input("input the value of n",n):
input("input the value of l",l):
n:=n+1:
X:=[i $ i=0..l]:
Y:=combinat::cartesianProduct(X $i=1..n):
W:=combinat::cartesianProduct(X $i=1..n):
for s from 1 to nops(Y) do
for t from 1 to nops(Y) do
m:=0:
for i from 1 to n do
if Y[s][i]=1 and Y[t][i]<>1 then m:=1 end_if:
for j from i to n do
for k from 1 to n do
if Y[s][i]+Y[s][j]=Y[s][k] and Y[t][i]+Y[t][j]<>Y[t][k]
then m:=1 end_if:
if Y[s][i]*Y[s][j]=Y[s][k] and Y[t][i]*Y[t][j]<>Y[t][k]
then m:=1 end_if:
end_for:
end_for:
end_for:
if m=0 and max(Y[t][i] $i=1..n)<max(Y[s][i] $i=1..n)
then W:=listlib::setDifference(W,[Y[s]]) end_if:
end_for:
end_for:
print(max(max(W[z][u] $u=1..n) $z=1..nops(W))):

Code 1
A Turing computation of \varphi(n,l)



input("input the value of n",n):
print(0):
A:=op(ifactor(210*(n+1))):
B:=[A[2*i+1] $i=1..(nops(A)-1)/2]:
S:={}:
for i from 1 to floor(nops(B)/4) do
if B[4*i]=1 then S:=S union {B[4*i-3]} end_if:
if B[4*i]=2 then S:=S union {[B[4*i-3],B[4*i-2],B[4*i-1],"+"]} end_if:
if B[4*i]>2 then S:=S union {[B[4*i-3],B[4*i-2],B[4*i-1],"*"]} end_if:
end_for:
m:=2:
repeat
C:=op(ifactor(m)):
W:=[C[2*i+1]-1 $i=1..(nops(C)-1)/2]:
T:={}:
for i from 1 to nops(W) do
for j from 1 to nops(W) do
for k from 1 to nops(W) do
if W[i]=1 then T:=T union {i} end_if:
if W[i]+W[j]=W[k] then T:=T union {[i,j,k,"+"]} end_if:
if W[i]*W[j]=W[k] then T:=T union {[i,j,k,"*"]} end_if:
end_for:
end_for:
end_for:
m:=m+1:
until S minus T={} end_repeat:
print(max(W[i] $i=1..nops(W))):

Code 2
A loop whose execution does not always terminate, and that defines
a partially computable function that cannot be bounded by any computable
function from N to N



input("input the value of n",n):
X:=[0]:
while TRUE do
Y:=combinat::cartesianProduct(X $i=1..n):
W:=combinat::cartesianProduct(X $i=1..n):
for s from 1 to nops(Y) do
for t from 1 to nops(Y) do
m:=0:
for i from 1 to n do
if Y[s][i]=1 and Y[t][i]<>1 then m:=1 end_if:
for j from i to n do
for k from 1 to n do
if Y[s][i]+Y[s][j]=Y[s][k] and Y[t][i]+Y[t][j]<>Y[t][k]
then m:=1 end_if:
if Y[s][i]*Y[s][j]=Y[s][k] and Y[t][i]*Y[t][j]<>Y[t][k]
then m:=1 end_if:
end_for:
end_for:
end_for:
if m=0 and s<>t then W:=listlib::setDifference(W,[Y[s]]) end_if:
end_for:
end_for:
print(max(max(W[z][u] $u=1..n) $z=1..nops(W))):
X:=append(X,nops(X)):
end_while:

Code 3
An infinite computation of a limit-computable
function f_2:N\{0}-->N



input("input the value of n",n):
X:=[0]:
while TRUE do
Y:=combinat::cartesianProduct(X $i=1..n):
W:=combinat::cartesianProduct(X $i=1..n):
for s from 1 to nops(Y) do
for t from 1 to nops(Y) do
m:=0:
for i from 1 to n do
if Y[s][i]=1 and Y[t][i]<>1 then m:=1 end_if:
for j from i to n do
for k from 1 to n do
if Y[s][i]+Y[s][j]=Y[s][k] and Y[t][i]+Y[t][j]<>Y[t][k]
then m:=1 end_if:
if Y[s][i]*Y[s][j]=Y[s][k] and Y[t][i]*Y[t][j]<>Y[t][k]
then m:=1 end_if:
end_for:
end_for:
end_for:
if m=0 and max(Y[t][i] $i=1..n)<max(Y[s][i] $i=1..n)
then W:=listlib::setDifference(W,[Y[s]]) end_if:
end_for:
end_for:
print(max(max(W[z][u] $u=1..n) $z=1..nops(W))):
X:=append(X,nops(X)):
end_while:

Code 4
An infinite computation of f(n)