/export/starexec/sandbox/solver/bin/starexec_run_hrs /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

******** General Schema criterion ********
Found constructors: xbminus, xbplus, xbtimes, 0, 1, cons, constant, false, nil, t, true
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>Regared as equal: filter2, filter
Checking  (1) d(t) => 1
 (fun d>1) >>True
Checking  (2) d(constant) => 0
 (fun d>0) >>True
Checking  (3) d(xbplus(X,Y)) => xbplus(d(X),d(Y))
 (fun d>xbplus)
 (fun d=d) subterm comparison of args w. LR LR
 (meta X)[is acc in xbplus(X,Y)] [is positive in xbplus(X,Y)] [is acc in X] 
 (fun d=d) subterm comparison of args w. LR LR
 (meta Y)[is acc in xbplus(X,Y)] [is positive in xbplus(X,Y)] [is acc in Y]  >>True
Checking  (4) d(xbtimes(U,V)) => xbplus(xbtimes(V,d(U)),xbtimes(U,d(V)))
 (fun d>xbplus)
 (fun d>xbtimes)
 (meta V)[is acc in xbtimes(U,V)] [is positive in xbtimes(U,V)] [is acc in V] 
 (fun d=d) subterm comparison of args w. LR LR
 (meta U)[is acc in xbtimes(U,V)] [is positive in xbtimes(U,V)] [is acc in U] 
 (fun d>xbtimes)
 (meta U)[is acc in xbtimes(U,V)] [is positive in xbtimes(U,V)] [is acc in U] 
 (fun d=d) subterm comparison of args w. LR LR
 (meta V)[is acc in xbtimes(U,V)] [is positive in xbtimes(U,V)] [is acc in V]  >>True
Checking  (5) d(xbminus(W,P)) => xbminus(d(W),d(P))
 (fun d>xbminus)
 (fun d=d) subterm comparison of args w. LR LR
 (meta W)[is acc in xbminus(W,P)] [is positive in xbminus(W,P)] [is acc in W] 
 (fun d=d) subterm comparison of args w. LR LR
 (meta P)[is acc in xbminus(W,P)] [is positive in xbminus(W,P)] [is acc in P]  >>True
Checking  (6) map(F1,nil) => nil
 (fun map>nil) >>True
Checking  (7) map(Z1,cons(U1,V1)) => cons(Z1[U1],map(Z1,V1))
 (fun map>cons)
 (meta Z1)[is acc in Z1,cons(U1,V1)] [is acc in Z1] 
 (meta U1)[is acc in Z1,cons(U1,V1)] [is positive in cons(U1,V1)] [is acc in U1] 
 (fun map=map) subterm comparison of args w. LR LR
 (meta Z1)[is acc in Z1,cons(U1,V1)] [is acc in Z1] 
 (meta V1)[is acc in Z1,cons(U1,V1)] [is positive in cons(U1,V1)] [is acc in V1]  >>True
Checking  (8) filter(I1,nil) => nil
 (fun filter>nil) >>True
Checking  (9) filter(J1,cons(X2,Y2)) => filter2(J1[X2],J1,X2,Y2)
 (fun filter=filter2) subterm comparison of args w. Arg [1,2] Arg [2,4,3,1]
 (meta J1)[is acc in J1,cons(X2,Y2)] [is acc in J1] 
 (meta X2)[is acc in J1,cons(X2,Y2)] [is positive in cons(X2,Y2)] [is acc in X2] 
 (meta J1)[is acc in J1,cons(X2,Y2)] [is acc in J1] 
 (meta X2)[is acc in J1,cons(X2,Y2)] [is positive in cons(X2,Y2)] [is acc in X2] 
 (meta Y2)[is acc in J1,cons(X2,Y2)] [is positive in cons(X2,Y2)] [is acc in Y2]  >>True
Checking  (10) filter2(true,G2,V2,W2) => cons(V2,filter(G2,W2))
 (fun filter2>cons)
 (meta V2)[is acc in true,G2,V2,W2] [is positive in true] [is acc in V2] 
 (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2]
 (meta G2)[is acc in true,G2,V2,W2] [is positive in true] [is acc in G2] 
 (meta W2)[is acc in true,G2,V2,W2] [is positive in true] [is acc in W2]  >>True
Checking  (11) filter2(false,J2,X3,Y3) => filter(J2,Y3)
 (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2]
 (meta J2)[is acc in false,J2,X3,Y3] [is positive in false] [is acc in J2] 
 (meta Y3)[is acc in false,J2,X3,Y3] [is positive in false] [is acc in Y3]  >>True
#SN!
******** Signature ********
 xbminus : (a,a) -> a
 xbplus : (a,a) -> a
 xbtimes : (a,a) -> a
 0 : a
 1 : a
 d : a -> a
 cons : (c,d) -> d
 constant : a
 false : b
 filter : ((c -> b),d) -> d
 filter2 : (b,(c -> b),c,d) -> d
 map : ((c -> c),d) -> d
 nil : d
 t : a
 true : b
******** Computation Rules ********
 (1)  d(t) => 1
 (2)  d(constant) => 0
 (3)  d(xbplus(X,Y)) => xbplus(d(X),d(Y))
 (4)  d(xbtimes(U,V)) => xbplus(xbtimes(V,d(U)),xbtimes(U,d(V)))
 (5)  d(xbminus(W,P)) => xbminus(d(W),d(P))
 (6)  map(F1,nil) => nil
 (7)  map(Z1,cons(U1,V1)) => cons(Z1[U1],map(Z1,V1))
 (8)  filter(I1,nil) => nil
 (9)  filter(J1,cons(X2,Y2)) => filter2(J1[X2],J1,X2,Y2)
 (10)  filter2(true,G2,V2,W2) => cons(V2,filter(G2,W2))
 (11)  filter2(false,J2,X3,Y3) => filter(J2,Y3)

YES