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) -> lbl62(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] (?,1) 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] (?,1) 3. lbl72(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && 0 >= A && D >= 0 && A >= 1 + D && B = 0 && F = A] (?,1) 4. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] (?,1) 5. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] (?,1) 6. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] (?,1) 7. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{5,6},2->{},3->{2,3,4},4->{5,6},5->{2,3,4},6->{5,6},7->{0,1}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [3] * 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) -> lbl62(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] (?,1) 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] (?,1) 4. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] (?,1) 5. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] (?,1) 6. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] (?,1) 7. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{5,6},2->{},4->{5,6},5->{2,4},6->{5,6},7->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,5)] * 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) -> lbl62(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] (?,1) 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] (?,1) 4. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] (?,1) 5. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] (?,1) 6. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] (?,1) 7. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{5,6},2->{},4->{6},5->{2,4},6->{5,6},7->{0,1}] + 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) -> lbl62(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{5,6},2->{},4->{6},5->{2,4},6->{5,6},7->{0,1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,4,5,6,7] | `- p:[5,6,4] c: [4,5] | `- p:[6] c: [6] * 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) -> lbl62(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{5,6},2->{},4->{6},5->{2,4},6->{5,6},7->{0,1}] ,We construct a looptree: P: [0,1,2,4,5,6,7] | `- p:[5,6,4] c: [4,5] | `- p:[6] c: [6]) + Applied Processor: CloseWith True + Details: () YES