1
s_
0
2
s_
s_
0
3
s_
s_
s_
0
4
s_
s_
s_
s_
0
5
s_
s_
s_
s_
s_
0
6
s_
s_
s_
s_
s_
s_
0
7
s_
s_
s_
s_
s_
s_
s_
0
U101
tt
M
N
d
N
M
U11
tt
0
U111
tt
0
U121
tt
M'
N'
U122
equal
_>_
N'
M'
true
M'
N'
U122
tt
M'
N'
gcd
d
N'
M'
M'
U131
tt
N'
N'
U141
tt
N
N
U151
tt
s_
0
U161
tt
M'
N
U162
equal
_>_
M'
N
true
U162
tt
0
U171
tt
M'
N
U172
equal
_>_
N
M'
true
M'
N
U172
tt
M'
N
s_
quot
d
N
M'
M'
U21
tt
M
N
s_
_+_
N
_+_
M
_*_
N
M
U31
tt
N
N
U41
tt
M
N
s_
s_
_+_
N
M
U51
tt
M
N
_>_
M
N
U61
tt
false
U71
tt
true
U81
tt
M
N
_>_
N
M
U91
tt
N
N
_*_
N
0
U11
isNat
N
_*_
s_
N
s_
M
U21
and
isNat
M
isNat
N
M
N
_+_
N
0
U31
isNat
N
N
_+_
s_
N
s_
M
U41
and
isNat
M
isNat
N
M
N
_<_
N
M
U51
and
isNat
M
isNat
N
M
N
_>_
0
M
U61
isNat
M
_>_
N'
0
U71
isNzNat
N'
_>_
s_
N
s_
M
U81
and
isNat
M
isNat
N
M
N
and
tt
X
X
d
0
N
U91
isNat
N
N
d
s_
N
s_
M
U101
and
isNat
M
isNat
N
M
N
equal
X
X
tt
gcd
0
N
U111
isNat
N
gcd
N'
M'
U121
and
isNzNat
M'
isNzNat
N'
M'
N'
gcd
N'
N'
U131
isNzNat
N'
N'
isBoolean
false
tt
isBoolean
true
tt
isBoolean
_<_
V1
V2
and
isNat
V1
isNat
V2
isBoolean
_>_
V1
V2
and
isNat
V1
isNat
V2
isNat
0
tt
isNat
V
isNzNat
V
isNat
_*_
V1
V2
and
isNat
V1
isNat
V2
isNat
_+_
V1
V2
and
isNat
V1
isNat
V2
isNat
d
V1
V2
and
isNat
V1
isNat
V2
isNat
gcd
V1
V2
and
isNat
V1
isNat
V2
isNat
p_
V1
isNzNat
V1
isNat
quot
V1
V2
and
isNat
V1
isNzNat
V2
isNzNat
1
tt
isNzNat
2
tt
isNzNat
3
tt
isNzNat
4
tt
isNzNat
5
tt
isNzNat
6
tt
isNzNat
7
tt
isNzNat
_*_
V1
V2
and
isNzNat
V1
isNzNat
V2
isNzNat
gcd
V1
V2
and
isNzNat
V1
isNzNat
V2
isNzNat
s_
V1
isNat
V1
p_
s_
N
U141
isNat
N
N
quot
M'
M'
U151
isNzNat
M'
quot
N
M'
U161
and
isNzNat
M'
isNat
N
M'
N
quot
N
M'
U171
and
isNzNat
M'
isNat
N
M'
N
d
_+_
_*_
gcd
2.2
_*_
x
y
_*_
y
x
_+_
x
y
_+_
y
x
d
x
y
d
y
x
gcd
x
y
gcd
y
x
d
x
y
d
y
x
_+_
x
y
_+_
y
x
gcd
x
y
gcd
y
x
_*_
x
y
_*_
y
x
_*_
s_
N
s_
M
and
isNat
M
isNat
N
isNzNat
gcd
V1
V2
isNzNat
V2
isBoolean
_<_
V1
V2
and
isNat
V1
isNat
V2
quot
N
M'
U161
and
isNzNat
M'
isNat
N
M'
N
isNat
d
V1
V2
and
isNat
V1
isNat
V2
U172
tt
M'
N
d
N
M'
U21
tt
M
N
_*_
N
M
U51
tt
M
N
_>_
M
N
isNat
quot
V1
V2
and
isNat
V1
isNzNat
V2
isNat
d
V1
V2
isNat
V2
isNat
_+_
V1
V2
and
isNat
V1
isNat
V2
isNat
quot
V1
V2
isNzNat
V2
quot
N
M'
isNat
N
_*_
N
0
U11
isNat
N
U122
tt
M'
N'
gcd
d
N'
M'
M'
isNzNat
_*_
V1
V2
and
isNzNat
V1
isNzNat
V2
p_
s_
N
U141
isNat
N
N
U122
tt
M'
N'
d
N'
M'
U41
tt
M
N
_+_
N
M
_*_
N
0
isNat
N
isNat
gcd
V1
V2
and
isNat
V1
isNat
V2
isNat
_*_
V1
V2
and
isNat
V1
isNat
V2
U121
tt
M'
N'
U122
equal
_>_
N'
M'
true
M'
N'
_>_
s_
N
s_
M
and
isNat
M
isNat
N
isNat
gcd
V1
V2
isNat
V1
isNzNat
_*_
V1
V2
isNzNat
V2
isNzNat
s_
V1
isNat
V1
U121
tt
M'
N'
_>_
N'
M'
quot
N
M'
isNzNat
M'
_+_
s_
N
s_
M
isNat
M
isBoolean
_>_
V1
V2
isNat
V2
quot
M'
M'
U151
isNzNat
M'
isBoolean
_>_
V1
V2
and
isNat
V1
isNat
V2
U101
tt
M
N
d
N
M
_+_
N
0
isNat
N
_>_
N'
0
U71
isNzNat
N'
U161
tt
M'
N
_>_
M'
N
isNat
V
isNzNat
V
_<_
N
M
isNat
N
_<_
N
M
U51
and
isNat
M
isNat
N
M
N
isBoolean
_<_
V1
V2
isNat
V2
isNat
quot
V1
V2
isNat
V1
_>_
0
M
isNat
M
isNat
_+_
V1
V2
isNat
V2
isBoolean
_>_
V1
V2
isNat
V1
quot
N
M'
isNzNat
M'
_<_
N
M
and
isNat
M
isNat
N
_+_
N
0
U31
isNat
N
N
quot
N
M'
and
isNzNat
M'
isNat
N
U172
tt
M'
N
quot
d
N
M'
M'
gcd
N'
N'
U131
isNzNat
N'
N'
isNat
_*_
V1
V2
isNat
V1
quot
N
M'
and
isNzNat
M'
isNat
N
_+_
s_
N
s_
M
isNat
N
_+_
s_
N
s_
M
U41
and
isNat
M
isNat
N
M
N
d
s_
N
s_
M
U101
and
isNat
M
isNat
N
M
N
d
0
N
U91
isNat
N
N
quot
N
M'
U171
and
isNzNat
M'
isNat
N
M'
N
_>_
s_
N
s_
M
isNat
M
U121
tt
M'
N'
equal
_>_
N'
M'
true
quot
M'
M'
isNzNat
M'
U161
tt
M'
N
U162
equal
_>_
M'
N
true
U161
tt
M'
N
equal
_>_
M'
N
true
U21
tt
M
N
_+_
N
_+_
M
_*_
N
M
gcd
0
N
U111
isNat
N
p_
s_
N
isNat
N
_>_
s_
N
s_
M
U81
and
isNat
M
isNat
N
M
N
isBoolean
_<_
V1
V2
isNat
V1
U21
tt
M
N
_+_
M
_*_
N
M
d
s_
N
s_
M
isNat
N
isNat
p_
V1
isNzNat
V1
gcd
0
N
isNat
N
isNzNat
gcd
V1
V2
and
isNzNat
V1
isNzNat
V2
U81
tt
M
N
_>_
N
M
d
s_
N
s_
M
isNat
M
isNat
gcd
V1
V2
isNat
V2
gcd
N'
M'
and
isNzNat
M'
isNzNat
N'
quot
N
M'
isNat
N
gcd
N'
M'
isNzNat
N'
isNat
_*_
V1
V2
isNat
V2
d
s_
N
s_
M
and
isNat
M
isNat
N
isNat
_+_
V1
V2
isNat
V1
isNzNat
gcd
V1
V2
isNzNat
V1
_>_
0
M
U61
isNat
M
isNat
d
V1
V2
isNat
V1
d
0
N
isNat
N
gcd
N'
M'
U121
and
isNzNat
M'
isNzNat
N'
M'
N'
_*_
s_
N
s_
M
isNat
M
_>_
N'
0
isNzNat
N'
_*_
s_
N
s_
M
U21
and
isNat
M
isNat
N
M
N
isNzNat
_*_
V1
V2
isNzNat
V1
_>_
s_
N
s_
M
isNat
N
gcd
N'
N'
isNzNat
N'
U171
tt
M'
N
U172
equal
_>_
N
M'
true
M'
N
U171
tt
M'
N
equal
_>_
N
M'
true
_*_
s_
N
s_
M
isNat
N
U171
tt
M'
N
_>_
N
M'
_<_
N
M
isNat
M
_+_
s_
N
s_
M
and
isNat
M
isNat
N
gcd
N'
M'
isNzNat
M'
_<_
N
M
isNat
M
false
_<_
N
M
and
isNat
M
isNat
N
false
isBoolean
_>_
V1
V2
isNat
V1
false
isBoolean
_<_
V1
V2
isNat
V2
false
_<_
N
M
U51
and
isNat
M
isNat
N
M
N
false
_<_
N
M
isNat
N
false
isBoolean
_>_
V1
V2
and
isNat
V1
isNat
V2
false
isBoolean
_>_
V1
V2
isNat
V2
false
p_
s_
N
U141
isNat
N
N
false
gcd
x
y
gcd
y
x
gcd
N'
M'
U121
and
isNzNat
M'
isNzNat
N'
M'
N'
U121
tt
M'
N'
U122
equal
_>_
N'
M'
true
M'
N'
U122
tt
M'
N'
gcd
d
N'
M'
M'
true
Failed!
NaTT
certifiable-1.6