/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, false, s, true
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) rec(F,ap(Z,0)) => Z
 (meta Z)[is acc in F,ap(Z,0)] [is acc in Z]  >>True
Checking  (ap) ap(x.M[x],N) => M[N]
 (meta M)[is acc in x.M[x],N] [is acc in M[x]] 
 (meta N)[is acc in x.M[x],N] [is acc in N]  >>True
Checking  (ap0) ap(M,N) => M[N]
 (meta M)[is acc in M,N] [is acc in M] 
 (meta N)[is acc in M,N] [is acc in N]  >>True
Checking  (2) g(U) => true
 (fun g>true) >>True
Checking  (3) h(V,I,P) => false
 (fun h>false) >>True
Checking  (4) iszero(X1,Y1) => rec(h,g(X1),Y1)
 (fun iszero>rec)
 (fun iszero>h)
 (fun iszero>g)
 (meta X1)[is acc in X1,Y1] [is acc in X1] 
 (meta Y1)[is acc in X1,Y1] [is acc in Y1]  >>True
Checking  (5) pred(0) => 0
 (fun pred>0) >>True
Checking  (6) pred(s(U1)) => U1
 (meta U1)[is acc in s(U1)] [is positive in s(U1)] [is acc in U1]  >>True
Checking  (7) g2(V1) => iszero(V1,0)
 (fun g2>iszero)
 (meta V1)[is acc in V1] [is acc in V1] 
 (fun g2>0) >>True
Checking  (8) h2(W1,J1,X2) => J1[pred(X2)]
 (meta J1)[is acc in W1,J1,X2] [is acc in J1] 
 (fun h2>pred)
 (meta X2)[is acc in W1,J1,X2] [is acc in X2]  >>True
Checking  (9) geq(Y2,U2) => rec(h2,g2(Y2),U2)
 (fun geq>rec)
 (fun geq>h2)
 (fun geq>g2)
 (meta Y2)[is acc in Y2,U2] [is acc in Y2] 
 (meta U2)[is acc in Y2,U2] [is acc in U2]  >>True
#SN!
******** Signature ********
 0 : N
 false : B
 g : N -> B
 g2 : N -> B
 geq : (N,N) -> B
 h : (N,(N -> B),N) -> B
 h2 : (N,(N -> B),N) -> B
 iszero : (N,N) -> B
 pred : N -> N
 rec : (((N,(N -> B),N) -> B),B,N) -> B
 s : N -> N
 true : B
 ap : ((a -> b),a) -> b
******** Computation Rules ********
 (1)  rec(F,ap(Z,0)) => Z
 (ap)  ap(x.M[x],N) => M[N]
 (ap0)  ap(M,N) => M[N]
 (2)  g(U) => true
 (3)  h(V,I,P) => false
 (4)  iszero(X1,Y1) => rec(h,g(X1),Y1)
 (5)  pred(0) => 0
 (6)  pred(s(U1)) => U1
 (7)  g2(V1) => iszero(V1,0)
 (8)  h2(W1,J1,X2) => J1[pred(X2)]
 (9)  geq(Y2,U2) => rec(h2,g2(Y2),U2)

YES