/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: 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) i(1) => 1
 (fun i>1) >>True
Checking  (8) i(i(U1)) => U1
 (meta U1)[is acc in i(U1)] [is positive in i(U1)] [is acc in U1]  >>True
Checking  (9) map(H1,nil) => nil
 (fun map>nil) >>True
Checking  (10) map(I1,cons(P1,X2)) => cons(I1[P1],map(I1,X2))
 (fun map>cons)
 (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] 
 (fun map=map) subterm comparison of args w. LR LR
 (meta I1)[is acc in I1,cons(P1,X2)] [is acc in I1] 
 (meta X2)[is acc in I1,cons(P1,X2)] [is positive in cons(P1,X2)] [is acc in X2]  >>True
Checking  (11) filter(Z2,nil) => nil
 (fun filter>nil) >>True
Checking  (12) filter(G2,cons(V2,W2)) => filter2(G2[V2],G2,V2,W2)
 (fun filter=filter2) subterm comparison of args w. Arg [1,2] Arg [2,4,3,1]
 (meta G2)[is acc in G2,cons(V2,W2)] [is acc in G2] 
 (meta V2)[is acc in G2,cons(V2,W2)] [is positive in cons(V2,W2)] [is acc in V2] 
 (meta G2)[is acc in G2,cons(V2,W2)] [is acc in G2] 
 (meta V2)[is acc in G2,cons(V2,W2)] [is positive in cons(V2,W2)] [is acc in V2] 
 (meta W2)[is acc in G2,cons(V2,W2)] [is positive in cons(V2,W2)] [is acc in W2]  >>True
Checking  (13) filter2(true,J2,X3,Y3) => cons(X3,filter(J2,Y3))
 (fun filter2>cons)
 (meta X3)[is acc in true,J2,X3,Y3] [is positive in true] [is acc in X3] 
 (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2]
 (meta J2)[is acc in true,J2,X3,Y3] [is positive in true] [is acc in J2] 
 (meta Y3)[is acc in true,J2,X3,Y3] [is positive in true] [is acc in Y3]  >>True
Checking  (14) filter2(false,G3,V3,W3) => filter(G3,W3)
 (fun filter2=filter) subterm comparison of args w. Arg [2,4,3,1] Arg [1,2]
 (meta G3)[is acc in false,G3,V3,W3] [is positive in false] [is acc in G3] 
 (meta W3)[is acc in false,G3,V3,W3] [is positive in false] [is acc in W3]  >>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)  i(1) => 1
 (8)  i(i(U1)) => U1
 (9)  map(H1,nil) => nil
 (10)  map(I1,cons(P1,X2)) => cons(I1[P1],map(I1,X2))
 (11)  filter(Z2,nil) => nil
 (12)  filter(G2,cons(V2,W2)) => filter2(G2[V2],G2,V2,W2)
 (13)  filter2(true,J2,X3,Y3) => cons(X3,filter(J2,Y3))
 (14)  filter2(false,G3,V3,W3) => filter(G3,W3)

YES