/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: nil, cons, 0, s, ascendingsort, descendingsort
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) max(0,N) => N
 (meta N)[is acc in 0,N] [is positive in 0] [is acc in N]  >>True
Checking  (2) max(N,0) => N
 (meta N)[is acc in N,0] [is acc in N]  >>True
Checking  (3) max(s(N),s(M)) => s(max(N,M))
 (fun max>s)
 (fun max=max) subterm comparison of args w. LR LR
 (meta N)[is acc in s(N),s(M)] [is positive in s(N)] [is acc in N] 
 (meta M)[is acc in s(N),s(M)] [is positive in s(N)] [is positive in s(M)] [is acc in M]  >>True
Checking  (4) min(0,N) => 0
 (fun min>0) >>True
Checking  (5) min(N,0) => 0
 (fun min>0) >>True
Checking  (6) min(s(N),s(M)) => s(min(N,M))
 (fun min>s)
 (fun min=min) subterm comparison of args w. LR LR
 (meta N)[is acc in s(N),s(M)] [is positive in s(N)] [is acc in N] 
 (meta M)[is acc in s(N),s(M)] [is positive in s(N)] [is positive in s(M)] [is acc in M]  >>True
Checking  (7) insert(N,nil,X,Y) => cons(N,nil)
 (fun insert>cons)
 (meta N)[is acc in N,nil,X,Y] [is acc in N] 
 (fun insert>nil) >>True
Checking  (8) insert(N,cons(M,L),X,Y) => cons(X[N,M],insert(Y[N,M],L,X,Y))
 (fun insert>cons)
 (meta X)[is acc in N,cons(M,L),X,Y] [is positive in cons(M,L)] [is acc in X] 
 (meta N)[is acc in N,cons(M,L),X,Y] [is acc in N] 
 (meta M)[is acc in N,cons(M,L),X,Y] [is positive in cons(M,L)] [is acc in M] 
 (fun insert=insert) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) max(0,N) => N
 (meta N)[is acc in 0,N] [is positive in 0] [is acc in N]  >>True
Checking  (2) max(N,0) => N
 (meta N)[is acc in N,0] [is acc in N]  >>True
Checking  (3) max(s(N),s(M)) => s(max(N,M))
 (fun max>s)
 (fun max=max) subterm comparison of args w. RL RL
 (meta N)[is acc in s(N),s(M)] [is positive in s(N)] [is acc in N] 
 (meta M)[is acc in s(N),s(M)] [is positive in s(N)] [is positive in s(M)] [is acc in M]  >>True
Checking  (4) min(0,N) => 0
 (fun min>0) >>True
Checking  (5) min(N,0) => 0
 (fun min>0) >>True
Checking  (6) min(s(N),s(M)) => s(min(N,M))
 (fun min>s)
 (fun min=min) subterm comparison of args w. RL RL
 (meta N)[is acc in s(N),s(M)] [is positive in s(N)] [is acc in N] 
 (meta M)[is acc in s(N),s(M)] [is positive in s(N)] [is positive in s(M)] [is acc in M]  >>True
Checking  (7) insert(N,nil,X,Y) => cons(N,nil)
 (fun insert>cons)
 (meta N)[is acc in N,nil,X,Y] [is acc in N] 
 (fun insert>nil) >>True
Checking  (8) insert(N,cons(M,L),X,Y) => cons(X[N,M],insert(Y[N,M],L,X,Y))
 (fun insert>cons)
 (meta X)[is acc in N,cons(M,L),X,Y] [is positive in cons(M,L)] [is acc in X] 
 (meta N)[is acc in N,cons(M,L),X,Y] [is acc in N] 
 (meta M)[is acc in N,cons(M,L),X,Y] [is positive in cons(M,L)] [is acc in M] 
 (fun insert=insert) subterm comparison of args w. RL RL
 (meta Y)[is acc in N,cons(M,L),X,Y] [is positive in cons(M,L)] [is acc in Y] 
 (meta N)[is acc in N,cons(M,L),X,Y] [is acc in N] 
 (meta M)[is acc in N,cons(M,L),X,Y] [is positive in cons(M,L)] [is acc in M] 
 (meta L)[is acc in N,cons(M,L),X,Y] [is positive in cons(M,L)] [is acc in L] 
 (meta X)[is acc in N,cons(M,L),X,Y] [is positive in cons(M,L)] [is acc in X] 
 (meta Y)[is acc in N,cons(M,L),X,Y] [is positive in cons(M,L)] [is acc in Y]  >>True
Checking  (9) sort(nil,X,Y) => nil
 (fun sort>nil) >>True
Checking  (10) sort(cons(N,L),X,Y) => insert(N,sort(L,X,Y),X,Y)
 (fun sort>insert)
 (meta N)[is acc in cons(N,L),X,Y] [is positive in cons(N,L)] [is acc in N] 
 (fun sort=sort) subterm comparison of args w. RL RL
 (meta L)[is acc in cons(N,L),X,Y] [is positive in cons(N,L)] [is acc in L] 
 (meta X)[is acc in cons(N,L),X,Y] [is positive in cons(N,L)] [is acc in X] 
 (meta Y)[is acc in cons(N,L),X,Y] [is positive in cons(N,L)] [is acc in Y] 
 (meta X)[is acc in cons(N,L),X,Y] [is positive in cons(N,L)] [is acc in X] 
 (meta Y)[is acc in cons(N,L),X,Y] [is positive in cons(N,L)] [is acc in Y]  >>True
Checking  (11) ascending_sort(L) => sort(L,x.y.min(x,y),x.y.max(x,y))
 (fun ascending_sort>sort)
 (meta L)[is acc in L] [is acc in L] 
 (fun ascending_sort>min)
 (fun ascending_sort>max) >>True
Checking  (12) descending_sort(L) => sort(L,x.y.max(x,y),x.y.min(x,y))
 (fun descending_sort>sort)
 (meta L)[is acc in L] [is acc in L] 
 (fun descending_sort>max)
 (fun descending_sort>min) >>True
#SN!
******** Signature ********
 nil : list
 cons : (nat,list) -> list
 0 : nat
 s : nat -> nat
 max : (nat,nat) -> nat
 min : (nat,nat) -> nat
 insert : (nat,list,((nat,nat) -> nat),((nat,nat) -> nat)) -> list
 sort : (list,((nat,nat) -> nat),((nat,nat) -> nat)) -> list
 ascendingsort : list -> list
 descendingsort : list -> list
******** Computation Rules ********
 (1)  max(0,N) => N
 (2)  max(N,0) => N
 (3)  max(s(N),s(M)) => s(max(N,M))
 (4)  min(0,N) => 0
 (5)  min(N,0) => 0
 (6)  min(s(N),s(M)) => s(min(N,M))
 (7)  insert(N,nil,X,Y) => cons(N,nil)
 (8)  insert(N,cons(M,L),X,Y) => cons(X[N,M],insert(Y[N,M],L,X,Y))
 (9)  sort(nil,X,Y) => nil
 (10)  sort(cons(N,L),X,Y) => insert(N,sort(L,X,Y),X,Y)
 (11)  ascending_sort(L) => sort(L,x.y.min(x,y),x.y.max(x,y))
 (12)  descending_sort(L) => sort(L,x.y.max(x,y),x.y.min(x,y))

YES