/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, s
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) xpls(X,0) => X
 (meta X)[is acc in X,0] [is acc in X]  >>True
Checking  (2) xpls(X,s(Y)) => s(xpls(X,Y))
 (fun xpls>s)
 (fun xpls=xpls) subterm comparison of args w. LR LR
 (meta X)[is acc in X,s(Y)] [is acc in X] 
 (meta Y)[is acc in X,s(Y)] [is positive in s(Y)] [is acc in Y]  >>True
Checking  (3) rec(0,U,F) => U
 (meta U)[is acc in 0,U,F] [is positive in 0] [is acc in U]  >>True
Checking  (4) rec(s(X),U,F) => F[X,rec(X,U,F)]
 (meta F)[is acc in s(X),U,F] [is positive in s(X)] [is acc in F] 
 (meta X)[is acc in s(X),U,F] [is positive in s(X)] [is acc in X] 
 (fun rec=rec) subterm comparison of args w. LR LR
 (meta X)[is acc in s(X),U,F] [is positive in s(X)] [is acc in X] 
 (meta U)[is acc in s(X),U,F] [is positive in s(X)] [is acc in U] 
 (meta F)[is acc in s(X),U,F] [is positive in s(X)] [is acc in F]  >>True
Checking  (5) xmul(X,Y) => rec(Y,0,z1.z2.xpls(X,z2))
 (fun xmul>rec)
 (meta Y)[is acc in X,Y] [is acc in Y] 
 (fun xmul>0)
 (fun xmul>xpls)
 (meta X)[is acc in X,Y] [is acc in X]  >>True
#SN!
******** Signature ********
 0 : nat
 s : nat -> nat
 xpls : (nat,nat) -> nat
 xmul : (nat,nat) -> nat
 rec : (nat,nat,((nat,nat) -> nat)) -> nat
******** Computation Rules ********
 (1)  xpls(X,0) => X
 (2)  xpls(X,s(Y)) => s(xpls(X,Y))
 (3)  rec(0,U,F) => U
 (4)  rec(s(X),U,F) => F[X,rec(X,U,F)]
 (5)  xmul(X,Y) => rec(Y,0,z1.z2.xpls(X,z2))

YES