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) [1 >= A && B = C && D = E && F = G && H = A] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,G,H) [A >= 2 && B = C && D = E && F = G && H = A] (?,1) 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] (?,1) 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] (?,1) 4. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [F >= 1 + D && 0 >= 1 + D && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] (?,1) 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] (?,1) 6. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] (?,1) 7. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] (?,1) 8. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [F >= 1 && A >= F && F >= 0 && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] (?,1) 9. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [F >= 1 + A && A >= 1 && F >= 0 && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] (?,1) 10. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [F >= 1 && 0 >= 1 + A && F >= 0 && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] (?,1) 11. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [F >= 1 && F >= 0 && 0 >= 2 + F && 0 >= B && F >= 1 + B && D = 0 && H = 0 && A = 0] (?,1) 12. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5,6},2->{},3->{3,4,5,6},4->{7,8,9,10,11},5->{7,8,9,10,11},6->{7,8,9,10,11},7->{2},8->{3,4,5 ,6},9->{7,8,9,10,11},10->{7,8,9,10,11},11->{7,8,9,10,11},12->{0,1}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [4,9,10,11] * 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) [1 >= A && B = C && D = E && F = G && H = A] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,G,H) [A >= 2 && B = C && D = E && F = G && H = A] (?,1) 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] (?,1) 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] (?,1) 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] (?,1) 6. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] (?,1) 7. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] (?,1) 8. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [F >= 1 && A >= F && F >= 0 && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] (?,1) 12. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,5,6},2->{},3->{3,5,6},5->{7,8},6->{7,8},7->{2},8->{3,5,6},12->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,6),(5,7),(8,6)] * 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) [1 >= A && B = C && D = E && F = G && H = A] (?,1) 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,G,H) [A >= 2 && B = C && D = E && F = G && H = A] (?,1) 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] (?,1) 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] (?,1) 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] (?,1) 6. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] (?,1) 7. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] (?,1) 8. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [F >= 1 && A >= F && F >= 0 && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] (?,1) 12. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,5},2->{},3->{3,5,6},5->{8},6->{7,8},7->{2},8->{3,5},12->{0,1}] + 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) [1 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,G,H) [A >= 2 && B = C && D = E && F = G && H = A] lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [F >= 1 && A >= F && F >= 0 && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{3,5},2->{},3->{3,5,6},5->{8},6->{7,8},7->{2},8->{3,5},12->{0,1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,5,6,7,8,12] | `- p:[3,8,5,6] c: [5,6,8] | `- p:[3] c: [3] * 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) [1 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,G,H) [A >= 2 && B = C && D = E && F = G && H = A] lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [F >= 1 && A >= F && F >= 0 && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{3,5},2->{},3->{3,5,6},5->{8},6->{7,8},7->{2},8->{3,5},12->{0,1}] ,We construct a looptree: P: [0,1,2,3,5,6,7,8,12] | `- p:[3,8,5,6] c: [5,6,8] | `- p:[3] c: [3]) + Applied Processor: CloseWith True + Details: () YES