/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, 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) rec(G,ap(H,s(W))) => ap(ap(G,W),rec(G,H[W]))
 (fun rec>ap)
 (fun rec>ap)
 (meta G)[is acc in G,ap(H,s(W))] [is acc in G] 
 (meta W)[is acc in G,ap(H,s(W))] [is positive in s(W)] [is acc in W] 
 (fun rec=rec) subterm comparison of args w. LR LR
 (meta G)[is acc in G,ap(H,s(W))] [is acc in G] 
 (meta H)[is acc in G,ap(H,s(W))] [is acc in H] 
 (meta W)[is acc in G,ap(H,s(W))] [is positive in s(W)] [is acc in W]  >>True
Checking  (3) g(P) => true
 (fun g>true) >>True
Checking  (4) h(X1,Z1,U1) => false
 (fun h>false) >>True
Checking  (5) iszero(V1,W1) => rec(h,g(V1),W1)
 (fun iszero>rec)
 (fun iszero>h)
 (fun iszero>g)
 (meta V1)[is acc in V1,W1] [is acc in V1] 
 (meta W1)[is acc in V1,W1] [is acc in W1]  >>True
Checking  (6) pred(0) => 0
 (fun pred>0) >>True
Checking  (7) pred(s(P1)) => P1
 (meta P1)[is acc in s(P1)] [is positive in s(P1)] [is acc in P1]  >>True
Checking  (8) g2(X2) => iszero(X2,0)
 (fun g2>iszero)
 (meta X2)[is acc in X2] [is acc in X2] 
 (fun g2>0) >>True
Checking  (9) h2(Y2,G2,V2) => G2[pred(V2)]
 (meta G2)[is acc in Y2,G2,V2] [is acc in G2] 
 (fun h2>pred)
 (meta V2)[is acc in Y2,G2,V2] [is acc in V2]  >>True
Checking  (10) geq(W2,P2) => rec(h2,g2(W2),P2)
 (fun geq>rec)
 (fun geq>h2)
 (fun geq>g2)
 (meta W2)[is acc in W2,P2] [is acc in W2] 
 (meta P2)[is acc in W2,P2] [is acc in P2]  >>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)  rec(G,ap(H,s(W))) => ap(ap(G,W),rec(G,H[W]))
 (3)  g(P) => true
 (4)  h(X1,Z1,U1) => false
 (5)  iszero(V1,W1) => rec(h,g(V1),W1)
 (6)  pred(0) => 0
 (7)  pred(s(P1)) => P1
 (8)  g2(X2) => iszero(X2,0)
 (9)  h2(Y2,G2,V2) => G2[pred(V2)]
 (10)  geq(W2,P2) => rec(h2,g2(W2),P2)

YES