start,10);(start0,10);(stop,10)} Rule Graph: [0->{},1->{4,5},2->{2,3},3->{6,7},4->{2,3},5->{6,7},6->{},7->{4,5},8->{0,1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[4,7,3,2,5] c: [3,4,5,7] | `- p:[2] c: [2] * Step 3: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,1,J) [1 >= A && B = C && D = E && F = A && G = H && I = J] start(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,1,J) [A >= 2 && B = C && D = E && F = A && G = H && I = J] lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-1 + G,H,I,J) [G >= 0 && I >= 2 + G && 1 + G >= 0 && A >= 1 + I && F = A] lbl43(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,G,H,1 + I,J) [I >= 2 + G && 1 + G >= 0 && A >= 1 + I && F = A] lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl43(A,B,C,D,E,F,-2 + I,H,I,J) [I >= 1 && A >= 1 + I && F = A] lbl31(A,B,C,D,E,F,G,H,I,J) -> lbl13(A,B,C,I,E,F,-1 + I,H,1 + I,J) [I >= 1 && A >= 1 + I && F = A] lbl13(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [A + G >= 2 && 1 + G >= 0 && A >= 2 + G && F = A && I = A && 1 + D = A] lbl13(A,B,C,D,E,F,G,H,I,J) -> lbl31(A,K,C,D,E,F,G,H,I,J) [A >= 2 + D && D + G >= 1 && 1 + G >= 0 && A >= 1 + D && D >= 1 + G && F = A && I = 1 + D] start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,A,H,H,J,J) True Signature: {(lbl13,10);(lbl31,10);(lbl43,10);(start,10);(start0,10);(stop,10)} Rule Graph: [0->{},1->{4,5},2->{2,3},3->{6,7},4->{2,3},5->{6,7},6->{},7->{4,5},8->{0,1}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[4,7,3,2,5] c: [3,4,5,7] | `- p:[2] c: [2]) + Applied Processor: CloseWith True + Details: () YES