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


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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) inc(V) => map(plus(s(0)),V)
 (fun inc>map)
 (fun inc>plus)
 (fun inc>s)
 (fun inc>0)
 (meta V)[is acc in V] [is acc in V]  >>True
Checking  (4) map(I,nil) => nil
 (fun map>nil) >>True
Checking  (5) map(J,cons(X1,Y1)) => cons(J[X1],map(J,Y1))
 (fun map>cons)
 (meta J)[is acc in J,cons(X1,Y1)] [is acc in J] 
 (meta X1)[is acc in J,cons(X1,Y1)] [is positive in cons(X1,Y1)] [is acc in X1] 
 (fun map=map) subterm comparison of args w. LR LR
 (meta J)[is acc in J,cons(X1,Y1)] [is acc in J] 
 (meta Y1)[is acc in J,cons(X1,Y1)] [is positive in cons(X1,Y1)] [is acc in Y1]  >>True
#SN!
******** Signature ********
 0 : a
 cons : (a,b) -> b
 inc : b -> b
 map : ((a -> a),b) -> b
 nil : b
 plus : (a,a) -> a
 s : a -> a
******** Computation Rules ********
 (1)  0 + X => X
 (2)  s(Y) + U => s(Y + U)
 (3)  inc(V) => map(plus(s(0)),V)
 (4)  map(I,nil) => nil
 (5)  map(J,cons(X1,Y1)) => cons(J[X1],map(J,Y1))

YES