/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

******** General Schema criterion ********
Found constructors: 0, cons, nil, s
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) 0 + X => X
 (meta X)[is acc in 0,X] [is positive in 0] [is acc in X]  >>True
Checking  (2) s(Y) + U => s(Y + U)
 (fun plus>s)
 (fun plus=plus) subterm comparison of args w. LR LR
 (meta Y)[is acc in s(Y),U] [is positive in s(Y)] [is acc in Y] 
 (meta U)[is acc in s(Y),U] [is positive in s(Y)] [is acc in U]  >>True
Checking  (3) 0 * V => 0
 (fun times>0) >>True
Checking  (4) s(W) * P => (W * P) + P
 (fun times>plus)
 (fun times=times) subterm comparison of args w. LR LR
 (meta W)[is acc in s(W),P] [is positive in s(W)] [is acc in W] 
 (meta P)[is acc in s(W),P] [is positive in s(W)] [is acc in P] 
 (meta P)[is acc in s(W),P] [is positive in s(W)] [is acc in P]  >>True
Checking  (5) inc(X1) => map(plus(s(0)),X1)
 (fun inc>map)
 (fun inc>plus)
 (fun inc>s)
 (fun inc>0)
 (meta X1)[is acc in X1] [is acc in X1]  >>True
Checking  (6) double(Y1) => map(times(s(s(0))),Y1)
 (fun double>map)
 (fun double>times)
 (fun double>s)
 (fun double>s)
 (fun double>0)
 (meta Y1)[is acc in Y1] [is acc in Y1]  >>True
Checking  (7) map(G1,nil) => nil
 (fun map>nil) >>True
Checking  (8) map(H1,cons(W1,P1)) => cons(H1[W1],map(H1,P1))
 (fun map>cons)
 (meta H1)[is acc in H1,cons(W1,P1)] [is acc in H1] 
 (meta W1)[is acc in H1,cons(W1,P1)] [is positive in cons(W1,P1)] [is acc in W1] 
 (fun map=map) subterm comparison of args w. LR LR
 (meta H1)[is acc in H1,cons(W1,P1)] [is acc in H1] 
 (meta P1)[is acc in H1,cons(W1,P1)] [is positive in cons(W1,P1)] [is acc in P1]  >>True
#SN!
******** Signature ********
 0 : a
 cons : (a,b) -> b
 double : b -> b
 inc : b -> b
 map : ((a -> a),b) -> b
 nil : b
 plus : (a,a) -> a
 s : a -> a
 times : (a,a) -> a
******** Computation Rules ********
 (1)  0 + X => X
 (2)  s(Y) + U => s(Y + U)
 (3)  0 * V => 0
 (4)  s(W) * P => (W * P) + P
 (5)  inc(X1) => map(plus(s(0)),X1)
 (6)  double(Y1) => map(times(s(s(0))),Y1)
 (7)  map(G1,nil) => nil
 (8)  map(H1,cons(W1,P1)) => cons(H1[W1],map(H1,P1))

YES