/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES ******** General Schema criterion ******** Found constructors: 1, cons, false, nil, true Checking type order >>OK Checking positivity of constructors >>OK Checking function dependency >>Regared as equal: filter2, filter Checking (1) xbdot(1,X) => X (meta X)[is acc in 1,X] [is positive in 1] [is acc in X] >>True Checking (2) xbdot(Y,1) => Y (meta Y)[is acc in Y,1] [is acc in Y] >>True Checking (3) xbdot(i(U),U) => 1 (fun xbdot>1) >>True Checking (4) xbdot(V,i(V)) => 1 (fun xbdot>1) >>True Checking (5) xbdot(i(W),xbdot(W,P)) => P (meta P)[is acc in i(W),xbdot(W,P)] [is positive in i(W)] [is positive in xbdot(W,P)] [is acc in P] >>True Checking (6) xbdot(X1,xbdot(i(X1),Y1)) => Y1 (meta Y1)[is acc in X1,xbdot(i(X1),Y1)] [is positive in xbdot(i(X1),Y1)] [is acc in Y1] >>True Checking (7) xbdot(xbdot(U1,V1),W1) => xbdot(U1,xbdot(V1,W1)) (fun xbdot=xbdot) subterm comparison of args w. LR LR (meta U1)[is acc in xbdot(U1,V1),W1] [is positive in xbdot(U1,V1)] [is acc in U1] (fun xbdot=xbdot) subterm comparison of args w. LR LR (meta V1)[is acc in xbdot(U1,V1),W1] [is positive in xbdot(U1,V1)] [is acc in V1] (meta W1)[is acc in xbdot(U1,V1),W1] [is positive in xbdot(U1,V1)] [is acc in W1] >>True Checking (8) i(1) => 1 (fun i>1) >>True Checking (9) i(i(P1)) => P1 (meta P1)[is acc in i(P1)] [is positive in i(P1)] [is acc in P1] >>True Checking (10) i(xbdot(X2,Y2)) => xbdot(i(Y2),i(X2)) (fun i>xbdot) (fun i=i) subterm comparison of args w. LR LR (meta Y2)[is acc in xbdot(X2,Y2)] [is positive in xbdot(X2,Y2)] [is acc in Y2] (fun i=i) subterm comparison of args w. LR LR (meta X2)[is acc in xbdot(X2,Y2)] [is positive in xbdot(X2,Y2)] [is acc in X2] >>True Checking (11) map(G2,nil) => nil (fun map>nil) >>True Checking (12) map(H2,cons(W2,P2)) => cons(H2[W2],map(H2,P2)) (fun map>cons) (meta H2)[is acc in H2,cons(W2,P2)] [is acc in H2] (meta W2)[is acc in H2,cons(W2,P2)] [is positive in cons(W2,P2)] [is acc in W2] (fun map=map) subterm comparison of args w. LR LR (meta H2)[is acc in H2,cons(W2,P2)] [is acc in H2] (meta P2)[is acc in H2,cons(W2,P2)] [is positive in cons(W2,P2)] [is acc in P2] >>True Checking (13) filter(F3,nil) => nil (fun filter>nil) >>True Checking (14) filter(Z3,cons(U3,V3)) => filter2(Z3[U3],Z3,U3,V3) (fun filter=filter2) subterm comparison of args w. Arg [1,2] Arg [2,4,3,1] (meta Z3)[is acc in Z3,cons(U3,V3)] [is acc in Z3] (meta U3)[is acc in Z3,cons(U3,V3)] [is positive in cons(U3,V3)] [is acc in U3] (meta Z3)[is acc in Z3,cons(U3,V3)] [is acc in Z3] (meta U3)[is acc in Z3,cons(U3,V3)] [is positive in cons(U3,V3)] [is acc in U3] (meta V3)[is acc in Z3,cons(U3,V3)] [is positive in cons(U3,V3)] [is acc in V3] >>True Checking (15) filter2(true,I3,P3,X4) => cons(P3,filter(I3,X4)) (fun filter2>cons) (meta P3)[is acc in true,I3,P3,X4] [is positive in true] [is acc in P3] (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2] (meta I3)[is acc in true,I3,P3,X4] [is positive in true] [is acc in I3] (meta X4)[is acc in true,I3,P3,X4] [is positive in true] [is acc in X4] >>True Checking (16) filter2(false,Z4,U4,V4) => filter(Z4,V4) (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2] (meta Z4)[is acc in false,Z4,U4,V4] [is positive in false] [is acc in Z4] (meta V4)[is acc in false,Z4,U4,V4] [is positive in false] [is acc in V4] >>True #SN! ******** Signature ******** xbdot : (a,a) -> a 1 : a cons : (c,d) -> d false : b filter : ((c -> b),d) -> d filter2 : (b,(c -> b),c,d) -> d i : a -> a map : ((c -> c),d) -> d nil : d true : b ******** Computation Rules ******** (1) xbdot(1,X) => X (2) xbdot(Y,1) => Y (3) xbdot(i(U),U) => 1 (4) xbdot(V,i(V)) => 1 (5) xbdot(i(W),xbdot(W,P)) => P (6) xbdot(X1,xbdot(i(X1),Y1)) => Y1 (7) xbdot(xbdot(U1,V1),W1) => xbdot(U1,xbdot(V1,W1)) (8) i(1) => 1 (9) i(i(P1)) => P1 (10) i(xbdot(X2,Y2)) => xbdot(i(Y2),i(X2)) (11) map(G2,nil) => nil (12) map(H2,cons(W2,P2)) => cons(H2[W2],map(H2,P2)) (13) filter(F3,nil) => nil (14) filter(Z3,cons(U3,V3)) => filter2(Z3[U3],Z3,U3,V3) (15) filter2(true,I3,P3,X4) => cons(P3,filter(I3,X4)) (16) filter2(false,Z4,U4,V4) => filter(Z4,V4) YES