The
1st
component contains the
pair(s)
|
mark#(
tail(
X
)
)
|
→ |
a__tail#(
mark(
X
)
)
|
|
a__tail#(
cons(
X
,
XS
)
)
|
→ |
mark#(
XS
)
|
|
mark#(
tail(
X
)
)
|
→ |
mark#(
X
)
|
|
mark#(
cons(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[mark
(x1)
]
|
= |
2
x1
+
2
|
|
[zeros]
|
= |
0
|
|
[a__zeros]
|
= |
2
|
|
[mark#
(x1)
]
|
= |
x1
|
|
[a__tail#
(x1)
]
|
= |
x1
|
|
[0]
|
= |
0
|
|
[a__tail
(x1)
]
|
= |
2
x1
+
2
|
|
[tail
(x1)
]
|
= |
2
x1
+
2
|
|
[cons
(x1, x2)
]
|
= |
x1 +
2
x2
|
|
[f(x1, ..., xn)]
|
= |
x1 + ... + xn + 1
|
for all other symbols f of arity n
|
one remains with the following pair(s).
|
mark#(
tail(
X
)
)
|
→ |
a__tail#(
mark(
X
)
)
|
|
a__tail#(
cons(
X
,
XS
)
)
|
→ |
mark#(
XS
)
|
|
mark#(
cons(
X1
,
X2
)
)
|
→ |
mark#(
X1
)
|
1.1.1.1: reduction pair processor
Using the following reduction pair
Linear polynomial
interpretation over
the naturals
|
[mark
(x1)
]
|
= |
x1
+
2
|
|
[zeros]
|
= |
0
|
|
[a__zeros]
|
= |
1
|
|
[mark#
(x1)
]
|
= |
3
x1
|
|
[a__tail#
(x1)
]
|
= |
2
x1
+
1
|
|
[0]
|
= |
0
|
|
[a__tail
(x1)
]
|
= |
x1
+
3
|
|
[tail
(x1)
]
|
= |
x1
+
3
|
|
[cons
(x1, x2)
]
|
= |
x1 +
2
x2
+
1
|
|
[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.