/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, 1, -, sin, cos, ln, xpls, xmul, xdiv
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) der(x.Y) => x.0
 (fun der>0) >>True
Checking  (2) der(x.x) => x.1
 (fun der>1) >>True
Checking  (3) der(x.sin(x)) => x.cos(x)
 (fun der>cos) >>True
Checking  (4) der(x.cos(x)) => x.-(sin(x))
 (fun der>-)
 (fun der>sin) >>True
Checking  (5) der(x.xpls(F[x],G[x])) => x.xpls(der(F,x),der(G,x))
 (fun der>xpls)
 (fun der=der) subterm comparison of args w. LR LR
 (meta F)[is acc in x.xpls(F[x],G[x])] [is positive in xpls(F[x],G[x])] [is acc in F[x]] 
 (fun der=der) subterm comparison of args w. LR LR
 (meta G)[is acc in x.xpls(F[x],G[x])] [is positive in xpls(F[x],G[x])] [is acc in G[x]]  >>True
Checking  (6) der(x.xmul(F[x],G[x])) => x.xpls(xmul(der(F,x),G[x]),xmul(F[x],der(G,x)))
 (fun der>xpls)
 (fun der>xmul)
 (fun der=der) subterm comparison of args w. LR LR
 (meta F)[is acc in x.xmul(F[x],G[x])] [is positive in xmul(F[x],G[x])] [is acc in F[x]] 
 (meta G)[is acc in x.xmul(F[x],G[x])] [is positive in xmul(F[x],G[x])] [is acc in G[x]] 
 (fun der>xmul)
 (meta F)[is acc in x.xmul(F[x],G[x])] [is positive in xmul(F[x],G[x])] [is acc in F[x]] 
 (fun der=der) subterm comparison of args w. LR LR
 (meta G)[is acc in x.xmul(F[x],G[x])] [is positive in xmul(F[x],G[x])] [is acc in G[x]]  >>True
Checking  (7) der(x.ln(F[x])) => x.xdiv(der(F,x),F[x])
 (fun der>xdiv)
 (fun der=der) subterm comparison of args w. LR LR
 (meta F)[is acc in x.ln(F[x])] [is positive in ln(F[x])] [is acc in F[x]] 
 (meta F)[is acc in x.ln(F[x])] [is positive in ln(F[x])] [is acc in F[x]]  >>True
#SN!
******** Signature ********
 0 : real
 1 : real
 - : real -> real
 sin : real -> real
 cos : real -> real
 ln : real -> real
 xpls : (real,real) -> real
 xmul : (real,real) -> real
 xdiv : (real,real) -> real
 der : ((real -> real),real) -> real
******** Computation Rules ********
 (1)  der(x.Y) => x.0
 (2)  der(x.x) => x.1
 (3)  der(x.sin(x)) => x.cos(x)
 (4)  der(x.cos(x)) => x.-(sin(x))
 (5)  der(x.xpls(F[x],G[x])) => x.xpls(der(F,x),der(G,x))
 (6)  der(x.xmul(F[x],G[x])) => x.xpls(xmul(der(F,x),G[x]),xmul(F[x],der(G,x)))
 (7)  der(x.ln(F[x])) => x.xdiv(der(F,x),F[x])

YES