|
active#(
__(
__(
X
,
Y
)
,
Z
)
)
|
→ |
__#(
X
,
__(
Y
,
Z
)
)
|
|
active#(
__(
__(
X
,
Y
)
,
Z
)
)
|
→ |
__#(
Y
,
Z
)
|
|
active#(
U21(
tt
,
V2
)
)
|
→ |
U22#(
isList(
V2
)
)
|
|
active#(
U21(
tt
,
V2
)
)
|
→ |
isList#(
V2
)
|
|
active#(
U41(
tt
,
V2
)
)
|
→ |
U42#(
isNeList(
V2
)
)
|
|
active#(
U41(
tt
,
V2
)
)
|
→ |
isNeList#(
V2
)
|
|
active#(
U51(
tt
,
V2
)
)
|
→ |
U52#(
isList(
V2
)
)
|
|
active#(
U51(
tt
,
V2
)
)
|
→ |
isList#(
V2
)
|
|
active#(
U71(
tt
,
P
)
)
|
→ |
U72#(
isPal(
P
)
)
|
|
active#(
U71(
tt
,
P
)
)
|
→ |
isPal#(
P
)
|
|
active#(
isList(
V
)
)
|
→ |
U11#(
isNeList(
V
)
)
|
|
active#(
isList(
V
)
)
|
→ |
isNeList#(
V
)
|
|
active#(
isList(
__(
V1
,
V2
)
)
)
|
→ |
U21#(
isList(
V1
)
,
V2
)
|
|
active#(
isList(
__(
V1
,
V2
)
)
)
|
→ |
isList#(
V1
)
|
|
active#(
isNeList(
V
)
)
|
→ |
U31#(
isQid(
V
)
)
|
|
active#(
isNeList(
V
)
)
|
→ |
isQid#(
V
)
|
|
active#(
isNeList(
__(
V1
,
V2
)
)
)
|
→ |
U41#(
isList(
V1
)
,
V2
)
|
|
active#(
isNeList(
__(
V1
,
V2
)
)
)
|
→ |
isList#(
V1
)
|
|
active#(
isNeList(
__(
V1
,
V2
)
)
)
|
→ |
U51#(
isNeList(
V1
)
,
V2
)
|
|
active#(
isNeList(
__(
V1
,
V2
)
)
)
|
→ |
isNeList#(
V1
)
|
|
active#(
isNePal(
V
)
)
|
→ |
U61#(
isQid(
V
)
)
|
|
active#(
isNePal(
V
)
)
|
→ |
isQid#(
V
)
|
|
active#(
isNePal(
__(
I
,
__(
P
,
I
)
)
)
)
|
→ |
U71#(
isQid(
I
)
,
P
)
|
|
active#(
isNePal(
__(
I
,
__(
P
,
I
)
)
)
)
|
→ |
isQid#(
I
)
|
|
active#(
isPal(
V
)
)
|
→ |
U81#(
isNePal(
V
)
)
|
|
active#(
isPal(
V
)
)
|
→ |
isNePal#(
V
)
|
|
active#(
__(
X1
,
X2
)
)
|
→ |
__#(
active(
X1
)
,
X2
)
|
|
active#(
__(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
__(
X1
,
X2
)
)
|
→ |
__#(
X1
,
active(
X2
)
)
|
|
active#(
__(
X1
,
X2
)
)
|
→ |
active#(
X2
)
|
|
active#(
U11(
X
)
)
|
→ |
U11#(
active(
X
)
)
|
|
active#(
U11(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U21(
X1
,
X2
)
)
|
→ |
U21#(
active(
X1
)
,
X2
)
|
|
active#(
U21(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
U22(
X
)
)
|
→ |
U22#(
active(
X
)
)
|
|
active#(
U22(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U31(
X
)
)
|
→ |
U31#(
active(
X
)
)
|
|
active#(
U31(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U41(
X1
,
X2
)
)
|
→ |
U41#(
active(
X1
)
,
X2
)
|
|
active#(
U41(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
U42(
X
)
)
|
→ |
U42#(
active(
X
)
)
|
|
active#(
U42(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U51(
X1
,
X2
)
)
|
→ |
U51#(
active(
X1
)
,
X2
)
|
|
active#(
U51(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
U52(
X
)
)
|
→ |
U52#(
active(
X
)
)
|
|
active#(
U52(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U61(
X
)
)
|
→ |
U61#(
active(
X
)
)
|
|
active#(
U61(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U71(
X1
,
X2
)
)
|
→ |
U71#(
active(
X1
)
,
X2
)
|
|
active#(
U71(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
U72(
X
)
)
|
→ |
U72#(
active(
X
)
)
|
|
active#(
U72(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U81(
X
)
)
|
→ |
U81#(
active(
X
)
)
|
|
active#(
U81(
X
)
)
|
→ |
active#(
X
)
|
|
__#(
mark(
X1
)
,
X2
)
|
→ |
__#(
X1
,
X2
)
|
|
__#(
X1
,
mark(
X2
)
)
|
→ |
__#(
X1
,
X2
)
|
|
U11#(
mark(
X
)
)
|
→ |
U11#(
X
)
|
|
U21#(
mark(
X1
)
,
X2
)
|
→ |
U21#(
X1
,
X2
)
|
|
U22#(
mark(
X
)
)
|
→ |
U22#(
X
)
|
|
U31#(
mark(
X
)
)
|
→ |
U31#(
X
)
|
|
U41#(
mark(
X1
)
,
X2
)
|
→ |
U41#(
X1
,
X2
)
|
|
U42#(
mark(
X
)
)
|
→ |
U42#(
X
)
|
|
U51#(
mark(
X1
)
,
X2
)
|
→ |
U51#(
X1
,
X2
)
|
|
U52#(
mark(
X
)
)
|
→ |
U52#(
X
)
|
|
U61#(
mark(
X
)
)
|
→ |
U61#(
X
)
|
|
U71#(
mark(
X1
)
,
X2
)
|
→ |
U71#(
X1
,
X2
)
|
|
U72#(
mark(
X
)
)
|
→ |
U72#(
X
)
|
|
U81#(
mark(
X
)
)
|
→ |
U81#(
X
)
|
|
proper#(
__(
X1
,
X2
)
)
|
→ |
__#(
proper(
X1
)
,
proper(
X2
)
)
|
|
proper#(
__(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
__(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
U11(
X
)
)
|
→ |
U11#(
proper(
X
)
)
|
|
proper#(
U11(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U21(
X1
,
X2
)
)
|
→ |
U21#(
proper(
X1
)
,
proper(
X2
)
)
|
|
proper#(
U21(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U21(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
U22(
X
)
)
|
→ |
U22#(
proper(
X
)
)
|
|
proper#(
U22(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isList(
X
)
)
|
→ |
isList#(
proper(
X
)
)
|
|
proper#(
isList(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U31(
X
)
)
|
→ |
U31#(
proper(
X
)
)
|
|
proper#(
U31(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U41(
X1
,
X2
)
)
|
→ |
U41#(
proper(
X1
)
,
proper(
X2
)
)
|
|
proper#(
U41(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U41(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
U42(
X
)
)
|
→ |
U42#(
proper(
X
)
)
|
|
proper#(
U42(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isNeList(
X
)
)
|
→ |
isNeList#(
proper(
X
)
)
|
|
proper#(
isNeList(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U51(
X1
,
X2
)
)
|
→ |
U51#(
proper(
X1
)
,
proper(
X2
)
)
|
|
proper#(
U51(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U51(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
U52(
X
)
)
|
→ |
U52#(
proper(
X
)
)
|
|
proper#(
U52(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U61(
X
)
)
|
→ |
U61#(
proper(
X
)
)
|
|
proper#(
U61(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U71(
X1
,
X2
)
)
|
→ |
U71#(
proper(
X1
)
,
proper(
X2
)
)
|
|
proper#(
U71(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U71(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
U72(
X
)
)
|
→ |
U72#(
proper(
X
)
)
|
|
proper#(
U72(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isPal(
X
)
)
|
→ |
isPal#(
proper(
X
)
)
|
|
proper#(
isPal(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U81(
X
)
)
|
→ |
U81#(
proper(
X
)
)
|
|
proper#(
U81(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isQid(
X
)
)
|
→ |
isQid#(
proper(
X
)
)
|
|
proper#(
isQid(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isNePal(
X
)
)
|
→ |
isNePal#(
proper(
X
)
)
|
|
proper#(
isNePal(
X
)
)
|
→ |
proper#(
X
)
|
|
__#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
__#(
X1
,
X2
)
|
|
U11#(
ok(
X
)
)
|
→ |
U11#(
X
)
|
|
U21#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
U21#(
X1
,
X2
)
|
|
U22#(
ok(
X
)
)
|
→ |
U22#(
X
)
|
|
isList#(
ok(
X
)
)
|
→ |
isList#(
X
)
|
|
U31#(
ok(
X
)
)
|
→ |
U31#(
X
)
|
|
U41#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
U41#(
X1
,
X2
)
|
|
U42#(
ok(
X
)
)
|
→ |
U42#(
X
)
|
|
isNeList#(
ok(
X
)
)
|
→ |
isNeList#(
X
)
|
|
U51#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
U51#(
X1
,
X2
)
|
|
U52#(
ok(
X
)
)
|
→ |
U52#(
X
)
|
|
U61#(
ok(
X
)
)
|
→ |
U61#(
X
)
|
|
U71#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
U71#(
X1
,
X2
)
|
|
U72#(
ok(
X
)
)
|
→ |
U72#(
X
)
|
|
isPal#(
ok(
X
)
)
|
→ |
isPal#(
X
)
|
|
U81#(
ok(
X
)
)
|
→ |
U81#(
X
)
|
|
isQid#(
ok(
X
)
)
|
→ |
isQid#(
X
)
|
|
isNePal#(
ok(
X
)
)
|
→ |
isNePal#(
X
)
|
|
top#(
mark(
X
)
)
|
→ |
top#(
proper(
X
)
)
|
|
top#(
mark(
X
)
)
|
→ |
proper#(
X
)
|
|
top#(
ok(
X
)
)
|
→ |
top#(
active(
X
)
)
|
|
top#(
ok(
X
)
)
|
→ |
active#(
X
)
|
The dependency pairs are split into 21 component(s).
-
The
1st
component contains the
pair(s)
|
top#(
ok(
X
)
)
|
→ |
top#(
active(
X
)
)
|
|
top#(
mark(
X
)
)
|
→ |
top#(
proper(
X
)
)
|
1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
+
1
|
|
[__
(x1, x2)
]
|
= |
3
x1 + x2
+
2
|
|
[a]
|
= |
3
|
|
[isNePal
(x1)
]
|
= |
2
x1
+
1
|
|
[U22
(x1)
]
|
= |
x1
+
1
|
|
[i]
|
= |
3
|
|
[U72
(x1)
]
|
= |
x1
+
2
|
|
[U21
(x1, x2)
]
|
= |
2
x1 +
3
x2
+
1
|
|
[u]
|
= |
3
|
|
[U71
(x1, x2)
]
|
= |
3
x1 +
2
x2
+
2
|
|
[isNeList
(x1)
]
|
= |
3
x1
+
1
|
|
[U52
(x1)
]
|
= |
x1
+
2
|
|
[isPal
(x1)
]
|
= |
2
x1
+
3
|
|
[U11
(x1)
]
|
= |
x1
+
1
|
|
[top#
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
3
x1
+
3
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1 +
3
x2
+
3
|
|
[U61
(x1)
]
|
= |
2
x1
|
|
[active
(x1)
]
|
= |
x1
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[U51
(x1, x2)
]
|
= |
2
x1 +
3
x2
+
2
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
3
|
|
[e]
|
= |
3
|
|
[isQid
(x1)
]
|
= |
x1
|
|
[ok
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
+
2
|
|
[proper
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
top#(
ok(
X
)
)
|
→ |
top#(
active(
X
)
)
|
1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
2
x1
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
2
x1
|
|
[U21
(x1, x2)
]
|
= |
3
x1 +
3
x2
+
2
|
|
[u]
|
= |
2
|
|
[U71
(x1, x2)
]
|
= |
3
x1
|
|
[isNeList
(x1)
]
|
= |
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
2
x1
|
|
[U11
(x1)
]
|
= |
2
x1
+
2
|
|
[top#
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
3
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
2
x1 +
3
x2
+
1
|
|
[U61
(x1)
]
|
= |
2
x1
|
|
[active
(x1)
]
|
= |
x1
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[U51
(x1, x2)
]
|
= |
3
x1
+
3
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
x1
+
1
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[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: P is empty
All dependency pairs have been removed.
-
The
2nd
component contains the
pair(s)
|
active#(
__(
X1
,
X2
)
)
|
→ |
active#(
X2
)
|
|
active#(
__(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
U11(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U21(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
U22(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U31(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U41(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
U42(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U51(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
U52(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U61(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U71(
X1
,
X2
)
)
|
→ |
active#(
X1
)
|
|
active#(
U72(
X
)
)
|
→ |
active#(
X
)
|
|
active#(
U81(
X
)
)
|
→ |
active#(
X
)
|
1.1.2: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
+
1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
2
x1 + x2
+
3
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[U22
(x1)
]
|
= |
2
x1
+
3
|
|
[i]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[U72
(x1)
]
|
= |
2
x1
+
3
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
3
|
|
[U52
(x1)
]
|
= |
2
x1
+
1
|
|
[isPal
(x1)
]
|
= |
0
|
|
[U11
(x1)
]
|
= |
2
x1
+
1
|
|
[isList
(x1)
]
|
= |
x1
+
3
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[active#
(x1)
]
|
= |
2
x1
|
|
[U61
(x1)
]
|
= |
x1
+
3
|
|
[U41
(x1, x2)
]
|
= |
x1
+
3
|
|
[active
(x1)
]
|
= |
3
x1
|
|
[U31
(x1)
]
|
= |
x1
+
3
|
|
[U51
(x1, x2)
]
|
= |
x1
+
3
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
0
|
|
[e]
|
= |
1
|
|
[isQid
(x1)
]
|
= |
2
|
|
[ok
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
2
x1
+
3
|
|
[proper
(x1)
]
|
= |
2
x1
+
1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.2.1: P is empty
All dependency pairs have been removed.
-
The
3rd
component contains the
pair(s)
|
proper#(
__(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
__(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U11(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U21(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U21(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
U22(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isList(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U31(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U41(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U41(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
U42(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isNeList(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U51(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U51(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
U52(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U61(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U71(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U71(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
U72(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isPal(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U81(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isQid(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
isNePal(
X
)
)
|
→ |
proper#(
X
)
|
1.1.3: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
+
3
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
x1 +
2
x2
|
|
[isNePal
(x1)
]
|
= |
x1
+
3
|
|
[U22
(x1)
]
|
= |
2
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U21
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1 + x2
+
2
|
|
[isNeList
(x1)
]
|
= |
2
x1
+
1
|
|
[U52
(x1)
]
|
= |
2
x1
+
3
|
|
[isPal
(x1)
]
|
= |
x1
+
3
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
2
x1
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U61
(x1)
]
|
= |
x1
+
3
|
|
[U41
(x1, x2)
]
|
= |
x1 +
2
x2
+
1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
3
|
|
[U51
(x1, x2)
]
|
= |
x1 + x2
+
3
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[proper#
(x1)
]
|
= |
2
x1
|
|
[isQid
(x1)
]
|
= |
x1
+
1
|
|
[ok
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
2
x1
+
3
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
proper#(
__(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
__(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U11(
X
)
)
|
→ |
proper#(
X
)
|
|
proper#(
U21(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U21(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
isList(
X
)
)
|
→ |
proper#(
X
)
|
1.1.3.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
1
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
2
x1 +
2
x2
|
|
[isNePal
(x1)
]
|
= |
x1
+
2
|
|
[U22
(x1)
]
|
= |
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
x1 +
2
x2
+
1
|
|
[u]
|
= |
2
|
|
[U71
(x1, x2)
]
|
= |
3
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
+
3
|
|
[U52
(x1)
]
|
= |
3
|
|
[isPal
(x1)
]
|
= |
x1
+
2
|
|
[U11
(x1)
]
|
= |
2
x1
|
|
[isList
(x1)
]
|
= |
2
x1
+
3
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
3
x1
|
|
[U61
(x1)
]
|
= |
0
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
|
|
[U51
(x1, x2)
]
|
= |
3
|
|
[nil]
|
= |
1
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[proper#
(x1)
]
|
= |
x1
|
|
[isQid
(x1)
]
|
= |
2
x1
+
1
|
|
[ok
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
3
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
proper#(
__(
X1
,
X2
)
)
|
→ |
proper#(
X2
)
|
|
proper#(
__(
X1
,
X2
)
)
|
→ |
proper#(
X1
)
|
|
proper#(
U11(
X
)
)
|
→ |
proper#(
X
)
|
1.1.3.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
+
2
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
2
x1 +
2
x2
+
3
|
|
[isNePal
(x1)
]
|
= |
2
x1
+
2
|
|
[U22
(x1)
]
|
= |
2
x1
+
2
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
+
2
|
|
[U21
(x1, x2)
]
|
= |
3
|
|
[u]
|
= |
2
|
|
[U71
(x1, x2)
]
|
= |
3
|
|
[isNeList
(x1)
]
|
= |
3
x1
+
2
|
|
[U52
(x1)
]
|
= |
2
x1
+
2
|
|
[isPal
(x1)
]
|
= |
x1
+
2
|
|
[U11
(x1)
]
|
= |
3
x1
|
|
[isList
(x1)
]
|
= |
3
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
3
|
|
[U41
(x1, x2)
]
|
= |
3
x1 +
2
x2
+
1
|
|
[U61
(x1)
]
|
= |
2
x1
+
2
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
3
x1 +
2
x2
+
1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
1
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[proper#
(x1)
]
|
= |
x1
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
3
|
|
[U42
(x1)
]
|
= |
2
x1
+
2
|
|
[proper
(x1)
]
|
= |
3
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
proper#(
U11(
X
)
)
|
→ |
proper#(
X
)
|
1.1.3.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
0
|
|
[a]
|
= |
3
|
|
[__
(x1, x2)
]
|
= |
x1
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[U22
(x1)
]
|
= |
0
|
|
[i]
|
= |
3
|
|
[U72
(x1)
]
|
= |
0
|
|
[U21
(x1, x2)
]
|
= |
x1 +
3
x2
+
3
|
|
[u]
|
= |
3
|
|
[U71
(x1, x2)
]
|
= |
0
|
|
[isNeList
(x1)
]
|
= |
3
|
|
[U52
(x1)
]
|
= |
x1
+
1
|
|
[isPal
(x1)
]
|
= |
3
x1
|
|
[U11
(x1)
]
|
= |
x1
+
1
|
|
[isList
(x1)
]
|
= |
2
x1
+
3
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1 +
3
x2
+
3
|
|
[U61
(x1)
]
|
= |
x1
+
1
|
|
[active
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
+
3
|
|
[U51
(x1, x2)
]
|
= |
3
x1
|
|
[nil]
|
= |
3
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
3
|
|
[e]
|
= |
3
|
|
[proper#
(x1)
]
|
= |
x1
|
|
[isQid
(x1)
]
|
= |
3
x1
|
|
[ok
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
x1
+
3
|
|
[proper
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.3.1.1.1.1: P is empty
All dependency pairs have been removed.
-
The
4th
component contains the
pair(s)
|
__#(
X1
,
mark(
X2
)
)
|
→ |
__#(
X1
,
X2
)
|
|
__#(
mark(
X1
)
,
X2
)
|
→ |
__#(
X1
,
X2
)
|
|
__#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
__#(
X1
,
X2
)
|
1.1.4: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 + x2
|
|
[isNePal
(x1)
]
|
= |
0
|
|
[U22
(x1)
]
|
= |
x1
|
|
[__#
(x1, x2)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
x1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[isPal
(x1)
]
|
= |
0
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
0
|
|
[e]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[ok
(x1)
]
|
= |
2
x1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
0
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
__#(
X1
,
mark(
X2
)
)
|
→ |
__#(
X1
,
X2
)
|
|
__#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
__#(
X1
,
X2
)
|
1.1.4.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
3
x1 +
3
x2
+
2
|
|
[isNePal
(x1)
]
|
= |
x1
|
|
[U22
(x1)
]
|
= |
2
x1
+
2
|
|
[__#
(x1, x2)
]
|
= |
x1
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
3
x1
+
3
|
|
[U21
(x1, x2)
]
|
= |
3
x1 +
3
x2
+
2
|
|
[u]
|
= |
2
|
|
[U71
(x1, x2)
]
|
= |
x1 +
3
x2
+
3
|
|
[isNeList
(x1)
]
|
= |
2
x1
+
2
|
|
[U52
(x1)
]
|
= |
2
x1
+
2
|
|
[isPal
(x1)
]
|
= |
x1
+
2
|
|
[U11
(x1)
]
|
= |
2
x1
+
2
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
3
x1 +
3
x2
+
2
|
|
[U61
(x1)
]
|
= |
2
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
3
x1 +
3
x2
+
2
|
|
[nil]
|
= |
1
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
2
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
__#(
X1
,
mark(
X2
)
)
|
→ |
__#(
X1
,
X2
)
|
1.1.4.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
3
x1 +
2
x2
+
1
|
|
[isNePal
(x1)
]
|
= |
2
x1
+
2
|
|
[U22
(x1)
]
|
= |
2
x1
+
1
|
|
[__#
(x1, x2)
]
|
= |
x1
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
+
3
|
|
[U21
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[u]
|
= |
2
|
|
[U71
(x1, x2)
]
|
= |
3
x1 + x2
+
1
|
|
[isNeList
(x1)
]
|
= |
x1
+
2
|
|
[U52
(x1)
]
|
= |
3
x1
+
1
|
|
[isPal
(x1)
]
|
= |
2
x1
+
3
|
|
[U11
(x1)
]
|
= |
x1
+
1
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
2
x1 +
2
x2
+
1
|
|
[U61
(x1)
]
|
= |
2
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[ok
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
3
x1
+
1
|
|
[proper
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.4.1.1.1: P is empty
All dependency pairs have been removed.
-
The
5th
component contains the
pair(s)
|
U11#(
ok(
X
)
)
|
→ |
U11#(
X
)
|
|
U11#(
mark(
X
)
)
|
→ |
U11#(
X
)
|
1.1.5: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 +
2
x2
+
2
|
|
[isNePal
(x1)
]
|
= |
1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U11#
(x1)
]
|
= |
2
x1
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
+
2
|
|
[active
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
2
|
|
[e]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[ok
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U11#(
ok(
X
)
)
|
→ |
U11#(
X
)
|
1.1.5.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U11#
(x1)
]
|
= |
x1
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.5.1.1: P is empty
All dependency pairs have been removed.
-
The
6th
component contains the
pair(s)
|
U21#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
U21#(
X1
,
X2
)
|
|
U21#(
mark(
X1
)
,
X2
)
|
→ |
U21#(
X1
,
X2
)
|
1.1.6: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
1
|
|
[U72
(x1)
]
|
= |
2
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
3
|
|
[U71
(x1, x2)
]
|
= |
3
x1 +
3
x2
+
1
|
|
[isNeList
(x1)
]
|
= |
x1
|
|
[U52
(x1)
]
|
= |
3
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
2
x1
|
|
[top
(x1)
]
|
= |
0
|
|
[U21#
(x1, x2)
]
|
= |
x1
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
x1
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
3
|
|
[o]
|
= |
1
|
|
[e]
|
= |
1
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[ok
(x1)
]
|
= |
2
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
|
|
[proper
(x1)
]
|
= |
3
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U21#(
mark(
X1
)
,
X2
)
|
→ |
U21#(
X1
,
X2
)
|
1.1.6.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
3
x1 +
2
x2
+
1
|
|
[isNePal
(x1)
]
|
= |
2
x1
+
2
|
|
[U22
(x1)
]
|
= |
2
x1
+
1
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
+
3
|
|
[U21
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[u]
|
= |
2
|
|
[U71
(x1, x2)
]
|
= |
3
x1 + x2
+
1
|
|
[isNeList
(x1)
]
|
= |
x1
+
2
|
|
[U52
(x1)
]
|
= |
3
x1
+
1
|
|
[isPal
(x1)
]
|
= |
2
x1
+
3
|
|
[U11
(x1)
]
|
= |
x1
+
1
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[U21#
(x1, x2)
]
|
= |
x1
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
2
x1 +
2
x2
+
1
|
|
[U61
(x1)
]
|
= |
2
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[ok
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
3
x1
+
1
|
|
[proper
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.6.1.1: P is empty
All dependency pairs have been removed.
-
The
7th
component contains the
pair(s)
|
U22#(
ok(
X
)
)
|
→ |
U22#(
X
)
|
|
U22#(
mark(
X
)
)
|
→ |
U22#(
X
)
|
1.1.7: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 +
2
x2
+
2
|
|
[isNePal
(x1)
]
|
= |
1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[U22#
(x1)
]
|
= |
2
x1
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
+
2
|
|
[active
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
2
|
|
[e]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[ok
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U22#(
ok(
X
)
)
|
→ |
U22#(
X
)
|
1.1.7.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[U22#
(x1)
]
|
= |
x1
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.7.1.1: P is empty
All dependency pairs have been removed.
-
The
8th
component contains the
pair(s)
|
U31#(
ok(
X
)
)
|
→ |
U31#(
X
)
|
|
U31#(
mark(
X
)
)
|
→ |
U31#(
X
)
|
1.1.8: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 +
2
x2
+
2
|
|
[isNePal
(x1)
]
|
= |
1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
+
2
|
|
[active
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[U31#
(x1)
]
|
= |
2
x1
|
|
[o]
|
= |
2
|
|
[e]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[ok
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U31#(
ok(
X
)
)
|
→ |
U31#(
X
)
|
1.1.8.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[U31#
(x1)
]
|
= |
x1
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.8.1.1: P is empty
All dependency pairs have been removed.
-
The
9th
component contains the
pair(s)
|
U41#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
U41#(
X1
,
X2
)
|
|
U41#(
mark(
X1
)
,
X2
)
|
→ |
U41#(
X1
,
X2
)
|
1.1.9: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
1
|
|
[U72
(x1)
]
|
= |
2
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
3
|
|
[U71
(x1, x2)
]
|
= |
3
x1 +
3
x2
+
1
|
|
[isNeList
(x1)
]
|
= |
x1
|
|
[U52
(x1)
]
|
= |
3
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
2
x1
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
x1
|
|
[U41#
(x1, x2)
]
|
= |
x1
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
3
|
|
[o]
|
= |
1
|
|
[e]
|
= |
1
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[ok
(x1)
]
|
= |
2
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
|
|
[proper
(x1)
]
|
= |
3
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U41#(
mark(
X1
)
,
X2
)
|
→ |
U41#(
X1
,
X2
)
|
1.1.9.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
3
x1 +
2
x2
+
1
|
|
[isNePal
(x1)
]
|
= |
2
x1
+
2
|
|
[U22
(x1)
]
|
= |
2
x1
+
1
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
+
3
|
|
[U21
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[u]
|
= |
2
|
|
[U71
(x1, x2)
]
|
= |
3
x1 + x2
+
1
|
|
[isNeList
(x1)
]
|
= |
x1
+
2
|
|
[U52
(x1)
]
|
= |
3
x1
+
1
|
|
[isPal
(x1)
]
|
= |
2
x1
+
3
|
|
[U11
(x1)
]
|
= |
x1
+
1
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
2
x1 +
2
x2
+
1
|
|
[U61
(x1)
]
|
= |
2
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U41#
(x1, x2)
]
|
= |
x1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[ok
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
3
x1
+
1
|
|
[proper
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.9.1.1: P is empty
All dependency pairs have been removed.
-
The
10th
component contains the
pair(s)
|
U42#(
ok(
X
)
)
|
→ |
U42#(
X
)
|
|
U42#(
mark(
X
)
)
|
→ |
U42#(
X
)
|
1.1.10: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 +
2
x2
+
2
|
|
[isNePal
(x1)
]
|
= |
1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
+
2
|
|
[active
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
2
|
|
[e]
|
= |
0
|
|
[U42#
(x1)
]
|
= |
2
x1
|
|
[isQid
(x1)
]
|
= |
0
|
|
[ok
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U42#(
ok(
X
)
)
|
→ |
U42#(
X
)
|
1.1.10.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[U42#
(x1)
]
|
= |
x1
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.10.1.1: P is empty
All dependency pairs have been removed.
-
The
11th
component contains the
pair(s)
|
U51#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
U51#(
X1
,
X2
)
|
|
U51#(
mark(
X1
)
,
X2
)
|
→ |
U51#(
X1
,
X2
)
|
1.1.11: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
1
|
|
[U72
(x1)
]
|
= |
2
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
3
|
|
[U71
(x1, x2)
]
|
= |
3
x1 +
3
x2
+
1
|
|
[isNeList
(x1)
]
|
= |
x1
|
|
[U52
(x1)
]
|
= |
3
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
2
x1
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
x1
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
3
|
|
[o]
|
= |
1
|
|
[e]
|
= |
1
|
|
[U51#
(x1, x2)
]
|
= |
x1
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[ok
(x1)
]
|
= |
2
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
|
|
[proper
(x1)
]
|
= |
3
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U51#(
mark(
X1
)
,
X2
)
|
→ |
U51#(
X1
,
X2
)
|
1.1.11.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
3
x1 +
2
x2
+
1
|
|
[isNePal
(x1)
]
|
= |
2
x1
+
2
|
|
[U22
(x1)
]
|
= |
2
x1
+
1
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
+
3
|
|
[U21
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[u]
|
= |
2
|
|
[U71
(x1, x2)
]
|
= |
3
x1 + x2
+
1
|
|
[isNeList
(x1)
]
|
= |
x1
+
2
|
|
[U52
(x1)
]
|
= |
3
x1
+
1
|
|
[isPal
(x1)
]
|
= |
2
x1
+
3
|
|
[U11
(x1)
]
|
= |
x1
+
1
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
2
x1 +
2
x2
+
1
|
|
[U61
(x1)
]
|
= |
2
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[U51#
(x1, x2)
]
|
= |
x1
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[ok
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
3
x1
+
1
|
|
[proper
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.11.1.1: P is empty
All dependency pairs have been removed.
-
The
12th
component contains the
pair(s)
|
U52#(
ok(
X
)
)
|
→ |
U52#(
X
)
|
|
U52#(
mark(
X
)
)
|
→ |
U52#(
X
)
|
1.1.12: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 +
2
x2
+
2
|
|
[isNePal
(x1)
]
|
= |
1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
+
2
|
|
[active
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[U52#
(x1)
]
|
= |
2
x1
|
|
[o]
|
= |
2
|
|
[e]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[ok
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U52#(
ok(
X
)
)
|
→ |
U52#(
X
)
|
1.1.12.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[U52#
(x1)
]
|
= |
x1
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.12.1.1: P is empty
All dependency pairs have been removed.
-
The
13th
component contains the
pair(s)
|
U61#(
ok(
X
)
)
|
→ |
U61#(
X
)
|
|
U61#(
mark(
X
)
)
|
→ |
U61#(
X
)
|
1.1.13: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 +
2
x2
+
2
|
|
[isNePal
(x1)
]
|
= |
1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U61#
(x1)
]
|
= |
2
x1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
+
2
|
|
[active
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
2
|
|
[e]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[ok
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U61#(
ok(
X
)
)
|
→ |
U61#(
X
)
|
1.1.13.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U61#
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.13.1.1: P is empty
All dependency pairs have been removed.
-
The
14th
component contains the
pair(s)
|
U71#(
ok(
X1
)
,
ok(
X2
)
)
|
→ |
U71#(
X1
,
X2
)
|
|
U71#(
mark(
X1
)
,
X2
)
|
→ |
U71#(
X1
,
X2
)
|
1.1.14: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
1
|
|
[U72
(x1)
]
|
= |
2
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
3
|
|
[U71
(x1, x2)
]
|
= |
3
x1 +
3
x2
+
1
|
|
[isNeList
(x1)
]
|
= |
x1
|
|
[U52
(x1)
]
|
= |
3
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
2
x1
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
x1
|
|
[U31
(x1)
]
|
= |
2
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
3
|
|
[o]
|
= |
1
|
|
[e]
|
= |
1
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[U71#
(x1, x2)
]
|
= |
x1
|
|
[ok
(x1)
]
|
= |
2
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
|
|
[proper
(x1)
]
|
= |
3
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U71#(
mark(
X1
)
,
X2
)
|
→ |
U71#(
X1
,
X2
)
|
1.1.14.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
2
|
|
[__
(x1, x2)
]
|
= |
3
x1 +
2
x2
+
1
|
|
[isNePal
(x1)
]
|
= |
2
x1
+
2
|
|
[U22
(x1)
]
|
= |
2
x1
+
1
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
+
3
|
|
[U21
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[u]
|
= |
2
|
|
[U71
(x1, x2)
]
|
= |
3
x1 + x2
+
1
|
|
[isNeList
(x1)
]
|
= |
x1
+
2
|
|
[U52
(x1)
]
|
= |
3
x1
+
1
|
|
[isPal
(x1)
]
|
= |
2
x1
+
3
|
|
[U11
(x1)
]
|
= |
x1
+
1
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
2
x1 +
2
x2
+
1
|
|
[U61
(x1)
]
|
= |
2
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
2
x1 +
3
x2
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
2
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
|
|
[U71#
(x1, x2)
]
|
= |
x1
|
|
[ok
(x1)
]
|
= |
0
|
|
[U42
(x1)
]
|
= |
3
x1
+
1
|
|
[proper
(x1)
]
|
= |
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.14.1.1: P is empty
All dependency pairs have been removed.
-
The
15th
component contains the
pair(s)
|
U72#(
ok(
X
)
)
|
→ |
U72#(
X
)
|
|
U72#(
mark(
X
)
)
|
→ |
U72#(
X
)
|
1.1.15: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 +
2
x2
+
2
|
|
[isNePal
(x1)
]
|
= |
1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[U72#
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
+
2
|
|
[active
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
2
|
|
[e]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[ok
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U72#(
ok(
X
)
)
|
→ |
U72#(
X
)
|
1.1.15.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[U72#
(x1)
]
|
= |
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.15.1.1: P is empty
All dependency pairs have been removed.
-
The
16th
component contains the
pair(s)
|
U81#(
ok(
X
)
)
|
→ |
U81#(
X
)
|
|
U81#(
mark(
X
)
)
|
→ |
U81#(
X
)
|
1.1.16: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
x1
|
|
[a]
|
= |
0
|
|
[__
(x1, x2)
]
|
= |
x1 +
2
x2
+
2
|
|
[isNePal
(x1)
]
|
= |
1
|
|
[U22
(x1)
]
|
= |
x1
|
|
[i]
|
= |
0
|
|
[U72
(x1)
]
|
= |
x1
+
1
|
|
[U21
(x1, x2)
]
|
= |
x1
|
|
[u]
|
= |
0
|
|
[U71
(x1, x2)
]
|
= |
2
x1
+
1
|
|
[isNeList
(x1)
]
|
= |
0
|
|
[U52
(x1)
]
|
= |
x1
|
|
[isPal
(x1)
]
|
= |
1
|
|
[U11
(x1)
]
|
= |
x1
|
|
[U81#
(x1)
]
|
= |
2
x1
|
|
[isList
(x1)
]
|
= |
0
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
x1
+
1
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
+
2
|
|
[active
(x1)
]
|
= |
2
x1
+
1
|
|
[U31
(x1)
]
|
= |
x1
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
0
|
|
[tt]
|
= |
0
|
|
[o]
|
= |
2
|
|
[e]
|
= |
0
|
|
[isQid
(x1)
]
|
= |
0
|
|
[ok
(x1)
]
|
= |
x1
|
|
[U42
(x1)
]
|
= |
x1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
U81#(
ok(
X
)
)
|
→ |
U81#(
X
)
|
1.1.16.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[U81#
(x1)
]
|
= |
x1
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.16.1.1: P is empty
All dependency pairs have been removed.
-
The
17th
component contains the
pair(s)
|
isList#(
ok(
X
)
)
|
→ |
isList#(
X
)
|
1.1.17: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[isList#
(x1)
]
|
= |
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.17.1: P is empty
All dependency pairs have been removed.
-
The
18th
component contains the
pair(s)
|
isNeList#(
ok(
X
)
)
|
→ |
isNeList#(
X
)
|
1.1.18: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isNeList#
(x1)
]
|
= |
x1
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.18.1: P is empty
All dependency pairs have been removed.
-
The
19th
component contains the
pair(s)
|
isPal#(
ok(
X
)
)
|
→ |
isPal#(
X
)
|
1.1.19: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[isPal#
(x1)
]
|
= |
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.19.1: P is empty
All dependency pairs have been removed.
-
The
20th
component contains the
pair(s)
|
isQid#(
ok(
X
)
)
|
→ |
isQid#(
X
)
|
1.1.20: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[isQid#
(x1)
]
|
= |
x1
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.20.1: P is empty
All dependency pairs have been removed.
-
The
21th
component contains the
pair(s)
|
isNePal#(
ok(
X
)
)
|
→ |
isNePal#(
X
)
|
1.1.21: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[U81
(x1)
]
|
= |
2
x1
|
|
[a]
|
= |
1
|
|
[__
(x1, x2)
]
|
= |
2
x1
|
|
[isNePal
(x1)
]
|
= |
2
x1
|
|
[U22
(x1)
]
|
= |
x1
+
3
|
|
[i]
|
= |
2
|
|
[U72
(x1)
]
|
= |
x1
|
|
[U21
(x1, x2)
]
|
= |
2
x1
|
|
[u]
|
= |
1
|
|
[U71
(x1, x2)
]
|
= |
2
x1
|
|
[isNeList
(x1)
]
|
= |
2
x1
|
|
[U52
(x1)
]
|
= |
2
x1
|
|
[isPal
(x1)
]
|
= |
x1
|
|
[U11
(x1)
]
|
= |
x1
+
3
|
|
[isList
(x1)
]
|
= |
2
x1
+
2
|
|
[top
(x1)
]
|
= |
0
|
|
[mark
(x1)
]
|
= |
0
|
|
[U41
(x1, x2)
]
|
= |
x1
|
|
[U61
(x1)
]
|
= |
x1
|
|
[active
(x1)
]
|
= |
2
x1
|
|
[U31
(x1)
]
|
= |
2
x1
+
2
|
|
[U51
(x1, x2)
]
|
= |
x1
|
|
[nil]
|
= |
2
|
|
[tt]
|
= |
2
|
|
[o]
|
= |
1
|
|
[e]
|
= |
2
|
|
[isNePal#
(x1)
]
|
= |
x1
|
|
[isQid
(x1)
]
|
= |
2
x1
+
2
|
|
[ok
(x1)
]
|
= |
x1
+
1
|
|
[U42
(x1)
]
|
= |
2
x1
+
1
|
|
[proper
(x1)
]
|
= |
2
x1
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
1.1.21.1: P is empty
All dependency pairs have been removed.