YES * Step 1: UnsatRules YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= A && B = C && D = E && F = G && H = A] (?,1) 1. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= 1 + G && B = C && D = E && F = G && H = A] (?,1) 2. start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] (?,1) 3. start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] (?,1) 4. lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] (?,1) 5. lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [D >= 1 && G >= A + D && A >= 1 && D >= 0 && B = A && H = A && F = G] (?,1) 6. lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && D >= 0 && H = A && F = G] (?,1) 7. lZZ1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= D && G >= A + D && A >= 2 && D >= 1 && B = 0 && H = A && F = G] (?,1) 8. lZZ1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [D >= 1 && 0 >= A && G >= A + D && A >= 2 && B = 0 && H = A && F = G] (?,1) 9. lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] (?,1) 10. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{},2->{},3->{4,5,6},4->{},5->{7,8,9},6->{4,5,6},7->{},8->{7,8,9},9->{4,5,6},10->{0,1,2,3}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [7,8] * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= A && B = C && D = E && F = G && H = A] (?,1) 1. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= 1 + G && B = C && D = E && F = G && H = A] (?,1) 2. start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] (?,1) 3. start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] (?,1) 4. lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] (?,1) 5. lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [D >= 1 && G >= A + D && A >= 1 && D >= 0 && B = A && H = A && F = G] (?,1) 6. lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && D >= 0 && H = A && F = G] (?,1) 9. lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] (?,1) 10. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{},2->{},3->{4,5,6},4->{},5->{9},6->{4,5,6},9->{4,5,6},10->{0,1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(9,5)] * Step 3: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= A && B = C && D = E && F = G && H = A] (?,1) 1. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= 1 + G && B = C && D = E && F = G && H = A] (?,1) 2. start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] (?,1) 3. start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] (?,1) 4. lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] (?,1) 5. lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [D >= 1 && G >= A + D && A >= 1 && D >= 0 && B = A && H = A && F = G] (?,1) 6. lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && D >= 0 && H = A && F = G] (?,1) 9. lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] (?,1) 10. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{},2->{},3->{4,5,6},4->{},5->{9},6->{4,5,6},9->{4,6},10->{0,1,2,3}] + Applied Processor: FromIts + Details: () * Step 4: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= 1 + G && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [D >= 1 && G >= A + D && A >= 1 && D >= 0 && B = A && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && D >= 0 && H = A && F = G] lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{},2->{},3->{4,5,6},4->{},5->{9},6->{4,5,6},9->{4,6},10->{0,1,2,3}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,9,10] | `- p:[5,6,9] c: [5,9] | `- p:[6] c: [6] * Step 5: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [0 >= 1 + G && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [D >= 1 && G >= A + D && A >= 1 && D >= 0 && B = A && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && D >= 0 && H = A && F = G] lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{},2->{},3->{4,5,6},4->{},5->{9},6->{4,5,6},9->{4,6},10->{0,1,2,3}] ,We construct a looptree: P: [0,1,2,3,4,5,6,9,10] | `- p:[5,6,9] c: [5,9] | `- p:[6] c: [6]) + Applied Processor: CloseWith True + Details: () YES