|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
a____#(
mark(
X
)
,
a____(
mark(
Y
)
,
mark(
Z
)
)
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
mark#(
X
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
a____#(
mark(
Y
)
,
mark(
Z
)
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
mark#(
Y
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
mark#(
Z
)
|
|
a____#(
X
,
nil
)
|
→ |
mark#(
X
)
|
|
a____#(
nil
,
X
)
|
→ |
mark#(
X
)
|
|
a__U21#(
tt
,
V2
)
|
→ |
a__U22#(
a__isList(
V2
)
)
|
|
a__U21#(
tt
,
V2
)
|
→ |
a__isList#(
V2
)
|
|
a__U41#(
tt
,
V2
)
|
→ |
a__U42#(
a__isNeList(
V2
)
)
|
|
a__U41#(
tt
,
V2
)
|
→ |
a__isNeList#(
V2
)
|
|
a__U51#(
tt
,
V2
)
|
→ |
a__U52#(
a__isList(
V2
)
)
|
|
a__U51#(
tt
,
V2
)
|
→ |
a__isList#(
V2
)
|
|
a__U71#(
tt
,
P
)
|
→ |
a__U72#(
a__isPal(
P
)
)
|
|
a__U71#(
tt
,
P
)
|
→ |
a__isPal#(
P
)
|
|
a__isList#(
V
)
|
→ |
a__U11#(
a__isNeList(
V
)
)
|
|
a__isList#(
V
)
|
→ |
a__isNeList#(
V
)
|
|
a__isList#(
__(
V1
,
V2
)
)
|
→ |
a__U21#(
a__isList(
V1
)
,
V2
)
|
|
a__isList#(
__(
V1
,
V2
)
)
|
→ |
a__isList#(
V1
)
|
|
a__isNeList#(
V
)
|
→ |
a__U31#(
a__isQid(
V
)
)
|
|
a__isNeList#(
V
)
|
→ |
a__isQid#(
V
)
|
|
a__isNeList#(
__(
V1
,
V2
)
)
|
→ |
a__U41#(
a__isList(
V1
)
,
V2
)
|
|
a__isNeList#(
__(
V1
,
V2
)
)
|
→ |
a__isList#(
V1
)
|
|
a__isNeList#(
__(
V1
,
V2
)
)
|
→ |
a__U51#(
a__isNeList(
V1
)
,
V2
)
|
|
a__isNeList#(
__(
V1
,
V2
)
)
|
→ |
a__isNeList#(
V1
)
|
|
a__isNePal#(
V
)
|
→ |
a__U61#(
a__isQid(
V
)
)
|
|
a__isNePal#(
V
)
|
→ |
a__isQid#(
V
)
|
|
a__isNePal#(
__(
I
,
__(
P
,
I
)
)
)
|
→ |
a__U71#(
a__isQid(
I
)
,
P
)
|
|
a__isNePal#(
__(
I
,
__(
P
,
I
)
)
)
|
→ |
a__isQid#(
I
)
|
|
a__isPal#(
V
)
|
→ |
a__U81#(
a__isNePal(
V
)
)
|
|
a__isPal#(
V
)
|
→ |
a__isNePal#(
V
)
|
|
mark#(
__(
X1
,
X2
)
)
|
→ |
a____#(
mark(
X1
)
,
mark(
X2
)
)
|
|
mark#(
__(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
__(
X1
,
X2
)
)
|
→ |
mark#(
X2
)
|
|
mark#(
U11(
X
)
)
|
→ |
a__U11#(
mark(
X
)
)
|
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
a__U21#(
mark(
X1
)
,
X2
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U22(
X
)
)
|
→ |
a__U22#(
mark(
X
)
)
|
|
mark#(
U22(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
isList(
X
)
)
|
→ |
a__isList#(
X
)
|
|
mark#(
U31(
X
)
)
|
→ |
a__U31#(
mark(
X
)
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
a__U41#(
mark(
X1
)
,
X2
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U42(
X
)
)
|
→ |
a__U42#(
mark(
X
)
)
|
|
mark#(
U42(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
isNeList(
X
)
)
|
→ |
a__isNeList#(
X
)
|
|
mark#(
U51(
X1
,
X2
)
)
|
→ |
a__U51#(
mark(
X1
)
,
X2
)
|
|
mark#(
U51(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U52(
X
)
)
|
→ |
a__U52#(
mark(
X
)
)
|
|
mark#(
U52(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U61(
X
)
)
|
→ |
a__U61#(
mark(
X
)
)
|
|
mark#(
U61(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U71(
X1
,
X2
)
)
|
→ |
a__U71#(
mark(
X1
)
,
X2
)
|
|
mark#(
U71(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U72(
X
)
)
|
→ |
a__U72#(
mark(
X
)
)
|
|
mark#(
U72(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
isPal(
X
)
)
|
→ |
a__isPal#(
X
)
|
|
mark#(
U81(
X
)
)
|
→ |
a__U81#(
mark(
X
)
)
|
|
mark#(
U81(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
isQid(
X
)
)
|
→ |
a__isQid#(
X
)
|
|
mark#(
isNePal(
X
)
)
|
→ |
a__isNePal#(
X
)
|
The dependency pairs are split into 3 component(s).
-
The
1st
component contains the
pair(s)
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
mark#(
X
)
|
|
mark#(
__(
X1
,
X2
)
)
|
→ |
a____#(
mark(
X1
)
,
mark(
X2
)
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
a____#(
mark(
X
)
,
a____(
mark(
Y
)
,
mark(
Z
)
)
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
a____#(
mark(
Y
)
,
mark(
Z
)
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
mark#(
Y
)
|
|
mark#(
__(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
__(
X1
,
X2
)
)
|
→ |
mark#(
X2
)
|
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U22(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U42(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U51(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U52(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U61(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U71(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U72(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U81(
X
)
)
|
→ |
mark#(
X
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
mark#(
Z
)
|
|
a____#(
X
,
nil
)
|
→ |
mark#(
X
)
|
|
a____#(
nil
,
X
)
|
→ |
mark#(
X
)
|
1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
2
x1
|
|
[U81
(x1)
]
|
= |
x1
|
|
[__
(x1, x2)
]
|
= |
x1 + x2
|
|
[a]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
0
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[U22
(x1)
]
|
= |
x1
|
|
[a__U51
(x1, x2)
]
|
= |
2
x1
|
|
[a__U22
(x1)
]
|
= |
x1
|
|
[a____
(x1, x2)
]
|
= |
x1 + x2
|
|
[a__U61
(x1)
]
|
= |
2
x1
|
|
[i]
|
= |
2
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[U72
(x1)
]
|
= |
x1
|
|
[a__U41
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[a__U81
(x1)
]
|
= |
x1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[a__U11
(x1)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[a__isPal
(x1)
]
|
= |
0
|
|
[isPal
(x1)
]
|
= |
0
|
|
[U11
(x1)
]
|
= |
2
x1
|
|
[a____#
(x1, x2)
]
|
= |
x1 + x2
|
|
[isList
(x1)
]
|
= |
0
|
|
[a__U42
(x1)
]
|
= |
x1
|
|
[a__U72
(x1)
]
|
= |
x1
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
2
x1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[mark#
(x1)
]
|
= |
x1
|
|
[a__U71
(x1, x2)
]
|
= |
2
x1
|
|
[U51
(x1, x2)
]
|
= |
2
x1
|
|
[nil]
|
= |
1
|
|
[a__isNeList
(x1)
]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[a__U52
(x1)
]
|
= |
2
x1
|
|
[a__isNePal
(x1)
]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[a__isList
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
mark#(
X
)
|
|
mark#(
__(
X1
,
X2
)
)
|
→ |
a____#(
mark(
X1
)
,
mark(
X2
)
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
a____#(
mark(
X
)
,
a____(
mark(
Y
)
,
mark(
Z
)
)
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
a____#(
mark(
Y
)
,
mark(
Z
)
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
mark#(
Y
)
|
|
mark#(
__(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
__(
X1
,
X2
)
)
|
→ |
mark#(
X2
)
|
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U22(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U42(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U51(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U52(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U61(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U71(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U72(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U81(
X
)
)
|
→ |
mark#(
X
)
|
|
a____#(
__(
X
,
Y
)
,
Z
)
|
→ |
mark#(
Z
)
|
1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
2
x1
|
|
[U81
(x1)
]
|
= |
x1
|
|
[__
(x1, x2)
]
|
= |
2
x1 + x2
+
2
|
|
[a]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
0
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[U22
(x1)
]
|
= |
x1
|
|
[a__U51
(x1, x2)
]
|
= |
2
x1
|
|
[a__U22
(x1)
]
|
= |
x1
|
|
[a____
(x1, x2)
]
|
= |
2
x1 + x2
+
2
|
|
[a__U61
(x1)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[U72
(x1)
]
|
= |
x1
|
|
[a__U41
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
0
|
|
[a__U81
(x1)
]
|
= |
x1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[a__U11
(x1)
]
|
= |
x1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[a__isPal
(x1)
]
|
= |
0
|
|
[isPal
(x1)
]
|
= |
0
|
|
[U11
(x1)
]
|
= |
x1
|
|
[a____#
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[isList
(x1)
]
|
= |
0
|
|
[a__U42
(x1)
]
|
= |
2
x1
|
|
[a__U72
(x1)
]
|
= |
x1
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[U41
(x1, x2)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[mark#
(x1)
]
|
= |
x1
+
1
|
|
[a__U71
(x1, x2)
]
|
= |
2
x1
|
|
[U51
(x1, x2)
]
|
= |
2
x1
|
|
[nil]
|
= |
0
|
|
[a__isNeList
(x1)
]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
3
|
|
[e]
|
= |
2
|
|
[a__U52
(x1)
]
|
= |
x1
|
|
[a__isNePal
(x1)
]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[a__isList
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U22(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U42(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U51(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U52(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U61(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U71(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U72(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U81(
X
)
)
|
→ |
mark#(
X
)
|
1.1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
x1
|
|
[U81
(x1)
]
|
= |
x1
|
|
[__
(x1, x2)
]
|
= |
x1 + x2
|
|
[a]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
0
|
|
[isNePal
(x1)
]
|
= |
1
|
|
[U22
(x1)
]
|
= |
2
x1
|
|
[a__U51
(x1, x2)
]
|
= |
x1
|
|
[a__U22
(x1)
]
|
= |
2
x1
|
|
[a____
(x1, x2)
]
|
= |
x1 + x2
|
|
[a__U61
(x1)
]
|
= |
2
x1
+
1
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[a__U41
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
0
|
|
[a__U81
(x1)
]
|
= |
x1
|
|
[U71
(x1, x2)
]
|
= |
x1
+
1
|
|
[a__U11
(x1)
]
|
= |
x1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[a__isPal
(x1)
]
|
= |
1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[a__U42
(x1)
]
|
= |
x1
|
|
[a__U72
(x1)
]
|
= |
x1
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
x1
|
|
[U41
(x1, x2)
]
|
= |
2
x1
|
|
[U61
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[mark#
(x1)
]
|
= |
x1
|
|
[a__U71
(x1, x2)
]
|
= |
x1
+
1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[a__isNeList
(x1)
]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
2
|
|
[a__U52
(x1)
]
|
= |
2
x1
|
|
[a__isNePal
(x1)
]
|
= |
1
|
|
[isQid
(x1)
]
|
= |
0
|
|
[a__isList
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U22(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U42(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U51(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U52(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U72(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U81(
X
)
)
|
→ |
mark#(
X
)
|
1.1.1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
x1
|
|
[U81
(x1)
]
|
= |
x1
+
1
|
|
[__
(x1, x2)
]
|
= |
2
x1 + x2
+
2
|
|
[a]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
0
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[a__U51
(x1, x2)
]
|
= |
x1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[a__U22
(x1)
]
|
= |
x1
|
|
[a____
(x1, x2)
]
|
= |
2
x1 + x2
+
2
|
|
[a__U61
(x1)
]
|
= |
0
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[a__U41
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[a__U81
(x1)
]
|
= |
x1
+
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[a__U11
(x1)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[a__isPal
(x1)
]
|
= |
2
x1
+
1
|
|
[isPal
(x1)
]
|
= |
2
x1
+
1
|
|
[U11
(x1)
]
|
= |
2
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[a__U42
(x1)
]
|
= |
2
x1
|
|
[a__U72
(x1)
]
|
= |
x1
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
2
x1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
0
|
|
[U31
(x1)
]
|
= |
x1
|
|
[mark#
(x1)
]
|
= |
2
x1
|
|
[a__U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[a__isNeList
(x1)
]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[a__U52
(x1)
]
|
= |
2
x1
|
|
[a__isNePal
(x1)
]
|
= |
2
x1
|
|
[isQid
(x1)
]
|
= |
0
|
|
[a__isList
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U22(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U42(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U51(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U52(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U72(
X
)
)
|
→ |
mark#(
X
)
|
1.1.1.1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
2
x1
|
|
[U81
(x1)
]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 + x2
+
2
|
|
[a]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
0
|
|
[isNePal
(x1)
]
|
= |
x1
+
1
|
|
[a__U51
(x1, x2)
]
|
= |
x1
|
|
[U22
(x1)
]
|
= |
2
x1
|
|
[a__U22
(x1)
]
|
= |
2
x1
|
|
[a____
(x1, x2)
]
|
= |
x1 + x2
+
2
|
|
[a__U61
(x1)
]
|
= |
0
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[a__U41
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[a__U81
(x1)
]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
x1
+
3
|
|
[a__U11
(x1)
]
|
= |
x1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[a__isPal
(x1)
]
|
= |
2
|
|
[isPal
(x1)
]
|
= |
2
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[a__U42
(x1)
]
|
= |
x1
|
|
[a__U72
(x1)
]
|
= |
x1
+
1
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
x1
|
|
[U41
(x1, x2)
]
|
= |
2
x1
|
|
[U61
(x1)
]
|
= |
0
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[mark#
(x1)
]
|
= |
x1
|
|
[a__U71
(x1, x2)
]
|
= |
x1
+
3
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[a__isNeList
(x1)
]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[a__U52
(x1)
]
|
= |
x1
|
|
[a__isNePal
(x1)
]
|
= |
x1
+
1
|
|
[isQid
(x1)
]
|
= |
0
|
|
[a__isList
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U22(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U42(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U51(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U52(
X
)
)
|
→ |
mark#(
X
)
|
1.1.1.1.1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
x1
|
|
[U81
(x1)
]
|
= |
x1
|
|
[__
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[a]
|
= |
1
|
|
[a__isQid
(x1)
]
|
= |
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[a__U51
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[U22
(x1)
]
|
= |
x1
+
2
|
|
[a__U22
(x1)
]
|
= |
x1
+
2
|
|
[a____
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[a__U61
(x1)
]
|
= |
x1
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
1
|
|
[U21
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[a__U41
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[u]
|
= |
1
|
|
[a__U81
(x1)
]
|
= |
x1
|
|
[U71
(x1, x2)
]
|
= |
2
x1 +
2
x2
|
|
[a__U11
(x1)
]
|
= |
x1
|
|
[isNeList
(x1)
]
|
= |
x1
|
|
[U52
(x1)
]
|
= |
x1
+
1
|
|
[a__isPal
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
2
x1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
x1
|
|
[a__U42
(x1)
]
|
= |
x1
+
2
|
|
[a__U72
(x1)
]
|
= |
1
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[U41
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[U61
(x1)
]
|
= |
x1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[mark#
(x1)
]
|
= |
2
x1
|
|
[a__U71
(x1, x2)
]
|
= |
2
x1 +
2
x2
|
|
[U51
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[nil]
|
= |
2
|
|
[a__isNeList
(x1)
]
|
= |
x1
|
|
[tt]
|
= |
1
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[a__U52
(x1)
]
|
= |
x1
+
1
|
|
[a__isNePal
(x1)
]
|
= |
2
x1
|
|
[isQid
(x1)
]
|
= |
x1
|
|
[a__isList
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
+
2
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U51(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
1.1.1.1.1.1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
2
x1
|
|
[U81
(x1)
]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
3
x1 + x2
+
2
|
|
[a]
|
= |
1
|
|
[a__isQid
(x1)
]
|
= |
0
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[a__U51
(x1, x2)
]
|
= |
x1 + x2
+
2
|
|
[U22
(x1)
]
|
= |
0
|
|
[a__U22
(x1)
]
|
= |
0
|
|
[a____
(x1, x2)
]
|
= |
3
x1 + x2
+
2
|
|
[a__U61
(x1)
]
|
= |
0
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[a__U41
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[a__U81
(x1)
]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
0
|
|
[a__U11
(x1)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
x1
|
|
[U52
(x1)
]
|
= |
2
|
|
[a__isPal
(x1)
]
|
= |
0
|
|
[isPal
(x1)
]
|
= |
0
|
|
[U11
(x1)
]
|
= |
2
x1
|
|
[isList
(x1)
]
|
= |
2
x1
|
|
[a__U42
(x1)
]
|
= |
0
|
|
[a__U72
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
0
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[mark#
(x1)
]
|
= |
2
x1
|
|
[a__U71
(x1, x2)
]
|
= |
0
|
|
[U51
(x1, x2)
]
|
= |
x1 + x2
+
2
|
|
[nil]
|
= |
2
|
|
[a__isNeList
(x1)
]
|
= |
x1
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[a__U52
(x1)
]
|
= |
2
|
|
[a__isNePal
(x1)
]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[a__isList
(x1)
]
|
= |
2
x1
|
|
[U42
(x1)
]
|
= |
0
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U41(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
1.1.1.1.1.1.1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
2
x1
|
|
[U81
(x1)
]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
2
x1 + x2
+
1
|
|
[a]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
x1
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[a__U51
(x1, x2)
]
|
= |
0
|
|
[U22
(x1)
]
|
= |
0
|
|
[a____
(x1, x2)
]
|
= |
2
x1 + x2
+
1
|
|
[a__U22
(x1)
]
|
= |
0
|
|
[a__U61
(x1)
]
|
= |
0
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[a__U41
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[u]
|
= |
0
|
|
[a__U81
(x1)
]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
0
|
|
[a__U11
(x1)
]
|
= |
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
0
|
|
[a__isPal
(x1)
]
|
= |
0
|
|
[isPal
(x1)
]
|
= |
0
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
2
x1
|
|
[a__U42
(x1)
]
|
= |
0
|
|
[a__U72
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
|
|
[U41
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[a__U21
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
0
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[mark#
(x1)
]
|
= |
x1
|
|
[a__U71
(x1, x2)
]
|
= |
0
|
|
[U51
(x1, x2)
]
|
= |
0
|
|
[nil]
|
= |
0
|
|
[a__isNeList
(x1)
]
|
= |
2
x1
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
1
|
|
[e]
|
= |
0
|
|
[a__U52
(x1)
]
|
= |
0
|
|
[a__isNePal
(x1)
]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
x1
|
|
[a__isList
(x1)
]
|
= |
2
x1
|
|
[U42
(x1)
]
|
= |
0
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U21(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
1.1.1.1.1.1.1.1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
2
x1
|
|
[U81
(x1)
]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
2
x1 + x2
+
2
|
|
[a]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
0
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[a__U51
(x1, x2)
]
|
= |
0
|
|
[U22
(x1)
]
|
= |
0
|
|
[a____
(x1, x2)
]
|
= |
2
x1 + x2
+
2
|
|
[a__U22
(x1)
]
|
= |
0
|
|
[a__U61
(x1)
]
|
= |
0
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
2
x1
+
2
|
|
[a__U41
(x1, x2)
]
|
= |
0
|
|
[u]
|
= |
0
|
|
[a__U81
(x1)
]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
0
|
|
[a__U11
(x1)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
0
|
|
[a__isPal
(x1)
]
|
= |
2
|
|
[isPal
(x1)
]
|
= |
2
|
|
[U11
(x1)
]
|
= |
2
x1
|
|
[isList
(x1)
]
|
= |
x1
|
|
[a__U42
(x1)
]
|
= |
0
|
|
[a__U72
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
2
x1
+
2
|
|
[U41
(x1, x2)
]
|
= |
0
|
|
[U61
(x1)
]
|
= |
0
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[mark#
(x1)
]
|
= |
x1
|
|
[a__U71
(x1, x2)
]
|
= |
0
|
|
[U51
(x1, x2)
]
|
= |
0
|
|
[nil]
|
= |
0
|
|
[a__isNeList
(x1)
]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[a__U52
(x1)
]
|
= |
0
|
|
[a__isNePal
(x1)
]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[a__isList
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
0
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
U31(
X
)
)
|
→ |
mark#(
X
)
|
1.1.1.1.1.1.1.1.1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
2
x1
+
1
|
|
[U81
(x1)
]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 + x2
|
|
[a]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
0
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[a__U51
(x1, x2)
]
|
= |
x1
|
|
[U22
(x1)
]
|
= |
1
|
|
[a____
(x1, x2)
]
|
= |
x1 + x2
|
|
[a__U22
(x1)
]
|
= |
1
|
|
[a__U61
(x1)
]
|
= |
0
|
|
[i]
|
= |
1
|
|
[U72
(x1)
]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
2
|
|
[a__U41
(x1, x2)
]
|
= |
0
|
|
[u]
|
= |
0
|
|
[a__U81
(x1)
]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
0
|
|
[a__U11
(x1)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
1
|
|
[U52
(x1)
]
|
= |
0
|
|
[a__isPal
(x1)
]
|
= |
0
|
|
[isPal
(x1)
]
|
= |
0
|
|
[U11
(x1)
]
|
= |
2
x1
|
|
[isList
(x1)
]
|
= |
2
|
|
[a__U42
(x1)
]
|
= |
0
|
|
[a__U72
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
2
|
|
[U41
(x1, x2)
]
|
= |
0
|
|
[U61
(x1)
]
|
= |
0
|
|
[U31
(x1)
]
|
= |
2
x1
+
1
|
|
[mark#
(x1)
]
|
= |
x1
|
|
[a__U71
(x1, x2)
]
|
= |
0
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[a__isNeList
(x1)
]
|
= |
1
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[a__isNePal
(x1)
]
|
= |
0
|
|
[a__U52
(x1)
]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[a__isList
(x1)
]
|
= |
2
|
|
[U42
(x1)
]
|
= |
0
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
U11(
X
)
)
|
→ |
mark#(
X
)
|
1.1.1.1.1.1.1.1.1.1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
0
|
|
[U81
(x1)
]
|
= |
0
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[a__isQid
(x1)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[a__U51
(x1, x2)
]
|
= |
0
|
|
[U22
(x1)
]
|
= |
0
|
|
[a____
(x1, x2)
]
|
= |
2
x1 + x2
|
|
[a__U22
(x1)
]
|
= |
0
|
|
[a__U61
(x1)
]
|
= |
0
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[a__U41
(x1, x2)
]
|
= |
0
|
|
[u]
|
= |
2
|
|
[a__U81
(x1)
]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
0
|
|
[a__U11
(x1)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
0
|
|
[a__isPal
(x1)
]
|
= |
0
|
|
[isPal
(x1)
]
|
= |
0
|
|
[U11
(x1)
]
|
= |
2
x1
+
1
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[a__U42
(x1)
]
|
= |
0
|
|
[a__U72
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
x1
|
|
[U41
(x1, x2)
]
|
= |
0
|
|
[U61
(x1)
]
|
= |
0
|
|
[U31
(x1)
]
|
= |
0
|
|
[mark#
(x1)
]
|
= |
2
x1
|
|
[a__U71
(x1, x2)
]
|
= |
0
|
|
[U51
(x1, x2)
]
|
= |
0
|
|
[nil]
|
= |
0
|
|
[a__isNeList
(x1)
]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[a__isNePal
(x1)
]
|
= |
0
|
|
[a__U52
(x1)
]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[a__isList
(x1)
]
|
= |
2
x1
+
2
|
|
[U42
(x1)
]
|
= |
0
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.1.1.1.1.1.1.1.1.1.1.1.1: P is empty
All dependency pairs have been removed.
-
The
2nd
component contains the
pair(s)
|
a__U21#(
tt
,
V2
)
|
→ |
a__isList#(
V2
)
|
|
a__isList#(
V
)
|
→ |
a__isNeList#(
V
)
|
|
a__isNeList#(
__(
V1
,
V2
)
)
|
→ |
a__U41#(
a__isList(
V1
)
,
V2
)
|
|
a__U41#(
tt
,
V2
)
|
→ |
a__isNeList#(
V2
)
|
|
a__isNeList#(
__(
V1
,
V2
)
)
|
→ |
a__isList#(
V1
)
|
|
a__isList#(
__(
V1
,
V2
)
)
|
→ |
a__U21#(
a__isList(
V1
)
,
V2
)
|
|
a__isList#(
__(
V1
,
V2
)
)
|
→ |
a__isList#(
V1
)
|
|
a__isNeList#(
__(
V1
,
V2
)
)
|
→ |
a__U51#(
a__isNeList(
V1
)
,
V2
)
|
|
a__U51#(
tt
,
V2
)
|
→ |
a__isList#(
V2
)
|
|
a__isNeList#(
__(
V1
,
V2
)
)
|
→ |
a__isNeList#(
V1
)
|
1.1.2: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
x1 + x2
+
3
|
|
[a]
|
= |
1
|
|
[isNePal
(x1)
]
|
= |
x1
|
|
[a__U51
(x1, x2)
]
|
= |
0
|
|
[a__U22
(x1)
]
|
= |
0
|
|
[i]
|
= |
2
|
|
[U21
(x1, x2)
]
|
= |
0
|
|
[U72
(x1)
]
|
= |
0
|
|
[a__isNeList#
(x1)
]
|
= |
2
x1
|
|
[U71
(x1, x2)
]
|
= |
3
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[a__isPal
(x1)
]
|
= |
1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
0
|
|
[a__U51#
(x1, x2)
]
|
= |
2
x1
+
2
|
|
[a__U72
(x1)
]
|
= |
0
|
|
[U61
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
0
|
|
[a__U21
(x1, x2)
]
|
= |
0
|
|
[U31
(x1)
]
|
= |
0
|
|
[a__U71
(x1, x2)
]
|
= |
3
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[a__U21#
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[a__isNePal
(x1)
]
|
= |
x1
|
|
[a__U31
(x1)
]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
0
|
|
[a____
(x1, x2)
]
|
= |
x1 + x2
+
3
|
|
[a__U61
(x1)
]
|
= |
0
|
|
[a__U41#
(x1, x2)
]
|
= |
2
x1
+
3
|
|
[a__U41
(x1, x2)
]
|
= |
0
|
|
[a__U81
(x1)
]
|
= |
1
|
|
[u]
|
= |
0
|
|
[a__U11
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[a__U42
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__isList#
(x1)
]
|
= |
2
x1
+
1
|
|
[U51
(x1, x2)
]
|
= |
0
|
|
[nil]
|
= |
0
|
|
[a__isNeList
(x1)
]
|
= |
0
|
|
[a__U52
(x1)
]
|
= |
2
x1
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[a__isList
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
0
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
a__U21#(
tt
,
V2
)
|
→ |
a__isList#(
V2
)
|
1.1.2.1: dependency graph processor
The dependency pairs are split into 0 component(s).
-
The
3rd
component contains the
pair(s)
|
a__U71#(
tt
,
P
)
|
→ |
a__isPal#(
P
)
|
|
a__isPal#(
V
)
|
→ |
a__isNePal#(
V
)
|
|
a__isNePal#(
__(
I
,
__(
P
,
I
)
)
)
|
→ |
a__U71#(
a__isQid(
I
)
,
P
)
|
1.1.3: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[a__U31
(x1)
]
|
= |
0
|
|
[U81
(x1)
]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 + x2
+
1
|
|
[a]
|
= |
0
|
|
[a__isQid
(x1)
]
|
= |
0
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[a__U51
(x1, x2)
]
|
= |
0
|
|
[U22
(x1)
]
|
= |
0
|
|
[a____
(x1, x2)
]
|
= |
x1 + x2
+
1
|
|
[a__U22
(x1)
]
|
= |
0
|
|
[a__U61
(x1)
]
|
= |
0
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
0
|
|
[a__isPal#
(x1)
]
|
= |
2
x1
+
1
|
|
[a__U41
(x1, x2)
]
|
= |
0
|
|
[u]
|
= |
2
|
|
[a__U81
(x1)
]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
0
|
|
[a__U11
(x1)
]
|
= |
0
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
0
|
|
[a__isPal
(x1)
]
|
= |
0
|
|
[isPal
(x1)
]
|
= |
0
|
|
[U11
(x1)
]
|
= |
0
|
|
[isList
(x1)
]
|
= |
0
|
|
[a__U42
(x1)
]
|
= |
0
|
|
[a__U72
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
|
|
[a__U21
(x1, x2)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
0
|
|
[U61
(x1)
]
|
= |
0
|
|
[U31
(x1)
]
|
= |
0
|
|
[a__U71
(x1, x2)
]
|
= |
0
|
|
[U51
(x1, x2)
]
|
= |
0
|
|
[nil]
|
= |
0
|
|
[a__isNeList
(x1)
]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[a__isNePal#
(x1)
]
|
= |
2
x1
|
|
[a__isNePal
(x1)
]
|
= |
2
x1
|
|
[a__U52
(x1)
]
|
= |
0
|
|
[a__U71#
(x1, x2)
]
|
= |
2
x1
+
2
|
|
[isQid
(x1)
]
|
= |
0
|
|
[a__isList
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
0
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.3.1: P is empty
All dependency pairs have been removed.