YES * Step 1: UnsatRules YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,1,F,G,H,I,J) [A >= 1 && B >= 1 + C && D = B && E = F && G = C && H = I && J = A] (?,1) 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,1 + D,1,F,G,H,I,J) [A >= 1 && C >= B && D = B && E = F && G = C && H = I && J = A] (?,1) 2. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,-1,F,G,H,I,J) [B >= 1 + C && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 3. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,1 + D,-1,F,G,H,I,J) [C >= B && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 4. lbl71(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [C >= B && A >= 1 && D = 1 + C && E = 1 && J = A && H = I && G = C] (?,1) 5. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && D >= 1 + B && 1 + C >= D && E = 1 && J = A && H = I && G = C] (?,1) 6. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && A >= 1 && E = 1 && J = A && H = I && G = C] (?,1) 7. lbl81(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [0 >= A && C >= B && D = 1 + C && 1 + E = 0 && J = A && H = I && G = C] (?,1) 8. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 9. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,B,C,B,F,F,C,I,I,A) True (1,1) Signature: {(lbl71,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5,6},2->{},3->{7,8,9},4->{},5->{4,5,6},6->{7,8,9},7->{},8->{4,5,6},9->{7,8,9},10->{0,1,2,3}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [6,8] * Step 2: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,1,F,G,H,I,J) [A >= 1 && B >= 1 + C && D = B && E = F && G = C && H = I && J = A] (?,1) 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,1 + D,1,F,G,H,I,J) [A >= 1 && C >= B && D = B && E = F && G = C && H = I && J = A] (?,1) 2. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,-1,F,G,H,I,J) [B >= 1 + C && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 3. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,1 + D,-1,F,G,H,I,J) [C >= B && 0 >= A && D = B && E = F && G = C && H = I && J = A] (?,1) 4. lbl71(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [C >= B && A >= 1 && D = 1 + C && E = 1 && J = A && H = I && G = C] (?,1) 5. lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && D >= 1 + B && 1 + C >= D && E = 1 && J = A && H = I && G = C] (?,1) 7. lbl81(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [0 >= A && C >= B && D = 1 + C && 1 + E = 0 && J = A && H = I && G = C] (?,1) 9. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,B,C,B,F,F,C,I,I,A) True (1,1) Signature: {(lbl71,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{4,5},2->{},3->{7,9},4->{},5->{4,5},7->{},9->{7,9},10->{0,1,2,3}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,1,F,G,H,I,J) [A >= 1 && B >= 1 + C && D = B && E = F && G = C && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,1 + D,1,F,G,H,I,J) [A >= 1 && C >= B && D = B && E = F && G = C && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,-1,F,G,H,I,J) [B >= 1 + C && 0 >= A && D = B && E = F && G = C && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,1 + D,-1,F,G,H,I,J) [C >= B && 0 >= A && D = B && E = F && G = C && H = I && J = A] lbl71(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [C >= B && A >= 1 && D = 1 + C && E = 1 && J = A && H = I && G = C] lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && D >= 1 + B && 1 + C >= D && E = 1 && J = A && H = I && G = C] lbl81(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [0 >= A && C >= B && D = 1 + C && 1 + E = 0 && J = A && H = I && G = C] lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] start0(A,B,C,D,E,F,G,H,I,J) -> start(A,B,C,B,F,F,C,I,I,A) True Signature: {(lbl71,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Rule Graph: [0->{},1->{4,5},2->{},3->{7,9},4->{},5->{4,5},7->{},9->{7,9},10->{0,1,2,3}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,7,9,10] | +- p:[9] c: [9] | `- p:[5] c: [5] * Step 4: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,1,F,G,H,I,J) [A >= 1 && B >= 1 + C && D = B && E = F && G = C && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,1 + D,1,F,G,H,I,J) [A >= 1 && C >= B && D = B && E = F && G = C && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,-1,F,G,H,I,J) [B >= 1 + C && 0 >= A && D = B && E = F && G = C && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,1 + D,-1,F,G,H,I,J) [C >= B && 0 >= A && D = B && E = F && G = C && H = I && J = A] lbl71(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [C >= B && A >= 1 && D = 1 + C && E = 1 && J = A && H = I && G = C] lbl71(A,B,C,D,E,F,G,H,I,J) -> lbl71(A,B,C,D + E,E,F,G,H,I,J) [A >= 1 && C >= D && D >= 1 + B && 1 + C >= D && E = 1 && J = A && H = I && G = C] lbl81(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [0 >= A && C >= B && D = 1 + C && 1 + E = 0 && J = A && H = I && G = C] lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D + -1*E,E,F,G,H,I,J) [C >= D && 0 >= A && D >= 1 + B && 1 + C >= D && 1 + E = 0 && J = A && H = I && G = C] start0(A,B,C,D,E,F,G,H,I,J) -> start(A,B,C,B,F,F,C,I,I,A) True Signature: {(lbl71,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Rule Graph: [0->{},1->{4,5},2->{},3->{7,9},4->{},5->{4,5},7->{},9->{7,9},10->{0,1,2,3}] ,We construct a looptree: P: [0,1,2,3,4,5,7,9,10] | +- p:[9] c: [9] | `- p:[5] c: [5]) + Applied Processor: CloseWith True + Details: () YES