YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(1,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A = 1] (1,1) 1. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [0 >= A] (1,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 3. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f20(A,B,1 + B,S,T,1,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= B] (?,1) 4. f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f20(A,B,C,D + S*T,E + U*V,1 + F,G,H,I,J,K,L,M,N,O,P,Q,R) [B >= F] (?,1) 5. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1 + F,G,H,I,J,K,L,M,N,O,P,Q,R) [B >= F] (?,1) 6. f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1 + F,G + S*T,H + U*V,I + W*X,J,K,L,M,N,O,P,Q,R) [B >= F] (?,1) 7. f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f60(A,B,C,D,E,1 + F,G,H,I,J,-1 + K,S,T,U,V,K,Q,R) [J >= F] (?,1) 8. f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [F >= 1 + J] (?,1) 9. f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f60(A,B,C,D,E,1,G,H,I,S,B,L,M,N,O,P,T,U) [1 + B >= 2*V && 3*V >= 2 + B && V >= S && 1 + B >= 2*W && 3*W >= 2 + B && S >= W && F >= 1 + B] (?,1) 10. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,A,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [F >= 1 + B && A = C] (?,1) 11. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1,S,T,U,J,K,L,M,N,O,P,Q,R) [A >= 1 + C && F >= 1 + B] (?,1) 12. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1,S,T,U,J,K,L,M,N,O,P,Q,R) [C >= 1 + A && F >= 1 + B] (?,1) 13. f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1,G,H,I,J,K,L,M,N,O,P,Q,R) [0 >= 1 + E && F >= 1 + B] (?,1) 14. f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1,G,H,I,J,K,L,M,N,O,P,Q,R) [E >= 1 && F >= 1 + B] (?,1) 15. f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,0,1,G,H,I,J,K,L,M,N,O,P,Q,R) [F >= 1 + B && E = 0] (?,1) 16. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [B >= 1 + A] (?,1) Signature: {(f1,18);(f13,18);(f2,18);(f20,18);(f31,18);(f45,18);(f60,18)} Flow Graph: [0->{},1->{3,16},2->{3,16},3->{4,13,14,15},4->{4,13,14,15},5->{5,10,11,12},6->{6,9},7->{7,8},8->{3,16} ,9->{7,8},10->{},11->{6,9},12->{6,9},13->{5,10,11,12},14->{5,10,11,12},15->{5,10,11,12},16->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3),(2,16),(9,8),(11,9),(12,9)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(1,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A = 1] (1,1) 1. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [0 >= A] (1,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 3. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f20(A,B,1 + B,S,T,1,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= B] (?,1) 4. f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f20(A,B,C,D + S*T,E + U*V,1 + F,G,H,I,J,K,L,M,N,O,P,Q,R) [B >= F] (?,1) 5. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1 + F,G,H,I,J,K,L,M,N,O,P,Q,R) [B >= F] (?,1) 6. f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1 + F,G + S*T,H + U*V,I + W*X,J,K,L,M,N,O,P,Q,R) [B >= F] (?,1) 7. f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f60(A,B,C,D,E,1 + F,G,H,I,J,-1 + K,S,T,U,V,K,Q,R) [J >= F] (?,1) 8. f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [F >= 1 + J] (?,1) 9. f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f60(A,B,C,D,E,1,G,H,I,S,B,L,M,N,O,P,T,U) [1 + B >= 2*V && 3*V >= 2 + B && V >= S && 1 + B >= 2*W && 3*W >= 2 + B && S >= W && F >= 1 + B] (?,1) 10. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,A,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [F >= 1 + B && A = C] (?,1) 11. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1,S,T,U,J,K,L,M,N,O,P,Q,R) [A >= 1 + C && F >= 1 + B] (?,1) 12. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1,S,T,U,J,K,L,M,N,O,P,Q,R) [C >= 1 + A && F >= 1 + B] (?,1) 13. f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1,G,H,I,J,K,L,M,N,O,P,Q,R) [0 >= 1 + E && F >= 1 + B] (?,1) 14. f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1,G,H,I,J,K,L,M,N,O,P,Q,R) [E >= 1 && F >= 1 + B] (?,1) 15. f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,0,1,G,H,I,J,K,L,M,N,O,P,Q,R) [F >= 1 + B && E = 0] (?,1) 16. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [B >= 1 + A] (?,1) Signature: {(f1,18);(f13,18);(f2,18);(f20,18);(f31,18);(f45,18);(f60,18)} Flow Graph: [0->{},1->{16},2->{3},3->{4,13,14,15},4->{4,13,14,15},5->{5,10,11,12},6->{6,9},7->{7,8},8->{3,16},9->{7} ,10->{},11->{6},12->{6},13->{5,10,11,12},14->{5,10,11,12},15->{5,10,11,12},16->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(1,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [A = 1] f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [0 >= A] f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [A >= 2] f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f20(A,B,1 + B,S,T,1,G,H,I,J,K,L,M,N,O,P,Q ,R) [A >= B] f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f20(A,B,C,D + S*T,E + U*V,1 + F,G,H,I,J,K,L,M,N,O,P,Q ,R) [B >= F] f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1 + F,G,H,I,J,K,L,M,N,O,P,Q ,R) [B >= F] f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1 + F,G + S*T,H + U*V,I + W*X,J,K,L,M,N,O,P,Q ,R) [B >= F] f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f60(A,B,C,D,E,1 + F,G,H,I,J,-1 + K,S,T,U,V,K,Q ,R) [J >= F] f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [F >= 1 + J] f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f60(A,B,C,D,E,1,G,H,I,S,B,L,M,N,O,P,T ,U) [1 + B >= 2*V && 3*V >= 2 + B && V >= S && 1 + B >= 2*W && 3*W >= 2 + B && S >= W && F >= 1 + B] f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,A,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [F >= 1 + B && A = C] f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1,S,T,U,J,K,L,M,N,O,P,Q ,R) [A >= 1 + C && F >= 1 + B] f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1,S,T,U,J,K,L,M,N,O,P,Q ,R) [C >= 1 + A && F >= 1 + B] f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1,G,H,I,J,K,L,M,N,O,P,Q ,R) [0 >= 1 + E && F >= 1 + B] f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1,G,H,I,J,K,L,M,N,O,P,Q ,R) [E >= 1 && F >= 1 + B] f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,0,1,G,H,I,J,K,L,M,N,O,P,Q ,R) [F >= 1 + B && E = 0] f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [B >= 1 + A] Signature: {(f1,18);(f13,18);(f2,18);(f20,18);(f31,18);(f45,18);(f60,18)} Rule Graph: [0->{},1->{16},2->{3},3->{4,13,14,15},4->{4,13,14,15},5->{5,10,11,12},6->{6,9},7->{7,8},8->{3,16},9->{7} ,10->{},11->{6},12->{6},13->{5,10,11,12},14->{5,10,11,12},15->{5,10,11,12},16->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[3,8,7,9,6,11,5,13,4,14,15,12] c: [3,8] | +- p:[4] c: [4] | +- p:[5] c: [5] | +- p:[6] c: [6] | `- p:[7] c: [7] * Step 4: CloseWith YES + Considered Problem: (Rules: f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(1,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [A = 1] f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [0 >= A] f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [A >= 2] f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f20(A,B,1 + B,S,T,1,G,H,I,J,K,L,M,N,O,P,Q ,R) [A >= B] f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f20(A,B,C,D + S*T,E + U*V,1 + F,G,H,I,J,K,L,M,N,O,P,Q ,R) [B >= F] f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1 + F,G,H,I,J,K,L,M,N,O,P,Q ,R) [B >= F] f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1 + F,G + S*T,H + U*V,I + W*X,J,K,L,M,N,O,P,Q ,R) [B >= F] f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f60(A,B,C,D,E,1 + F,G,H,I,J,-1 + K,S,T,U,V,K,Q ,R) [J >= F] f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [F >= 1 + J] f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f60(A,B,C,D,E,1,G,H,I,S,B,L,M,N,O,P,T ,U) [1 + B >= 2*V && 3*V >= 2 + B && V >= S && 1 + B >= 2*W && 3*W >= 2 + B && S >= W && F >= 1 + B] f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,A,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [F >= 1 + B && A = C] f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1,S,T,U,J,K,L,M,N,O,P,Q ,R) [A >= 1 + C && F >= 1 + B] f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f45(A,B,C,D,E,1,S,T,U,J,K,L,M,N,O,P,Q ,R) [C >= 1 + A && F >= 1 + B] f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1,G,H,I,J,K,L,M,N,O,P,Q ,R) [0 >= 1 + E && F >= 1 + B] f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,E,1,G,H,I,J,K,L,M,N,O,P,Q ,R) [E >= 1 && F >= 1 + B] f20(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f31(A,B,C,D,0,1,G,H,I,J,K,L,M,N,O,P,Q ,R) [F >= 1 + B && E = 0] f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q ,R) [B >= 1 + A] Signature: {(f1,18);(f13,18);(f2,18);(f20,18);(f31,18);(f45,18);(f60,18)} Rule Graph: [0->{},1->{16},2->{3},3->{4,13,14,15},4->{4,13,14,15},5->{5,10,11,12},6->{6,9},7->{7,8},8->{3,16},9->{7} ,10->{},11->{6},12->{6},13->{5,10,11,12},14->{5,10,11,12},15->{5,10,11,12},16->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[3,8,7,9,6,11,5,13,4,14,15,12] c: [3,8] | +- p:[4] c: [4] | +- p:[5] c: [5] | +- p:[6] c: [6] | `- p:[7] c: [7]) + Applied Processor: CloseWith True + Details: () YES