/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: cons, false, nil, or, true
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>Regared as equal: filter2, filter
Checking  (1) not(not(X)) => X
 (meta X)[is acc in not(X)] [is positive in not(X)] [is acc in X]  >>True
Checking  (2) not(or(Y,U)) => and(not(Y),not(U))
 (fun not>and)
 (fun not=not) subterm comparison of args w. LR LR
 (meta Y)[is acc in or(Y,U)] [is positive in or(Y,U)] [is acc in Y] 
 (fun not=not) subterm comparison of args w. LR LR
 (meta U)[is acc in or(Y,U)] [is positive in or(Y,U)] [is acc in U]  >>True
Checking  (3) not(and(V,W)) => or(not(V),not(W))
 (fun not>or)
 (fun not=not) subterm comparison of args w. LR LR
 (meta V)[is acc in and(V,W)] [is positive in and(V,W)] [is acc in V] 
 (fun not=not) subterm comparison of args w. LR LR
 (meta W)[is acc in and(V,W)] [is positive in and(V,W)] [is acc in W]  >>True
Checking  (4) and(P,or(X1,Y1)) => or(and(P,X1),and(P,Y1))
 (fun and>or)
 (fun and=and) subterm comparison of args w. LR LR
 (meta P)[is acc in P,or(X1,Y1)] [is acc in P] 
 (meta X1)[is acc in P,or(X1,Y1)] [is positive in or(X1,Y1)] [is acc in X1] 
 (fun and=and) subterm comparison of args w. LR LR
 (meta P)[is acc in P,or(X1,Y1)] [is acc in P] 
 (meta Y1)[is acc in P,or(X1,Y1)] [is positive in or(X1,Y1)] [is acc in Y1]  >>True
Checking  (5) and(or(V1,W1),U1) => or(and(U1,V1),and(U1,W1))
 (fun and>or)
 (fun and=and) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) not(not(X)) => X
 (meta X)[is acc in not(X)] [is positive in not(X)] [is acc in X]  >>True
Checking  (2) not(or(Y,U)) => and(not(Y),not(U))
 (fun not>and)
 (fun not=not) subterm comparison of args w. RL RL
 (meta Y)[is acc in or(Y,U)] [is positive in or(Y,U)] [is acc in Y] 
 (fun not=not) subterm comparison of args w. RL RL
 (meta U)[is acc in or(Y,U)] [is positive in or(Y,U)] [is acc in U]  >>True
Checking  (3) not(and(V,W)) => or(not(V),not(W))
 (fun not>or)
 (fun not=not) subterm comparison of args w. RL RL
 (meta V)[is acc in and(V,W)] [is positive in and(V,W)] [is acc in V] 
 (fun not=not) subterm comparison of args w. RL RL
 (meta W)[is acc in and(V,W)] [is positive in and(V,W)] [is acc in W]  >>True
Checking  (4) and(P,or(X1,Y1)) => or(and(P,X1),and(P,Y1))
 (fun and>or)
 (fun and=and) subterm comparison of args w. RL RL
 (meta P)[is acc in P,or(X1,Y1)] [is acc in P] 
 (meta X1)[is acc in P,or(X1,Y1)] [is positive in or(X1,Y1)] [is acc in X1] 
 (fun and=and) subterm comparison of args w. RL RL
 (meta P)[is acc in P,or(X1,Y1)] [is acc in P] 
 (meta Y1)[is acc in P,or(X1,Y1)] [is positive in or(X1,Y1)] [is acc in Y1]  >>True
Checking  (5) and(or(V1,W1),U1) => or(and(U1,V1),and(U1,W1))
 (fun and>or)
 (fun and=and) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (1) not(not(X)) => X
 (meta X)[is acc in not(X)] [is positive in not(X)] [is acc in X]  >>True
Checking  (2) not(or(Y,U)) => and(not(Y),not(U))
 (fun not>and)
 (fun not=not) subterm comparison of args w. Mul Mul
 (meta Y)[is acc in or(Y,U)] [is positive in or(Y,U)] [is acc in Y] 
 (fun not=not) subterm comparison of args w. Mul Mul
 (meta U)[is acc in or(Y,U)] [is positive in or(Y,U)] [is acc in U]  >>True
Checking  (3) not(and(V,W)) => or(not(V),not(W))
 (fun not>or)
 (fun not=not) subterm comparison of args w. Mul Mul
 (meta V)[is acc in and(V,W)] [is positive in and(V,W)] [is acc in V] 
 (fun not=not) subterm comparison of args w. Mul Mul
 (meta W)[is acc in and(V,W)] [is positive in and(V,W)] [is acc in W]  >>True
Checking  (4) and(P,or(X1,Y1)) => or(and(P,X1),and(P,Y1))
 (fun and>or)
 (fun and=and) subterm comparison of args w. Mul Mul
 (meta P)[is acc in P,or(X1,Y1)] [is acc in P] 
 (meta X1)[is acc in P,or(X1,Y1)] [is positive in or(X1,Y1)] [is acc in X1] 
 (fun and=and) subterm comparison of args w. Mul Mul
 (meta P)[is acc in P,or(X1,Y1)] [is acc in P] 
 (meta Y1)[is acc in P,or(X1,Y1)] [is positive in or(X1,Y1)] [is acc in Y1]  >>True
Checking  (5) and(or(V1,W1),U1) => or(and(U1,V1),and(U1,W1))
 (fun and>or)
 (fun and=and) subterm comparison of args w. Mul Mul
 (meta U1)[is acc in or(V1,W1),U1] [is positive in or(V1,W1)] [is acc in U1] 
 (meta V1)[is acc in or(V1,W1),U1] [is positive in or(V1,W1)] [is acc in V1] 
 (fun and=and) subterm comparison of args w. Mul Mul
 (meta U1)[is acc in or(V1,W1),U1] [is positive in or(V1,W1)] [is acc in U1] 
 (meta W1)[is acc in or(V1,W1),U1] [is positive in or(V1,W1)] [is acc in W1]  >>True
Checking  (6) map(J1,nil) => nil
 (fun map>nil) >>True
Checking  (7) 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. Mul Mul
 (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  (8) filter(H2,nil) => nil
 (fun filter>nil) >>True
Checking  (9) 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  (10) 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  (11) 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 ********
 and : (a,a) -> a
 cons : (c,d) -> d
 false : b
 filter : ((c -> b),d) -> d
 filter2 : (b,(c -> b),c,d) -> d
 map : ((c -> c),d) -> d
 nil : d
 not : a -> a
 or : (a,a) -> a
 true : b
******** Computation Rules ********
 (1)  not(not(X)) => X
 (2)  not(or(Y,U)) => and(not(Y),not(U))
 (3)  not(and(V,W)) => or(not(V),not(W))
 (4)  and(P,or(X1,Y1)) => or(and(P,X1),and(P,Y1))
 (5)  and(or(V1,W1),U1) => or(and(U1,V1),and(U1,W1))
 (6)  map(J1,nil) => nil
 (7)  map(F2,cons(Y2,U2)) => cons(F2[Y2],map(F2,U2))
 (8)  filter(H2,nil) => nil
 (9)  filter(I2,cons(P2,X3)) => filter2(I2[P2],I2,P2,X3)
 (10)  filter2(true,Z3,U3,V3) => cons(U3,filter(Z3,V3))
 (11)  filter2(false,I3,P3,X4) => filter(I3,X4)

YES