/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

Using the interpretation [[filtersub]](B,Z,cons(U,V)) = ifo(B,cons(U,filter(Z,V)),filter(Z,V))
given system is strictly simulated by
 (1)  filter(F,nil) => nil
 (2if)  filter(Z,cons(U,V)) => ifo(Z[U],cons(U,filter(Z,V)),filter(Z,V))
 (ift)  ifo(true,T,E) => T
 (iff)  ifo(false,T,E) => E

Hene we try to show SN of this.
******** General Schema criterion ********
Found constructors: cons, false, nil, true
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>Regared as equal: filtersub, filter
Checking  (1) filter(F,nil) => nil
 (fun filter>nil) >>True
Checking  (2) filter(Z,cons(U,V)) => filtersub(Z[U],Z,cons(U,V))
 (fun filter=filtersub) subterm comparison of args w. Arg [1,2] Arg [2,3,1] >>False

Try again using status RL
Checking  (1) filter(F,nil) => nil
 (fun filter>nil) >>True
Checking  (2) filter(Z,cons(U,V)) => filtersub(Z[U],Z,cons(U,V))
 (fun filter=filtersub) subterm comparison of args w. Arg [1,2] Arg [2,3,1] >>False

Try again using status Mul
Checking  (1) filter(F,nil) => nil
 (fun filter>nil) >>True
Checking  (2) filter(Z,cons(U,V)) => filtersub(Z[U],Z,cons(U,V))
 (fun filter=filtersub) subterm comparison of args w. Arg [1,2] Arg [2,3,1] >>False
Found constructors: cons, false, filtersub, nil, true
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) filter(F,nil) => nil
 (fun filter>nil) >>True
Checking  (2if) filter(Z,cons(U,V)) => ifo(Z[U],cons(U,filter(Z,V)),filter(Z,V))
 (fun filter>ifo)
 (meta Z)[is acc in Z,cons(U,V)] [is acc in Z] 
 (meta U)[is acc in Z,cons(U,V)] [is positive in cons(U,V)] [is acc in U] 
 (fun filter>cons)
 (meta U)[is acc in Z,cons(U,V)] [is positive in cons(U,V)] [is acc in U] 
 (fun filter=filter) subterm comparison of args w. Arg [1,2] Arg [1,2]
 (meta Z)[is acc in Z,cons(U,V)] [is acc in Z] 
 (meta V)[is acc in Z,cons(U,V)] [is positive in cons(U,V)] [is acc in V] 
 (fun filter=filter) subterm comparison of args w. Arg [1,2] Arg [1,2]
 (meta Z)[is acc in Z,cons(U,V)] [is acc in Z] 
 (meta V)[is acc in Z,cons(U,V)] [is positive in cons(U,V)] [is acc in V]  >>True
Checking  (ift) ifo(true,T,E) => T
 (meta T)[is acc in true,T,E] [is positive in true] [is acc in T]  >>True
Checking  (iff) ifo(false,T,E) => E
 (meta E)[is acc in false,T,E] [is positive in false] [is acc in E]  >>True
#SN!
******** Signature ********
 cons : (b,c) -> c
 false : a
 filter : ((b -> a),c) -> c
 filtersub : (a,(b -> a),c) -> c
 nil : c
 true : a
******** Computation Rules ********
 (1)  filter(F,nil) => nil
 (2)  filter(Z,cons(U,V)) => filtersub(Z[U],Z,cons(U,V))
 (3)  filtersub(true,I,cons(P,X1)) => cons(P,filter(I,X1))
 (4)  filtersub(false,Z1,cons(U1,V1)) => filter(Z1,V1)

YES