YES * Step 1: UnreachableRules YES + Considered Problem: Rules: 0. f12(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(A,1,M1,O1,P1,1 + G,G,Q1,G,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) [A >= 0 && M1 >= 2 && N1 >= M1 && B = 1] (?,1) 1. f13(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(A,B,M1,O1,E,F,G,H,I,P1,Q1,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) [M1 >= 2 && I >= 0] (?,1) 2. f16(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(A,1 + B,M1,O1,P1,F,-1 + G,H,I,J,K,M,M,Q1,1 + B,-1 + G,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1[B >= 0 && G >= 0 && M1 >= 2] (?,1) ,J1,K1,L1) 3. 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f1(1 + A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,S,M1,S,O1,A,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) [Q >= 1 + A && A >= 0] (?,1) 4. 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(G,0,M1,R,E,F,G,H,I,J,K,L,R,N,O,P,O1,P1,S1,N1,U,V,Q1,T1,U1,R1,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) [A >= Q && A >= 0 && M1 >= 2 && R1 >= M1 && G >= M1 && B = 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A,B,M1,O1,E,F,G,H,I,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,0,O1,0,O1,G1,G1,H1,I1,J1,K1,L1) [M1 >= 2 && A1 >= 0 && B1 = 0] (?,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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(A,B,M1,T1,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,U1,Z,A1,N1,O1,P1,Q1,R1,S1,H1,I1,J1,K1,L1) [M1 >= 2 && A1 >= 0 && B1 = G1] (?,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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A,B,M1,O1,P1,F,G,H,I,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,0,O1,0,O1,G1,G1,-1 + H1,-1 + H1,J1,K1,L1) [M1 >= 2 && H1 >= 0 && B1 = 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(A,B,M1,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,T1,Z,A1,N1,O1,P1,Q1,U1,S1,H1,I1,J1,K1,L1) [M1 >= 2 && H1 >= 0 && B1 = G1] (?,1) 9. f13(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A,1 + H1,M1,D,E,F,G,H,0,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,H1,0,D,0,D,D,D,H1,I1,J1,K1,L1) [O1 >= 2 && M1 >= 2 && M = 0 && I = 0 && B = 1] (?,1) 10. f16(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A,1 + H1,M1,D,E,F,G,H,I,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,H1,0,D,0,D,D,D,H1,I1,J1,K1,L1) [O1 >= 2 && M1 >= 2 && B >= 0 && G >= 0 && M = 0] (?,1) 11. 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f1(2,B,M1,D,E,F,G,H,I,J,K,L,M,N,O,P,M1,P1,Q1,P1,U,V,P1,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,O1,N1,2) [M1 >= 2] (1,1) 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(T1,B,M1,0,E,F,G,H,I,J,K,L,0,N,O,P,R1,Y1,B2,A2,U,V,Z1,C2,D2,Z,A1,N1,O1,P1,Q1,E2,S1,H1,I1,U1,K1,L1) [0 >= V1 && 0 >= W1 && 0 >= M1 && 0 >= X1] (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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(T1,B,1,S1,E,F,G,H,I,J,K,L,0,N,O,P,R1,Y1,B2,A2,U,V,Z1,C2,D2,Z,A1,Q1,M1,O1,P1,E2,N1,H1,I1,U1,K1,L1) [S = 0] (1,1) Signature: {(f1,38);(f10,38);(f12,38);(f13,38);(f16,38);(f7,38);(f8,38);(f9,38)} Flow Graph: [0->{2,10},1->{2,10},2->{2,10},3->{3,4},4->{2,10},5->{7,8},6->{},7->{7,8},8->{},9->{7,8},10->{7,8},11->{3 ,4},12->{},13->{}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [0,1,5,6,9] * Step 2: FromIts YES + Considered Problem: Rules: 2. f16(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(A,1 + B,M1,O1,P1,F,-1 + G,H,I,J,K,M,M,Q1,1 + B,-1 + G,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1[B >= 0 && G >= 0 && M1 >= 2] (?,1) ,J1,K1,L1) 3. 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f1(1 + A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,S,M1,S,O1,A,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) [Q >= 1 + A && A >= 0] (?,1) 4. 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(G,0,M1,R,E,F,G,H,I,J,K,L,R,N,O,P,O1,P1,S1,N1,U,V,Q1,T1,U1,R1,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) [A >= Q && A >= 0 && M1 >= 2 && R1 >= M1 && G >= M1 && 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A,B,M1,O1,P1,F,G,H,I,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,0,O1,0,O1,G1,G1,-1 + H1,-1 + H1,J1,K1,L1) [M1 >= 2 && H1 >= 0 && B1 = 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(A,B,M1,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,T1,Z,A1,N1,O1,P1,Q1,U1,S1,H1,I1,J1,K1,L1) [M1 >= 2 && H1 >= 0 && B1 = G1] (?,1) 10. f16(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A,1 + H1,M1,D,E,F,G,H,I,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,H1,0,D,0,D,D,D,H1,I1,J1,K1,L1) [O1 >= 2 && M1 >= 2 && B >= 0 && G >= 0 && M = 0] (?,1) 11. 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f1(2,B,M1,D,E,F,G,H,I,J,K,L,M,N,O,P,M1,P1,Q1,P1,U,V,P1,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,O1,N1,2) [M1 >= 2] (1,1) 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(T1,B,M1,0,E,F,G,H,I,J,K,L,0,N,O,P,R1,Y1,B2,A2,U,V,Z1,C2,D2,Z,A1,N1,O1,P1,Q1,E2,S1,H1,I1,U1,K1,L1) [0 >= V1 && 0 >= W1 && 0 >= M1 && 0 >= X1] (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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(T1,B,1,S1,E,F,G,H,I,J,K,L,0,N,O,P,R1,Y1,B2,A2,U,V,Z1,C2,D2,Z,A1,Q1,M1,O1,P1,E2,N1,H1,I1,U1,K1,L1) [S = 0] (1,1) Signature: {(f1,38);(f10,38);(f12,38);(f13,38);(f16,38);(f7,38);(f8,38);(f9,38)} Flow Graph: [2->{2,10},3->{3,4},4->{2,10},7->{7,8},8->{},10->{7,8},11->{3,4},12->{},13->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f16(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(A ,1 + B,M1,O1,P1,F,-1 + G,H,I,J,K,M,M,Q1,1 + B,-1 + G,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1 ,L1) [B >= 0 && G >= 0 && M1 >= 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f1(1 + A,B ,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,S,M1,S,O1,A,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1 ,L1) [Q >= 1 + A && A >= 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(G,0,M1 ,R,E,F,G,H,I,J,K,L,R,N,O,P,O1,P1,S1,N1,U,V,Q1,T1,U1,R1,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1 ,L1) [A >= Q && A >= 0 && M1 >= 2 && R1 >= M1 && G >= M1 && 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A,B,M1 ,O1,P1,F,G,H,I,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,0,O1,0,O1,G1,G1,-1 + H1,-1 + H1,J1,K1 ,L1) [M1 >= 2 && H1 >= 0 && B1 = 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(A,B,M1 ,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,T1,Z,A1,N1,O1,P1,Q1,U1,S1,H1,I1,J1,K1 ,L1) [M1 >= 2 && H1 >= 0 && B1 = G1] f16(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A ,1 + H1,M1,D,E,F,G,H,I,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,H1,0,D,0,D,D,D,H1,I1,J1,K1 ,L1) [O1 >= 2 && M1 >= 2 && B >= 0 && G >= 0 && M = 0] 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f1(2,B,M1 ,D,E,F,G,H,I,J,K,L,M,N,O,P,M1,P1,Q1,P1,U,V,P1,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,O1,N1 ,2) [M1 >= 2] 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(T1,B ,M1,0,E,F,G,H,I,J,K,L,0,N,O,P,R1,Y1,B2,A2,U,V,Z1,C2,D2,Z,A1,N1,O1,P1,Q1,E2,S1,H1,I1,U1,K1 ,L1) [0 >= V1 && 0 >= W1 && 0 >= M1 && 0 >= X1] 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(T1,B,1 ,S1,E,F,G,H,I,J,K,L,0,N,O,P,R1,Y1,B2,A2,U,V,Z1,C2,D2,Z,A1,Q1,M1,O1,P1,E2,N1,H1,I1,U1,K1 ,L1) [S = 0] Signature: {(f1,38);(f10,38);(f12,38);(f13,38);(f16,38);(f7,38);(f8,38);(f9,38)} Rule Graph: [2->{2,10},3->{3,4},4->{2,10},7->{7,8},8->{},10->{7,8},11->{3,4},12->{},13->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [2,3,4,7,8,10,11,12,13] | +- p:[3] c: [3] | +- p:[2] c: [2] | `- p:[7] c: [7] * Step 4: CloseWith YES + Considered Problem: (Rules: f16(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(A ,1 + B,M1,O1,P1,F,-1 + G,H,I,J,K,M,M,Q1,1 + B,-1 + G,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1 ,L1) [B >= 0 && G >= 0 && M1 >= 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f1(1 + A,B ,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,S,M1,S,O1,A,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1 ,L1) [Q >= 1 + A && A >= 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f16(G,0,M1 ,R,E,F,G,H,I,J,K,L,R,N,O,P,O1,P1,S1,N1,U,V,Q1,T1,U1,R1,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1 ,L1) [A >= Q && A >= 0 && M1 >= 2 && R1 >= M1 && G >= M1 && 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A,B,M1 ,O1,P1,F,G,H,I,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,0,O1,0,O1,G1,G1,-1 + H1,-1 + H1,J1,K1 ,L1) [M1 >= 2 && H1 >= 0 && B1 = 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(A,B,M1 ,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,T1,Z,A1,N1,O1,P1,Q1,U1,S1,H1,I1,J1,K1 ,L1) [M1 >= 2 && H1 >= 0 && B1 = G1] f16(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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f8(A ,1 + H1,M1,D,E,F,G,H,I,J,K,L,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,H1,0,D,0,D,D,D,H1,I1,J1,K1 ,L1) [O1 >= 2 && M1 >= 2 && B >= 0 && G >= 0 && M = 0] 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f1(2,B,M1 ,D,E,F,G,H,I,J,K,L,M,N,O,P,M1,P1,Q1,P1,U,V,P1,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,O1,N1 ,2) [M1 >= 2] 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(T1,B ,M1,0,E,F,G,H,I,J,K,L,0,N,O,P,R1,Y1,B2,A2,U,V,Z1,C2,D2,Z,A1,N1,O1,P1,Q1,E2,S1,H1,I1,U1,K1 ,L1) [0 >= V1 && 0 >= W1 && 0 >= M1 && 0 >= X1] 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) -> f10(T1,B,1 ,S1,E,F,G,H,I,J,K,L,0,N,O,P,R1,Y1,B2,A2,U,V,Z1,C2,D2,Z,A1,Q1,M1,O1,P1,E2,N1,H1,I1,U1,K1 ,L1) [S = 0] Signature: {(f1,38);(f10,38);(f12,38);(f13,38);(f16,38);(f7,38);(f8,38);(f9,38)} Rule Graph: [2->{2,10},3->{3,4},4->{2,10},7->{7,8},8->{},10->{7,8},11->{3,4},12->{},13->{}] ,We construct a looptree: P: [2,3,4,7,8,10,11,12,13] | +- p:[3] c: [3] | +- p:[2] c: [2] | `- p:[7] c: [7]) + Applied Processor: CloseWith True + Details: () YES