YES * Step 1: UnsatRules YES + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A,1 + B,D,Z,D,A1,B,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) [A >= 1 + B && B >= 0] (?,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [B1 >= 1 + H && I >= 0 && A1 >= 1 + B1 && Z >= 2 && J = 0] (?,1) 2. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [B1 >= 1 + H && I >= 0 && B1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 3. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [H >= 1 + B1 && I >= 0 && A1 >= 1 + B1 && Z >= 2 && J = 0] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [H >= 1 + B1 && I >= 0 && B1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 5. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,G1,I,F1,Z,B1,C1,D1,E1,H1,A1,R,S,T,U,V,W,X,Y) [I >= 0 && 0 >= 1 + B1 && Z >= 2 && J = H] (?,1) 6. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,G1,I,F1,Z,B1,C1,D1,E1,H1,A1,R,S,T,U,V,W,X,Y) [I >= 0 && B1 >= 1 && Z >= 2 && J = H] (?,1) 7. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [C1 >= 1 + H && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] (?,1) 8. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [C1 >= 1 + H && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 9. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [H >= 1 + C1 && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] (?,1) 10. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [H >= 1 + C1 && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 11. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,F1,I,E1,Z,L,B1,C1,D1,G1,A1,R,S,T,U,V,W,X,Y) [Z >= 2 && R >= 0 && J = H] (?,1) 12. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(B1,D1,C1,K1,H1,F,G,P1,I,O1,A1,0,L1,M1,N1,Q1,F1,R,S,T,Z,E1,G1,X,Y) [0 >= I1 && 0 >= A1 && 0 >= J1] (1,1) 13. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A1,2,B1,C1,B1,F,G,H,I,J,A1,L,M,N,O,P,Q,R,S,T,Z,V,B1,D1,Y) [A1 >= 2] (1,1) 14. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && C >= 1 && C1 >= 0 && Z >= 2 && 0 >= 1 + C] (?,1) 15. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && C >= 1 && C1 >= 0 && Z >= 2] (?,1) 16. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && 0 >= 1 + C && C1 >= 0 && Z >= 2] (?,1) 17. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && 0 >= 1 + C && C1 >= 0 && Z >= 2 && C >= 1] (?,1) Signature: {(f1,25);(f10,25);(f7,25);(f8,25);(f9,25)} Flow Graph: [0->{0,14,15,16,17},1->{7,8,9,10,11},2->{7,8,9,10,11},3->{7,8,9,10,11},4->{7,8,9,10,11},5->{},6->{},7->{7 ,8,9,10,11},8->{7,8,9,10,11},9->{7,8,9,10,11},10->{7,8,9,10,11},11->{},12->{},13->{0,14,15,16,17},14->{7,8,9 ,10,11},15->{7,8,9,10,11},16->{7,8,9,10,11},17->{7,8,9,10,11}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [14,17] * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A,1 + B,D,Z,D,A1,B,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) [A >= 1 + B && B >= 0] (?,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [B1 >= 1 + H && I >= 0 && A1 >= 1 + B1 && Z >= 2 && J = 0] (?,1) 2. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [B1 >= 1 + H && I >= 0 && B1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 3. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [H >= 1 + B1 && I >= 0 && A1 >= 1 + B1 && Z >= 2 && J = 0] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [H >= 1 + B1 && I >= 0 && B1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 5. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,G1,I,F1,Z,B1,C1,D1,E1,H1,A1,R,S,T,U,V,W,X,Y) [I >= 0 && 0 >= 1 + B1 && Z >= 2 && J = H] (?,1) 6. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,G1,I,F1,Z,B1,C1,D1,E1,H1,A1,R,S,T,U,V,W,X,Y) [I >= 0 && B1 >= 1 && Z >= 2 && J = H] (?,1) 7. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [C1 >= 1 + H && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] (?,1) 8. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [C1 >= 1 + H && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 9. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [H >= 1 + C1 && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] (?,1) 10. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [H >= 1 + C1 && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 11. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,F1,I,E1,Z,L,B1,C1,D1,G1,A1,R,S,T,U,V,W,X,Y) [Z >= 2 && R >= 0 && J = H] (?,1) 12. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(B1,D1,C1,K1,H1,F,G,P1,I,O1,A1,0,L1,M1,N1,Q1,F1,R,S,T,Z,E1,G1,X,Y) [0 >= I1 && 0 >= A1 && 0 >= J1] (1,1) 13. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A1,2,B1,C1,B1,F,G,H,I,J,A1,L,M,N,O,P,Q,R,S,T,Z,V,B1,D1,Y) [A1 >= 2] (1,1) 15. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && C >= 1 && C1 >= 0 && Z >= 2] (?,1) 16. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && 0 >= 1 + C && C1 >= 0 && Z >= 2] (?,1) Signature: {(f1,25);(f10,25);(f7,25);(f8,25);(f9,25)} Flow Graph: [0->{0,15,16},1->{7,8,9,10,11},2->{7,8,9,10,11},3->{7,8,9,10,11},4->{7,8,9,10,11},5->{},6->{},7->{7,8,9,10 ,11},8->{7,8,9,10,11},9->{7,8,9,10,11},10->{7,8,9,10,11},11->{},12->{},13->{0,15,16},15->{7,8,9,10,11} ,16->{7,8,9,10,11}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(15,11),(16,11)] * Step 3: UnreachableRules YES + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A,1 + B,D,Z,D,A1,B,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) [A >= 1 + B && B >= 0] (?,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [B1 >= 1 + H && I >= 0 && A1 >= 1 + B1 && Z >= 2 && J = 0] (?,1) 2. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [B1 >= 1 + H && I >= 0 && B1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 3. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [H >= 1 + B1 && I >= 0 && A1 >= 1 + B1 && Z >= 2 && J = 0] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,R,S,T,U,V,W,X,Y) [H >= 1 + B1 && I >= 0 && B1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 5. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,G1,I,F1,Z,B1,C1,D1,E1,H1,A1,R,S,T,U,V,W,X,Y) [I >= 0 && 0 >= 1 + B1 && Z >= 2 && J = H] (?,1) 6. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,G1,I,F1,Z,B1,C1,D1,E1,H1,A1,R,S,T,U,V,W,X,Y) [I >= 0 && B1 >= 1 && Z >= 2 && J = H] (?,1) 7. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [C1 >= 1 + H && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] (?,1) 8. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [C1 >= 1 + H && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 9. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [H >= 1 + C1 && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] (?,1) 10. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [H >= 1 + C1 && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 11. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,F1,I,E1,Z,L,B1,C1,D1,G1,A1,R,S,T,U,V,W,X,Y) [Z >= 2 && R >= 0 && J = H] (?,1) 12. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(B1,D1,C1,K1,H1,F,G,P1,I,O1,A1,0,L1,M1,N1,Q1,F1,R,S,T,Z,E1,G1,X,Y) [0 >= I1 && 0 >= A1 && 0 >= J1] (1,1) 13. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A1,2,B1,C1,B1,F,G,H,I,J,A1,L,M,N,O,P,Q,R,S,T,Z,V,B1,D1,Y) [A1 >= 2] (1,1) 15. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && C >= 1 && C1 >= 0 && Z >= 2] (?,1) 16. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && 0 >= 1 + C && C1 >= 0 && Z >= 2] (?,1) Signature: {(f1,25);(f10,25);(f7,25);(f8,25);(f9,25)} Flow Graph: [0->{0,15,16},1->{7,8,9,10,11},2->{7,8,9,10,11},3->{7,8,9,10,11},4->{7,8,9,10,11},5->{},6->{},7->{7,8,9,10 ,11},8->{7,8,9,10,11},9->{7,8,9,10,11},10->{7,8,9,10,11},11->{},12->{},13->{0,15,16},15->{7,8,9,10},16->{7,8 ,9,10}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [1,2,3,4,5,6] * Step 4: FromIts YES + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A,1 + B,D,Z,D,A1,B,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) [A >= 1 + B && B >= 0] (?,1) 7. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [C1 >= 1 + H && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] (?,1) 8. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [C1 >= 1 + H && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 9. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [H >= 1 + C1 && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] (?,1) 10. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1,-1 + R,U,V,W,X,Y) [H >= 1 + C1 && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] (?,1) 11. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,F1,I,E1,Z,L,B1,C1,D1,G1,A1,R,S,T,U,V,W,X,Y) [Z >= 2 && R >= 0 && J = H] (?,1) 12. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(B1,D1,C1,K1,H1,F,G,P1,I,O1,A1,0,L1,M1,N1,Q1,F1,R,S,T,Z,E1,G1,X,Y) [0 >= I1 && 0 >= A1 && 0 >= J1] (1,1) 13. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A1,2,B1,C1,B1,F,G,H,I,J,A1,L,M,N,O,P,Q,R,S,T,Z,V,B1,D1,Y) [A1 >= 2] (1,1) 15. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && C >= 1 && C1 >= 0 && Z >= 2] (?,1) 16. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U,D1,F1,X,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && 0 >= 1 + C && C1 >= 0 && Z >= 2] (?,1) Signature: {(f1,25);(f10,25);(f7,25);(f8,25);(f9,25)} Flow Graph: [0->{0,15,16},7->{7,8,9,10,11},8->{7,8,9,10,11},9->{7,8,9,10,11},10->{7,8,9,10,11},11->{},12->{},13->{0,15 ,16},15->{7,8,9,10},16->{7,8,9,10}] + Applied Processor: FromIts + Details: () * Step 5: Decompose YES + Considered Problem: Rules: f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A,1 + B,D,Z,D,A1,B,H,I,J,K,L,M,N,O,P,Q,R,S,T ,U,V,W,X ,Y) [A >= 1 + B && B >= 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1 ,-1 + R,U,V,W,X ,Y) [C1 >= 1 + H && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1 ,-1 + R,U,V,W,X ,Y) [C1 >= 1 + H && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1 ,-1 + R,U,V,W,X ,Y) [H >= 1 + C1 && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1 ,-1 + R,U,V,W,X ,Y) [H >= 1 + C1 && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,F1,I,E1,Z,L,B1,C1,D1,G1,A1,R,S,T ,U,V,W,X ,Y) [Z >= 2 && R >= 0 && J = H] f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(B1,D1,C1,K1,H1,F,G,P1,I,O1,A1,0,L1,M1,N1,Q1,F1 ,R,S,T,Z,E1,G1,X ,Y) [0 >= I1 && 0 >= A1 && 0 >= J1] f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A1,2,B1,C1,B1,F,G,H,I,J,A1,L,M,N,O,P,Q,R,S,T,Z ,V,B1,D1 ,Y) [A1 >= 2] f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U ,D1,F1,X ,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && C >= 1 && C1 >= 0 && Z >= 2] f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U ,D1,F1,X ,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && 0 >= 1 + C && C1 >= 0 && Z >= 2] Signature: {(f1,25);(f10,25);(f7,25);(f8,25);(f9,25)} Rule Graph: [0->{0,15,16},7->{7,8,9,10,11},8->{7,8,9,10,11},9->{7,8,9,10,11},10->{7,8,9,10,11},11->{},12->{},13->{0,15 ,16},15->{7,8,9,10},16->{7,8,9,10}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,7,8,9,10,11,12,13,15,16] | +- p:[0] c: [0] | `- p:[7,8,9,10] c: [10] | `- p:[7,8,9] c: [9] | `- p:[7,8] c: [8] | `- p:[7] c: [7] * Step 6: CloseWith YES + Considered Problem: (Rules: f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A,1 + B,D,Z,D,A1,B,H,I,J,K,L,M,N,O,P,Q,R,S,T ,U,V,W,X ,Y) [A >= 1 + B && B >= 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1 ,-1 + R,U,V,W,X ,Y) [C1 >= 1 + H && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1 ,-1 + R,U,V,W,X ,Y) [C1 >= 1 + H && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1 ,-1 + R,U,V,W,X ,Y) [H >= 1 + C1 && R >= 0 && A1 >= 1 + C1 && Z >= 2 && J = 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A,B,C,D,E,F,G,H,I,0,Z,A1,A1,0,A1,H,Q,-1 + R,B1 ,-1 + R,U,V,W,X ,Y) [H >= 1 + C1 && R >= 0 && C1 >= 1 + A1 && Z >= 2 && J = 0] f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(A,B,C,D,E,F,G,F1,I,E1,Z,L,B1,C1,D1,G1,A1,R,S,T ,U,V,W,X ,Y) [Z >= 2 && R >= 0 && J = H] f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f10(B1,D1,C1,K1,H1,F,G,P1,I,O1,A1,0,L1,M1,N1,Q1,F1 ,R,S,T,Z,E1,G1,X ,Y) [0 >= I1 && 0 >= A1 && 0 >= J1] f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f1(A1,2,B1,C1,B1,F,G,H,I,J,A1,L,M,N,O,P,Q,R,S,T,Z ,V,B1,D1 ,Y) [A1 >= 2] f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U ,D1,F1,X ,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && C >= 1 && C1 >= 0 && Z >= 2] f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) -> f8(A1,C1,B1,H1,G1,F,G,C,R,0,Z,C,C,0,C,C,E1,R,S,T,U ,D1,F1,X ,1 + R) [K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && 0 >= 1 + C && C1 >= 0 && Z >= 2] Signature: {(f1,25);(f10,25);(f7,25);(f8,25);(f9,25)} Rule Graph: [0->{0,15,16},7->{7,8,9,10,11},8->{7,8,9,10,11},9->{7,8,9,10,11},10->{7,8,9,10,11},11->{},12->{},13->{0,15 ,16},15->{7,8,9,10},16->{7,8,9,10}] ,We construct a looptree: P: [0,7,8,9,10,11,12,13,15,16] | +- p:[0] c: [0] | `- p:[7,8,9,10] c: [10] | `- p:[7,8,9] c: [9] | `- p:[7,8] c: [8] | `- p:[7] c: [7]) + Applied Processor: CloseWith True + Details: () YES