/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: 0, s
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) X + 0 => X
 (meta X)[is acc in X,0] [is acc in X]  >>True
Checking  (2) Y + s(U) => s(Y + U)
 (fun xplus>s)
 (fun xplus=xplus) subterm comparison of args w. LR LR
 (meta Y)[is acc in Y,s(U)] [is acc in Y] 
 (meta U)[is acc in Y,s(U)] [is positive in s(U)] [is acc in U]  >>True
Checking  (3) rec(0,V,%Y.%X.I[%Y,%X]) => V
 (meta V)[is acc in 0,V,%Y.%X.I[%Y,%X]] [is positive in 0] [is acc in V]  >>True
Checking  (4) rec(s(P),X1,%U.%Z.Z1[%U,%Z]) => Z1[P,rec(P,X1,%W.%V.Z1[%W,%V])]
 (meta Z1)[is acc in s(P),X1,%U.%Z.Z1[%U,%Z]] [is positive in s(P)] [is acc in Z1[%U,%Z]] 
 (meta P)[is acc in s(P),X1,%U.%Z.Z1[%U,%Z]] [is positive in s(P)] [is acc in P] 
 (fun rec=rec) subterm comparison of args w. LR LR
 (meta P)[is acc in s(P),X1,%U.%Z.Z1[%U,%Z]] [is positive in s(P)] [is acc in P] 
 (meta X1)[is acc in s(P),X1,%U.%Z.Z1[%U,%Z]] [is positive in s(P)] [is acc in X1] 
 (meta Z1)[is acc in s(P),X1,%U.%Z.Z1[%U,%Z]] [is positive in s(P)] [is acc in Z1[%U,%Z]]  >>True
Checking  (5) U1 * V1 => rec(V1,0,%G.%F.(U1 + %F))
 (fun xtimes>rec)
 (meta V1)[is acc in U1,V1] [is acc in V1] 
 (fun xtimes>0)
 (fun xtimes>xplus)
 (meta U1)[is acc in U1,V1] [is acc in U1]  >>True
#SN!
******** Signature ********
 0 : nat
 rec : (nat,nat,((nat,nat) -> nat)) -> nat
 s : nat -> nat
 xplus : (nat,nat) -> nat
 xtimes : (nat,nat) -> nat
******** Computation Rules ********
 (1)  X + 0 => X
 (2)  Y + s(U) => s(Y + U)
 (3)  rec(0,V,%Y.%X.I[%Y,%X]) => V
 (4)  rec(s(P),X1,%U.%Z.Z1[%U,%Z]) => Z1[P,rec(P,X1,%W.%V.Z1[%W,%V])]
 (5)  U1 * V1 => rec(V1,0,%G.%F.(U1 + %F))

YES