YES * Step 1: UnsatRules YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 3. lbl52(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= D && B >= 0 && D >= 1 && A >= D && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 8. lbl72(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && 0 >= A && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{6,7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [3,8] * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{6,7},4->{4,5},5->{6,7},6->{},7->{4,5},9->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,5)] * Step 3: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{6,7},4->{4,5},5->{6,7},6->{},7->{4},9->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 4: Decompose YES + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{4,5},2->{6,7},4->{4,5},5->{6,7},6->{},7->{4},9->{0,1,2}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,4,5,6,7,9] | `- p:[4,7,5] c: [5,7] | `- p:[4] c: [4] * Step 5: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{4,5},2->{6,7},4->{4,5},5->{6,7},6->{},7->{4},9->{0,1,2}] ,We construct a looptree: P: [0,1,2,4,5,6,7,9] | `- p:[4,7,5] c: [5,7] | `- p:[4] c: [4]) + Applied Processor: CloseWith True + Details: () YES