/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, hd, nil
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) ap(ap(F,0),Y) => hd(map(F,cons(0,nil)),Y)
 (fun ap>hd)
 (fun ap>map)
 (meta F)[is acc in ap(F,0),Y] [is acc in F] 
 (fun ap>cons)
 (fun ap>0)
 (fun ap>nil)
 (meta Y)[is acc in ap(F,0),Y] [is positive in 0] [is acc in Y]  >>True
Checking  (ap) ap(x.M[x],N) => M[N]
 (meta M)[is acc in x.M[x],N] [is acc in M[x]] 
 (meta N)[is acc in x.M[x],N] [is acc in N]  >>True
Checking  (ap0) ap(M,N) => M[N]
 (meta M)[is acc in M,N] [is acc in M] 
 (meta N)[is acc in M,N] [is acc in N]  >>True
Checking  (2) map(G,nil) => nil
 (fun map>nil) >>True
Checking  (3) map(H,cons(I,P)) => cons(H[I],map(H,P))
 (fun map>cons)
 (meta H)[is acc in H,cons(I,P)] [is acc in H] 
 (meta I)[is acc in H,cons(I,P)] [is positive in cons(I,P)] [is acc in I] 
 (fun map=map) subterm comparison of args w. LR LR
 (meta H)[is acc in H,cons(I,P)] [is acc in H] 
 (meta P)[is acc in H,cons(I,P)] [is positive in cons(I,P)] [is acc in P]  >>True
#SN!
******** Signature ********
 0 : a -> b
 cons : ((a -> b),c) -> c
 hd : (c,a) -> b
 map : ((((a -> b),a) -> b),c) -> c
 nil : c
 ap : ((a -> b),a) -> b
******** Computation Rules ********
 (1)  ap(ap(F,0),Y) => hd(map(F,cons(0,nil)),Y)
 (ap)  ap(x.M[x],N) => M[N]
 (ap0)  ap(M,N) => M[N]
 (2)  map(G,nil) => nil
 (3)  map(H,cons(I,P)) => cons(H[I],map(H,P))

YES