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


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YES

******** General Schema criterion ********
Found constructors: 0, cons, false, nil, s, true
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>Regared as equal: filter2, filter
Checking  (1) p(0) => 0
 (fun p>0) >>True
Checking  (2) p(s(X)) => X
 (meta X)[is acc in s(X)] [is positive in s(X)] [is acc in X]  >>True
Checking  (3) le(0,Y) => true
 (fun le>true) >>True
Checking  (4) le(s(U),0) => false
 (fun le>false) >>True
Checking  (5) le(s(V),s(W)) => le(V,W)
 (fun le=le) subterm comparison of args w. LR LR
 (meta V)[is acc in s(V),s(W)] [is positive in s(V)] [is acc in V] 
 (meta W)[is acc in s(V),s(W)] [is positive in s(V)] [is positive in s(W)] [is acc in W]  >>True
Checking  (6) minus(P,X1) => if(le(P,X1),P,X1)
 (fun minus>if)
 (fun minus>le)
 (meta P)[is acc in P,X1] [is acc in P] 
 (meta X1)[is acc in P,X1] [is acc in X1] 
 (meta P)[is acc in P,X1] [is acc in P] 
 (meta X1)[is acc in P,X1] [is acc in X1]  >>True
Checking  (7) if(true,Y1,U1) => 0
 (fun if>0) >>True
Checking  (8) if(false,V1,W1) => s(minus(p(V1),W1))
 (fun if>s)
 (fun if>minus)
 (fun if>p)
 (meta V1)[is acc in false,V1,W1] [is positive in false] [is acc in V1] 
 (meta W1)[is acc in false,V1,W1] [is positive in false] [is acc in W1]  >>True
Checking  (9) map(J1,nil) => nil
 (fun map>nil) >>True
Checking  (10) map(F2,cons(Y2,U2)) => cons(F2[Y2],map(F2,U2))
 (fun map>cons)
 (meta F2)[is acc in F2,cons(Y2,U2)] [is acc in F2] 
 (meta Y2)[is acc in F2,cons(Y2,U2)] [is positive in cons(Y2,U2)] [is acc in Y2] 
 (fun map=map) subterm comparison of args w. LR LR
 (meta F2)[is acc in F2,cons(Y2,U2)] [is acc in F2] 
 (meta U2)[is acc in F2,cons(Y2,U2)] [is positive in cons(Y2,U2)] [is acc in U2]  >>True
Checking  (11) filter(H2,nil) => nil
 (fun filter>nil) >>True
Checking  (12) filter(I2,cons(P2,X3)) => filter2(I2[P2],I2,P2,X3)
 (fun filter=filter2) subterm comparison of args w. Arg [1,2] Arg [2,4,3,1]
 (meta I2)[is acc in I2,cons(P2,X3)] [is acc in I2] 
 (meta P2)[is acc in I2,cons(P2,X3)] [is positive in cons(P2,X3)] [is acc in P2] 
 (meta I2)[is acc in I2,cons(P2,X3)] [is acc in I2] 
 (meta P2)[is acc in I2,cons(P2,X3)] [is positive in cons(P2,X3)] [is acc in P2] 
 (meta X3)[is acc in I2,cons(P2,X3)] [is positive in cons(P2,X3)] [is acc in X3]  >>True
Checking  (13) filter2(true,Z3,U3,V3) => cons(U3,filter(Z3,V3))
 (fun filter2>cons)
 (meta U3)[is acc in true,Z3,U3,V3] [is positive in true] [is acc in U3] 
 (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2]
 (meta Z3)[is acc in true,Z3,U3,V3] [is positive in true] [is acc in Z3] 
 (meta V3)[is acc in true,Z3,U3,V3] [is positive in true] [is acc in V3]  >>True
Checking  (14) filter2(false,I3,P3,X4) => filter(I3,X4)
 (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2]
 (meta I3)[is acc in false,I3,P3,X4] [is positive in false] [is acc in I3] 
 (meta X4)[is acc in false,I3,P3,X4] [is positive in false] [is acc in X4]  >>True
#SN!
******** Signature ********
 0 : b
 cons : (c,d) -> d
 false : a
 filter : ((c -> a),d) -> d
 filter2 : (a,(c -> a),c,d) -> d
 if : (a,b,b) -> b
 le : (b,b) -> a
 map : ((c -> c),d) -> d
 minus : (b,b) -> b
 nil : d
 p : b -> b
 s : b -> b
 true : a
******** Computation Rules ********
 (1)  p(0) => 0
 (2)  p(s(X)) => X
 (3)  le(0,Y) => true
 (4)  le(s(U),0) => false
 (5)  le(s(V),s(W)) => le(V,W)
 (6)  minus(P,X1) => if(le(P,X1),P,X1)
 (7)  if(true,Y1,U1) => 0
 (8)  if(false,V1,W1) => s(minus(p(V1),W1))
 (9)  map(J1,nil) => nil
 (10)  map(F2,cons(Y2,U2)) => cons(F2[Y2],map(F2,U2))
 (11)  filter(H2,nil) => nil
 (12)  filter(I2,cons(P2,X3)) => filter2(I2[P2],I2,P2,X3)
 (13)  filter2(true,Z3,U3,V3) => cons(U3,filter(Z3,V3))
 (14)  filter2(false,I3,P3,X4) => filter(I3,X4)

YES