/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, add, cons, mul, nil, s
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) fold(%Y.%X.F[%Y,%X],Y,nil) => Y
 (meta Y)[is acc in %Y.%X.F[%Y,%X],Y,nil] [is acc in Y]  >>True
Checking  (2) fold(%U.%Z.G[%U,%Z],V,cons(W,P)) => G[W,fold(%W.%V.G[%W,%V],V,P)]
 (meta G)[is acc in %U.%Z.G[%U,%Z],V,cons(W,P)] [is acc in G[%U,%Z]] 
 (meta W)[is acc in %U.%Z.G[%U,%Z],V,cons(W,P)] [is positive in cons(W,P)] [is acc in W] 
 (fun fold=fold) subterm comparison of args w. LR LR
 (meta G)[is acc in %U.%Z.G[%U,%Z],V,cons(W,P)] [is acc in G[%U,%Z]] 
 (meta V)[is acc in %U.%Z.G[%U,%Z],V,cons(W,P)] [is acc in V] 
 (meta P)[is acc in %U.%Z.G[%U,%Z],V,cons(W,P)] [is positive in cons(W,P)] [is acc in P]  >>True
Checking  (3) 0 + X1 => X1
 (meta X1)[is acc in 0,X1] [is positive in 0] [is acc in X1]  >>True
Checking  (4) s(Y1) + U1 => s(Y1 + U1)
 (fun plus>s)
 (fun plus=plus) subterm comparison of args w. LR LR
 (meta Y1)[is acc in s(Y1),U1] [is positive in s(Y1)] [is acc in Y1] 
 (meta U1)[is acc in s(Y1),U1] [is positive in s(Y1)] [is acc in U1]  >>True
Checking  (5) 0 * V1 => 0
 (fun times>0) >>True
Checking  (6) s(W1) * P1 => (W1 * P1) + P1
 (fun times>plus)
 (fun times=times) subterm comparison of args w. LR LR
 (meta W1)[is acc in s(W1),P1] [is positive in s(W1)] [is acc in W1] 
 (meta P1)[is acc in s(W1),P1] [is positive in s(W1)] [is acc in P1] 
 (meta P1)[is acc in s(W1),P1] [is positive in s(W1)] [is acc in P1]  >>True
Checking  (7) sum(X2) => fold(%G.%F.add(%G,%F),0,X2)
 (fun sum>fold)
 (fun sum>add)
 (fun sum>0)
 (meta X2)[is acc in X2] [is acc in X2]  >>True
Checking  (8) prod(Y2) => fold(%I.%H.mul(%I,%H),s(0),Y2)
 (fun prod>fold)
 (fun prod>mul)
 (fun prod>s)
 (fun prod>0)
 (meta Y2)[is acc in Y2] [is acc in Y2]  >>True
#SN!
******** Signature ********
 0 : c
 add : (a,c) -> c
 cons : (a,b) -> b
 fold : (((a,c) -> c),c,b) -> c
 mul : (a,c) -> c
 nil : b
 plus : (c,c) -> c
 prod : b -> c
 s : c -> c
 sum : b -> c
 times : (c,c) -> c
******** Computation Rules ********
 (1)  fold(%Y.%X.F[%Y,%X],Y,nil) => Y
 (2)  fold(%U.%Z.G[%U,%Z],V,cons(W,P)) => G[W,fold(%W.%V.G[%W,%V],V,P)]
 (3)  0 + X1 => X1
 (4)  s(Y1) + U1 => s(Y1 + U1)
 (5)  0 * V1 => 0
 (6)  s(W1) * P1 => (W1 * P1) + P1
 (7)  sum(X2) => fold(%G.%F.add(%G,%F),0,X2)
 (8)  prod(Y2) => fold(%I.%H.mul(%I,%H),s(0),Y2)

YES