/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) minus(X,0) => X
 (meta X)[is acc in X,0] [is acc in X]  >>True
Checking  (2) minus(s(Y),s(U)) => minus(Y,U)
 (fun minus=minus) subterm comparison of args w. LR LR
 (meta Y)[is acc in s(Y),s(U)] [is positive in s(Y)] [is acc in Y] 
 (meta U)[is acc in s(Y),s(U)] [is positive in s(Y)] [is positive in s(U)] [is acc in U]  >>True
Checking  (3) f(0) => s(0)
 (fun f>s)
 (fun f>0) >>True
Checking  (4) f(s(V)) => minus(s(V),g(f(V)))
 (fun f>minus)
 (fun f>s)
 (meta V)[is acc in s(V)] [is positive in s(V)] [is acc in V] 
 (fun f>g)
 (fun f=f) subterm comparison of args w. LR LR
 (meta V)[is acc in s(V)] [is positive in s(V)] [is acc in V]  >>True
Checking  (5) g(0) => 0
 (fun g>0) >>True
Checking  (6) g(s(W)) => minus(s(W),f(g(W)))
 (fun g>minus)
 (fun g>s)
 (meta W)[is acc in s(W)] [is positive in s(W)] [is acc in W] 
 (fun g>f)
 (fun g=g) subterm comparison of args w. LR LR
 (meta W)[is acc in s(W)] [is positive in s(W)] [is acc in W]  >>True
Checking  (7) map(J,nil) => nil
 (fun map>nil) >>True
Checking  (8) map(F1,cons(Y1,U1)) => cons(F1[Y1],map(F1,U1))
 (fun map>cons)
 (meta F1)[is acc in F1,cons(Y1,U1)] [is acc in F1] 
 (meta Y1)[is acc in F1,cons(Y1,U1)] [is positive in cons(Y1,U1)] [is acc in Y1] 
 (fun map=map) subterm comparison of args w. LR LR
 (meta F1)[is acc in F1,cons(Y1,U1)] [is acc in F1] 
 (meta U1)[is acc in F1,cons(Y1,U1)] [is positive in cons(Y1,U1)] [is acc in U1]  >>True
Checking  (9) filter(H1,nil) => nil
 (fun filter>nil) >>True
Checking  (10) filter(I1,cons(P1,X2)) => filter2(I1[P1],I1,P1,X2)
 (fun filter=filter2) subterm comparison of args w. Arg [1,2] Arg [2,4,3,1]
 (meta I1)[is acc in I1,cons(P1,X2)] [is acc in I1] 
 (meta P1)[is acc in I1,cons(P1,X2)] [is positive in cons(P1,X2)] [is acc in P1] 
 (meta I1)[is acc in I1,cons(P1,X2)] [is acc in I1] 
 (meta P1)[is acc in I1,cons(P1,X2)] [is positive in cons(P1,X2)] [is acc in P1] 
 (meta X2)[is acc in I1,cons(P1,X2)] [is positive in cons(P1,X2)] [is acc in X2]  >>True
Checking  (11) filter2(true,Z2,U2,V2) => cons(U2,filter(Z2,V2))
 (fun filter2>cons)
 (meta U2)[is acc in true,Z2,U2,V2] [is positive in true] [is acc in U2] 
 (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2]
 (meta Z2)[is acc in true,Z2,U2,V2] [is positive in true] [is acc in Z2] 
 (meta V2)[is acc in true,Z2,U2,V2] [is positive in true] [is acc in V2]  >>True
Checking  (12) filter2(false,I2,P2,X3) => filter(I2,X3)
 (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2]
 (meta I2)[is acc in false,I2,P2,X3] [is positive in false] [is acc in I2] 
 (meta X3)[is acc in false,I2,P2,X3] [is positive in false] [is acc in X3]  >>True
#SN!
******** Signature ********
 0 : a
 cons : (c,d) -> d
 f : a -> a
 false : b
 filter : ((c -> b),d) -> d
 filter2 : (b,(c -> b),c,d) -> d
 g : a -> a
 map : ((c -> c),d) -> d
 minus : (a,a) -> a
 nil : d
 s : a -> a
 true : b
******** Computation Rules ********
 (1)  minus(X,0) => X
 (2)  minus(s(Y),s(U)) => minus(Y,U)
 (3)  f(0) => s(0)
 (4)  f(s(V)) => minus(s(V),g(f(V)))
 (5)  g(0) => 0
 (6)  g(s(W)) => minus(s(W),f(g(W)))
 (7)  map(J,nil) => nil
 (8)  map(F1,cons(Y1,U1)) => cons(F1[Y1],map(F1,U1))
 (9)  filter(H1,nil) => nil
 (10)  filter(I1,cons(P1,X2)) => filter2(I1[P1],I1,P1,X2)
 (11)  filter2(true,Z2,U2,V2) => cons(U2,filter(Z2,V2))
 (12)  filter2(false,I2,P2,X3) => filter(I2,X3)

YES