Tool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ sel(s(X), cons(Y, Z)) -> sel(X, Z)
, sel(0(), cons(X, Z)) -> X
, first(0(), Z) -> nil()
, first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
, from(X) -> cons(X, from(s(X)))
, sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
, sel1(0(), cons(X, Z)) -> quote(X)
, first1(0(), Z) -> nil1()
, first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, Z))
, quote(0()) -> 01()
, quote1(cons(X, Z)) -> cons1(quote(X), quote1(Z))
, quote1(nil()) -> nil1()
, quote(s(X)) -> s1(quote(X))
, quote(sel(X, Z)) -> sel1(X, Z)
, quote1(first(X, Z)) -> first1(X, Z)
, unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
Proof Output:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
, 2: sel^#(0(), cons(X, Z)) -> c_1()
, 3: first^#(0(), Z) -> c_2()
, 4: first^#(s(X), cons(Y, Z)) -> c_3(first^#(X, Z))
, 5: from^#(X) -> c_4(from^#(s(X)))
, 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
, 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
, 8: first1^#(0(), Z) -> c_7()
, 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
, 10: quote^#(0()) -> c_9()
, 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
, 12: quote1^#(nil()) -> c_11()
, 13: quote^#(s(X)) -> c_12(quote^#(X))
, 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
, 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
, 16: unquote^#(01()) -> c_15()
, 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
, 18: unquote1^#(nil1()) -> c_17()
, 19: unquote1^#(cons1(X, Z)) ->
c_18(fcons^#(unquote(X), unquote1(Z)))
, 20: fcons^#(X, Z) -> c_19()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{19} [ NA ]
|
`->{20} [ NA ]
->{18} [ YES(?,O(1)) ]
->{17} [ YES(?,O(n^2)) ]
|
`->{16} [ YES(?,O(n^2)) ]
->{11} [ YES(?,O(n^3)) ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{10} [ NA ]
|
|->{12} [ NA ]
|
`->{15} [ NA ]
|
|->{8} [ NA ]
|
`->{9} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{8} [ NA ]
|
`->{10} [ NA ]
->{5} [ MAYBE ]
->{4} [ YES(?,O(n^3)) ]
|
`->{3} [ NA ]
->{1} [ NA ]
|
`->{2} [ NA ]
Sub-problems:
-------------
* Path {1}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 3 0] x1 + [0 0 0] x2 + [0]
[0 1 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_0(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {1}->{2}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {4}: YES(?,O(n^3))
-----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 3 0] x1 + [0 0 0] x2 + [0]
[0 1 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^3))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {first^#(s(X), cons(Y, Z)) -> c_3(first^#(X, Z))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(cons) = {}, Uargs(first^#) = {},
Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 4 4] x1 + [2]
[0 1 2] [2]
[0 0 0] [2]
cons(x1, x2) = [0 0 0] x1 + [1 4 4] x2 + [2]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 1] [2]
first^#(x1, x2) = [0 2 0] x1 + [0 0 2] x2 + [0]
[2 0 2] [2 0 0] [0]
[0 2 2] [1 0 0] [0]
c_3(x1) = [1 0 0] x1 + [5]
[2 0 2] [3]
[0 0 0] [7]
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {5}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {1}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 1 0] x1 + [0]
[0 0 1] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [3 3 3] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_4(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {from^#(X) -> c_4(from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {11}: YES(?,O(n^3))
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [3 0 0] x1 + [0]
[3 0 0] [0]
[3 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 1 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^3))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules:
{quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(cons) = {}, Uargs(quote^#) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
cons(x1, x2) = [1 2 3] x1 + [1 4 3] x2 + [2]
[0 1 0] [0 0 1] [0]
[0 0 1] [0 0 1] [2]
quote^#(x1) = [0 0 2] x1 + [0]
[0 0 0] [2]
[0 0 2] [2]
quote1^#(x1) = [2 4 0] x1 + [0]
[2 0 2] [0]
[0 0 4] [2]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [1]
[0 0 2] [0 0 2] [0]
[2 2 0] [0 0 0] [3]
* Path {11}->{6,14,13,7}: NA
--------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_6(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_13(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}->{10}: NA
--------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_6(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_13(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{10}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{12}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{8}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [3 0 0] x1 + [0]
[3 0 0] [0]
[3 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 1 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}: NA
-------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_6(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_13(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}->{10}: NA
-------------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_6(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_13(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{8}: NA
-----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{10}: NA
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {17}: YES(?,O(n^2))
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^2))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s1(x1) = [1 2 2] x1 + [2]
[0 1 2] [2]
[0 0 0] [0]
unquote^#(x1) = [0 1 0] x1 + [2]
[6 0 0] [0]
[2 3 0] [2]
c_16(x1) = [1 0 0] x1 + [1]
[2 0 2] [0]
[0 0 0] [0]
* Path {17}->{16}: YES(?,O(n^2))
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^2))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {unquote^#(01()) -> c_15()}
Weak Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
Proof Output:
The following argument positions are usable:
Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
01() = [2]
[2]
[2]
s1(x1) = [1 1 0] x1 + [0]
[0 1 1] [1]
[0 0 0] [0]
unquote^#(x1) = [2 2 2] x1 + [0]
[0 6 0] [0]
[0 0 2] [0]
c_15() = [1]
[0]
[0]
c_16(x1) = [1 0 0] x1 + [2]
[0 0 0] [3]
[0 0 0] [0]
* Path {18}: YES(?,O(1))
----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {unquote1^#(nil1()) -> c_17()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(unquote1^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil1() = [2]
[2]
[2]
unquote1^#(x1) = [0 2 0] x1 + [7]
[2 2 0] [3]
[2 2 2] [3]
c_17() = [0]
[1]
[1]
* Path {19}: NA
-------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 0] [3]
[0 0 1] [0]
cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [1]
0() = [0]
[1]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[3]
[0]
cons1(x1, x2) = [1 2 3] x1 + [1 3 3] x2 + [3]
[0 1 0] [0 0 0] [3]
[0 0 1] [0 0 1] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [1 0 0] x1 + [2]
[0 0 0] [2]
[0 0 0] [1]
unquote(x1) = [2 0 0] x1 + [1]
[0 2 1] [3]
[0 0 0] [0]
unquote1(x1) = [3 3 0] x1 + [0]
[3 0 0] [0]
[2 0 2] [0]
fcons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [2]
[0 0 0] [0 0 0] [2]
[0 0 0] [0 0 0] [1]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [3 1 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
fcons^#(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_19() = [0]
[0]
[0]
Complexity induced by the adequate RMI: YES(?,O(n^3))
We have not generated a proof for the resulting sub-problem.
* Path {19}->{20}: NA
-------------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 0 0] x1 + [1]
[0 0 1] [3]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [1]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [1]
[0]
[0]
cons1(x1, x2) = [1 0 1] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 1] [3]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [1 0 0] x1 + [0]
[0 0 0] [0]
[0 0 1] [3]
unquote(x1) = [0 0 1] x1 + [1]
[0 0 1] [0]
[0 0 1] [0]
unquote1(x1) = [2 0 3] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
fcons^#(x1, x2) = [3 0 0] x1 + [3 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19() = [0]
[0]
[0]
Complexity induced by the adequate RMI: YES(?,O(n^2))
We have not generated a proof for the resulting sub-problem.
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
, 2: sel^#(0(), cons(X, Z)) -> c_1()
, 3: first^#(0(), Z) -> c_2()
, 4: first^#(s(X), cons(Y, Z)) -> c_3(first^#(X, Z))
, 5: from^#(X) -> c_4(from^#(s(X)))
, 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
, 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
, 8: first1^#(0(), Z) -> c_7()
, 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
, 10: quote^#(0()) -> c_9()
, 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
, 12: quote1^#(nil()) -> c_11()
, 13: quote^#(s(X)) -> c_12(quote^#(X))
, 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
, 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
, 16: unquote^#(01()) -> c_15()
, 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
, 18: unquote1^#(nil1()) -> c_17()
, 19: unquote1^#(cons1(X, Z)) ->
c_18(fcons^#(unquote(X), unquote1(Z)))
, 20: fcons^#(X, Z) -> c_19()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{19} [ NA ]
|
`->{20} [ NA ]
->{18} [ YES(?,O(1)) ]
->{17} [ YES(?,O(n^1)) ]
|
`->{16} [ YES(?,O(n^1)) ]
->{11} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{10} [ NA ]
|
|->{12} [ NA ]
|
`->{15} [ NA ]
|
|->{8} [ NA ]
|
`->{9} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{8} [ NA ]
|
`->{10} [ NA ]
->{5} [ MAYBE ]
->{4} [ NA ]
|
`->{3} [ NA ]
->{1} [ NA ]
|
`->{2} [ NA ]
Sub-problems:
-------------
* Path {1}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 3] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [3 3] x1 + [1 3] x2 + [0]
[3 3] [3 3] [0]
c_0(x1) = [1 0] x1 + [0]
[0 1] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {1}->{2}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [1 0] x1 + [0]
[0 1] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {4}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 3] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [3 3] x1 + [1 3] x2 + [0]
[3 3] [3 3] [0]
c_2() = [0]
[0]
c_3(x1) = [1 0] x1 + [0]
[0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [1 0] x1 + [0]
[0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {5}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {1}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 0] x1 + [0]
[0 1] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_4(x1) = [1 0] x1 + [0]
[0 1] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {from^#(X) -> c_4(from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {11}: NA
-------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [3 0] x1 + [0]
[3 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [1 3] x1 + [0]
[3 3] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}: NA
--------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [3 3] x1 + [0 0] x2 + [0]
[3 3] [0 0] [0]
s(x1) = [1 3] x1 + [0]
[0 1] [0]
cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[3 3] [3 3] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
c_6(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[3 3] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
c_13(x1) = [1 0] x1 + [0]
[0 1] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}->{10}: NA
--------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
c_6(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
c_13(x1) = [1 0] x1 + [0]
[0 1] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{10}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{12}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{8}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [3 0] x1 + [0]
[0 1] [0]
first1^#(x1, x2) = [3 3] x1 + [1 2] x2 + [0]
[3 3] [3 3] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 3] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}: NA
-------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [3 3] x1 + [0 0] x2 + [0]
[3 3] [0 0] [0]
s(x1) = [1 3] x1 + [0]
[0 1] [0]
cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[3 3] [3 3] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
c_6(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[3 3] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
c_13(x1) = [1 0] x1 + [0]
[0 1] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}->{10}: NA
-------------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
c_6(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
c_13(x1) = [1 0] x1 + [0]
[0 1] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{8}: NA
-----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{10}: NA
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We have not generated a proof for the resulting sub-problem.
* Path {17}: YES(?,O(n^1))
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [1 2] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_15() = [0]
[0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s1(x1) = [1 0] x1 + [0]
[0 1] [1]
unquote^#(x1) = [0 1] x1 + [1]
[0 0] [0]
c_16(x1) = [1 0] x1 + [0]
[0 0] [0]
* Path {17}->{16}: YES(?,O(n^1))
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {unquote^#(01()) -> c_15()}
Weak Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
Proof Output:
The following argument positions are usable:
Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
01() = [2]
[2]
s1(x1) = [1 2] x1 + [1]
[0 0] [3]
unquote^#(x1) = [1 2] x1 + [2]
[6 1] [0]
c_15() = [1]
[0]
c_16(x1) = [1 0] x1 + [5]
[2 0] [3]
* Path {18}: YES(?,O(1))
----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {unquote1^#(nil1()) -> c_17()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(unquote1^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil1() = [2]
[2]
unquote1^#(x1) = [2 0] x1 + [7]
[2 2] [7]
c_17() = [0]
[1]
* Path {19}: NA
-------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 0] x1 + [0]
[0 1] [0]
cons(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [1]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [1]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [1 3] x1 + [1 0] x2 + [3]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [1 0] x1 + [2]
[0 0] [0]
unquote(x1) = [1 0] x1 + [1]
[0 0] [0]
unquote1(x1) = [2 0] x1 + [2]
[2 0] [2]
fcons(x1, x2) = [2 0] x1 + [1 0] x2 + [1]
[0 0] [0 0] [3]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [3 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [1 0] x1 + [0]
[0 1] [0]
fcons^#(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[3 3] [3 3] [0]
c_19() = [0]
[0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
* Path {19}->{20}: NA
-------------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [1]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [1]
[1]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [3]
[0]
cons1(x1, x2) = [1 0] x1 + [1 0] x2 + [3]
[0 0] [0 1] [3]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [1 0] x1 + [2]
[0 0] [0]
unquote(x1) = [1 0] x1 + [1]
[0 0] [0]
unquote1(x1) = [2 1] x1 + [0]
[3 3] [0]
fcons(x1, x2) = [2 0] x1 + [1 0] x2 + [1]
[0 0] [0 0] [3]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [1 0] x1 + [0]
[0 1] [0]
fcons^#(x1, x2) = [3 0] x1 + [3 0] x2 + [0]
[0 0] [0 0] [0]
c_19() = [0]
[0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
, 2: sel^#(0(), cons(X, Z)) -> c_1()
, 3: first^#(0(), Z) -> c_2()
, 4: first^#(s(X), cons(Y, Z)) -> c_3(first^#(X, Z))
, 5: from^#(X) -> c_4(from^#(s(X)))
, 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
, 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
, 8: first1^#(0(), Z) -> c_7()
, 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
, 10: quote^#(0()) -> c_9()
, 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
, 12: quote1^#(nil()) -> c_11()
, 13: quote^#(s(X)) -> c_12(quote^#(X))
, 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
, 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
, 16: unquote^#(01()) -> c_15()
, 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
, 18: unquote1^#(nil1()) -> c_17()
, 19: unquote1^#(cons1(X, Z)) ->
c_18(fcons^#(unquote(X), unquote1(Z)))
, 20: fcons^#(X, Z) -> c_19()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{19} [ NA ]
|
`->{20} [ NA ]
->{18} [ YES(?,O(1)) ]
->{17} [ NA ]
|
`->{16} [ NA ]
->{11} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{10} [ NA ]
|
|->{12} [ NA ]
|
`->{15} [ NA ]
|
|->{8} [ NA ]
|
`->{9} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{8} [ NA ]
|
`->{10} [ NA ]
->{5} [ MAYBE ]
->{4} [ NA ]
|
`->{3} [ NA ]
->{1} [ NA ]
|
`->{2} [ NA ]
Sub-problems:
-------------
* Path {1}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_0(x1) = [1] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {1}->{2}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [1] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_2() = [0]
c_3(x1) = [1] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {1},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [1] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {5}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {1}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [3] x1 + [0]
c_4(x1) = [1] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {from^#(X) -> c_4(from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {11}: NA
-------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [1] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [3] x1 + [0]
c_10(x1, x2) = [3] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}: NA
--------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [3] x1 + [3] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [2] x2 + [0]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [1] x1 + [0]
quote^#(x1) = [2] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
c_13(x1) = [1] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}->{10}: NA
--------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [1] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
c_13(x1) = [1] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{10}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{12}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [3] x1 + [3] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [1] x1 + [1] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [1] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [3] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{8}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [1] x1 + [0]
first1^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [3] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}: NA
-------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [2] x1 + [2] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [1] x1 + [0]
quote^#(x1) = [3] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [1] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
c_13(x1) = [1] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}->{10}: NA
-------------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {1}, Uargs(c_13) = {1},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [1] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [1] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
c_13(x1) = [1] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{8}: NA
-----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {2}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{10}: NA
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {1, 2}, Uargs(quote1^#) = {},
Uargs(c_10) = {1, 2}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {1}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [1] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {17}: NA
-------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [1] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [3] x1 + [0]
c_15() = [0]
c_16(x1) = [1] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {17}->{16}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [1] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We have not generated a proof for the resulting sub-problem.
* Path {18}: YES(?,O(1))
----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {}, Uargs(fcons^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19() = [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {unquote1^#(nil1()) -> c_17()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(unquote1^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil1() = [7]
unquote1^#(x1) = [1] x1 + [7]
c_17() = [1]
* Path {19}: NA
-------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [3]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [1]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [1]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [3]
cons1(x1, x2) = [1] x1 + [1] x2 + [2]
01() = [3]
quote1(x1) = [0] x1 + [0]
s1(x1) = [1] x1 + [2]
unquote(x1) = [2] x1 + [0]
unquote1(x1) = [2] x1 + [0]
fcons(x1, x2) = [1] x1 + [1] x2 + [1]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [3] x1 + [0]
c_17() = [0]
c_18(x1) = [1] x1 + [0]
fcons^#(x1, x2) = [1] x1 + [1] x2 + [0]
c_19() = [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
* Path {19}->{20}: NA
-------------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(first^#) = {}, Uargs(c_3) = {},
Uargs(from^#) = {}, Uargs(c_4) = {}, Uargs(sel1^#) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}, Uargs(quote^#) = {},
Uargs(first1^#) = {}, Uargs(c_8) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {}, Uargs(c_12) = {}, Uargs(c_13) = {},
Uargs(c_14) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {},
Uargs(unquote1^#) = {}, Uargs(c_18) = {1}, Uargs(fcons^#) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [3]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [1]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [1]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [3]
cons1(x1, x2) = [1] x1 + [1] x2 + [2]
01() = [3]
quote1(x1) = [0] x1 + [0]
s1(x1) = [1] x1 + [2]
unquote(x1) = [2] x1 + [0]
unquote1(x1) = [2] x1 + [0]
fcons(x1, x2) = [1] x1 + [1] x2 + [1]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1() = [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [1] x1 + [0]
fcons^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_19() = [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
4) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
Tool RC1
stdout:
MAYBE
Tool RC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ sel(s(X), cons(Y, Z)) -> sel(X, Z)
, sel(0(), cons(X, Z)) -> X
, first(0(), Z) -> nil()
, first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
, from(X) -> cons(X, from(s(X)))
, sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
, sel1(0(), cons(X, Z)) -> quote(X)
, first1(0(), Z) -> nil1()
, first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, Z))
, quote(0()) -> 01()
, quote1(cons(X, Z)) -> cons1(quote(X), quote1(Z))
, quote1(nil()) -> nil1()
, quote(s(X)) -> s1(quote(X))
, quote(sel(X, Z)) -> sel1(X, Z)
, quote1(first(X, Z)) -> first1(X, Z)
, unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
Proof Output:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
, 2: sel^#(0(), cons(X, Z)) -> c_1(X)
, 3: first^#(0(), Z) -> c_2()
, 4: first^#(s(X), cons(Y, Z)) -> c_3(Y, first^#(X, Z))
, 5: from^#(X) -> c_4(X, from^#(s(X)))
, 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
, 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
, 8: first1^#(0(), Z) -> c_7()
, 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
, 10: quote^#(0()) -> c_9()
, 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
, 12: quote1^#(nil()) -> c_11()
, 13: quote^#(s(X)) -> c_12(quote^#(X))
, 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
, 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
, 16: unquote^#(01()) -> c_15()
, 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
, 18: unquote1^#(nil1()) -> c_17()
, 19: unquote1^#(cons1(X, Z)) ->
c_18(fcons^#(unquote(X), unquote1(Z)))
, 20: fcons^#(X, Z) -> c_19(X, Z)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{19} [ NA ]
|
`->{20} [ NA ]
->{18} [ YES(?,O(1)) ]
->{17} [ YES(?,O(n^2)) ]
|
`->{16} [ YES(?,O(n^2)) ]
->{11} [ YES(?,O(n^3)) ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{10} [ NA ]
|
|->{12} [ NA ]
|
`->{15} [ NA ]
|
|->{8} [ NA ]
|
`->{9} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{8} [ NA ]
|
`->{10} [ NA ]
->{5} [ MAYBE ]
->{4} [ NA ]
|
`->{3} [ NA ]
->{1} [ YES(?,O(n^3)) ]
|
`->{2} [ NA ]
Sub-problems:
-------------
* Path {1}: YES(?,O(n^3))
-----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 3 0] x1 + [0 0 0] x2 + [0]
[0 1 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_0(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^3))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(cons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 4 4] x1 + [2]
[0 1 2] [2]
[0 0 0] [2]
cons(x1, x2) = [0 0 0] x1 + [1 4 4] x2 + [2]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 1] [2]
sel^#(x1, x2) = [0 2 0] x1 + [0 0 2] x2 + [0]
[2 0 2] [2 0 0] [0]
[0 2 2] [1 0 0] [0]
c_0(x1) = [1 0 0] x1 + [5]
[2 0 2] [3]
[0 0 0] [7]
* Path {1}->{2}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 1 1] x1 + [0 0 0] x2 + [0]
[0 1 3] [0 0 0] [0]
[0 0 1] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [3 1 3] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_1(x1) = [1 0 1] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 3 3] x1 + [1 3 0] x2 + [0]
[0 1 3] [0 1 0] [0]
[0 0 1] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {5}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {2},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 1 0] x1 + [0]
[0 0 0] [0]
[0 0 1] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [1 3 3] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_4(x1, x2) = [0 1 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules: {from^#(X) -> c_4(X, from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {11}: YES(?,O(n^3))
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [3 0 0] x1 + [0]
[3 0 0] [0]
[3 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 1 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^3))
Input Problem: DP runtime-complexity with respect to
Strict Rules:
{quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(cons) = {}, Uargs(quote^#) = {}, Uargs(quote1^#) = {},
Uargs(c_10) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
cons(x1, x2) = [1 2 3] x1 + [1 4 3] x2 + [2]
[0 1 0] [0 0 1] [0]
[0 0 1] [0 0 1] [2]
quote^#(x1) = [0 0 2] x1 + [0]
[0 0 0] [2]
[0 0 2] [2]
quote1^#(x1) = [2 4 0] x1 + [0]
[2 0 2] [0]
[0 0 4] [2]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [1]
[0 0 2] [0 0 2] [0]
[2 2 0] [0 0 0] [3]
* Path {11}->{6,14,13,7}: NA
--------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_6(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_13(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}->{10}: NA
--------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_6(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_13(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{10}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{12}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{8}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [3 0 0] x1 + [0]
[3 0 0] [0]
[3 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 1 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}: NA
-------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_6(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_13(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}->{10}: NA
-------------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_6(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_13(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{8}: NA
-----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{10}: NA
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {17}: YES(?,O(n^2))
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^2))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s1(x1) = [1 2 2] x1 + [2]
[0 1 2] [2]
[0 0 0] [0]
unquote^#(x1) = [0 1 0] x1 + [2]
[6 0 0] [0]
[2 3 0] [2]
c_16(x1) = [1 0 0] x1 + [1]
[2 0 2] [0]
[0 0 0] [0]
* Path {17}->{16}: YES(?,O(n^2))
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^2))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {unquote^#(01()) -> c_15()}
Weak Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
Proof Output:
The following argument positions are usable:
Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
01() = [2]
[2]
[2]
s1(x1) = [1 1 0] x1 + [0]
[0 1 1] [1]
[0 0 0] [0]
unquote^#(x1) = [2 2 2] x1 + [0]
[0 6 0] [0]
[0 0 2] [0]
c_15() = [1]
[0]
[0]
c_16(x1) = [1 0 0] x1 + [2]
[0 0 0] [3]
[0 0 0] [0]
* Path {18}: YES(?,O(1))
----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
cons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
fcons^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {unquote1^#(nil1()) -> c_17()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(unquote1^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil1() = [2]
[2]
[2]
unquote1^#(x1) = [0 2 0] x1 + [7]
[2 2 0] [3]
[2 2 2] [3]
c_17() = [0]
[1]
[1]
* Path {19}: NA
-------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 1] [2]
[0 0 0] [1]
cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 0 0] [1]
[0 0 0] [0 0 0] [1]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [0]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[0]
cons1(x1, x2) = [1 0 0] x1 + [1 0 3] x2 + [3]
[0 1 2] [0 0 3] [3]
[0 0 1] [0 0 1] [3]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [1 0 0] x1 + [0]
[0 0 0] [0]
[0 0 1] [2]
unquote(x1) = [0 0 1] x1 + [1]
[0 0 1] [0]
[0 0 1] [0]
unquote1(x1) = [0 0 1] x1 + [1]
[3 0 0] [0]
[0 3 0] [0]
fcons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
[0 0 0] [0 0 0] [3]
[0 0 0] [0 0 0] [3]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 1 2] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
fcons^#(x1, x2) = [2 0 0] x1 + [2 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_19(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
Complexity induced by the adequate RMI: YES(?,O(n^3))
We have not generated a proof for the resulting sub-problem.
* Path {19}->{20}: NA
-------------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 1 0] [1]
[0 0 0] [0]
cons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
first(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil() = [1]
[0]
[0]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quote(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
nil1() = [0]
[0]
[1]
cons1(x1, x2) = [1 0 0] x1 + [1 3 3] x2 + [0]
[0 0 0] [0 1 0] [2]
[0 0 1] [0 0 0] [2]
01() = [0]
[0]
[0]
quote1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s1(x1) = [1 0 1] x1 + [0]
[0 1 2] [0]
[0 0 0] [2]
unquote(x1) = [1 0 1] x1 + [1]
[2 1 1] [0]
[0 0 0] [0]
unquote1(x1) = [1 2 2] x1 + [0]
[3 0 0] [0]
[0 0 0] [0]
fcons(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [2]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
first1^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_7() = [0]
[0]
[0]
c_8(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_9() = [0]
[0]
[0]
quote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_10(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_13(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15() = [0]
[0]
[0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
unquote1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_17() = [0]
[0]
[0]
c_18(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
fcons^#(x1, x2) = [3 3 3] x1 + [3 3 3] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_19(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
Complexity induced by the adequate RMI: YES(?,O(n^3))
We have not generated a proof for the resulting sub-problem.
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
, 2: sel^#(0(), cons(X, Z)) -> c_1(X)
, 3: first^#(0(), Z) -> c_2()
, 4: first^#(s(X), cons(Y, Z)) -> c_3(Y, first^#(X, Z))
, 5: from^#(X) -> c_4(X, from^#(s(X)))
, 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
, 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
, 8: first1^#(0(), Z) -> c_7()
, 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
, 10: quote^#(0()) -> c_9()
, 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
, 12: quote1^#(nil()) -> c_11()
, 13: quote^#(s(X)) -> c_12(quote^#(X))
, 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
, 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
, 16: unquote^#(01()) -> c_15()
, 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
, 18: unquote1^#(nil1()) -> c_17()
, 19: unquote1^#(cons1(X, Z)) ->
c_18(fcons^#(unquote(X), unquote1(Z)))
, 20: fcons^#(X, Z) -> c_19(X, Z)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{19} [ NA ]
|
`->{20} [ NA ]
->{18} [ YES(?,O(1)) ]
->{17} [ YES(?,O(n^1)) ]
|
`->{16} [ YES(?,O(n^1)) ]
->{11} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{10} [ NA ]
|
|->{12} [ NA ]
|
`->{15} [ NA ]
|
|->{8} [ NA ]
|
`->{9} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{8} [ NA ]
|
`->{10} [ NA ]
->{5} [ MAYBE ]
->{4} [ NA ]
|
`->{3} [ NA ]
->{1} [ NA ]
|
`->{2} [ NA ]
Sub-problems:
-------------
* Path {1}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 3] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [3 3] x1 + [1 3] x2 + [0]
[3 3] [3 3] [0]
c_0(x1) = [1 0] x1 + [0]
[0 1] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {1}->{2}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 3] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [1 3] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [1 0] x1 + [0]
[0 1] [0]
c_1(x1) = [1 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 3] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [3 3] x1 + [1 3] x2 + [0]
[3 3] [3 3] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {5}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {2},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 1] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [1 3] x1 + [0]
[3 3] [0]
c_4(x1, x2) = [0 1] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules: {from^#(X) -> c_4(X, from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {11}: NA
-------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [3 0] x1 + [0]
[3 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [1 3] x1 + [0]
[3 3] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}: NA
--------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [3 3] x1 + [0 0] x2 + [0]
[3 3] [0 0] [0]
s(x1) = [1 3] x1 + [0]
[0 1] [0]
cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[3 3] [3 3] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
c_6(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[3 3] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
c_13(x1) = [1 0] x1 + [0]
[0 1] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}->{10}: NA
--------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
c_6(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
c_13(x1) = [1 0] x1 + [0]
[0 1] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{10}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{12}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{8}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [3 0] x1 + [0]
[0 1] [0]
first1^#(x1, x2) = [3 3] x1 + [1 2] x2 + [0]
[3 3] [3 3] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 3] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}: NA
-------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [3 3] x1 + [0 0] x2 + [0]
[3 3] [0 0] [0]
s(x1) = [1 3] x1 + [0]
[0 1] [0]
cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[3 3] [3 3] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
c_6(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[3 3] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
c_13(x1) = [1 0] x1 + [0]
[0 1] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}->{10}: NA
-------------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
c_6(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
c_13(x1) = [1 0] x1 + [0]
[0 1] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{8}: NA
-----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{10}: NA
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {17}: YES(?,O(n^1))
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [1 2] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_15() = [0]
[0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s1(x1) = [1 0] x1 + [0]
[0 1] [1]
unquote^#(x1) = [0 1] x1 + [1]
[0 0] [0]
c_16(x1) = [1 0] x1 + [0]
[0 0] [0]
* Path {17}->{16}: YES(?,O(n^1))
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {unquote^#(01()) -> c_15()}
Weak Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
Proof Output:
The following argument positions are usable:
Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
01() = [2]
[2]
s1(x1) = [1 2] x1 + [1]
[0 0] [3]
unquote^#(x1) = [1 2] x1 + [2]
[6 1] [0]
c_15() = [1]
[0]
c_16(x1) = [1 0] x1 + [5]
[2 0] [3]
* Path {18}: YES(?,O(1))
----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [0 0] x1 + [0]
[0 0] [0]
fcons^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {unquote1^#(nil1()) -> c_17()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(unquote1^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil1() = [2]
[2]
unquote1^#(x1) = [2 0] x1 + [7]
[2 2] [7]
c_17() = [0]
[1]
* Path {19}: NA
-------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 0] x1 + [0]
[0 0] [0]
cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [1]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [2]
[0]
cons1(x1, x2) = [1 1] x1 + [1 0] x2 + [2]
[0 1] [0 0] [0]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [1 0] x1 + [2]
[0 0] [0]
unquote(x1) = [1 0] x1 + [1]
[0 0] [0]
unquote1(x1) = [2 0] x1 + [0]
[0 0] [0]
fcons(x1, x2) = [2 0] x1 + [1 0] x2 + [1]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [2 2] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [1 0] x1 + [0]
[0 1] [0]
fcons^#(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[3 3] [3 3] [0]
c_19(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
Complexity induced by the adequate RMI: YES(?,O(n^2))
We have not generated a proof for the resulting sub-problem.
* Path {19}->{20}: NA
-------------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
s(x1) = [1 0] x1 + [0]
[0 1] [0]
cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
first(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quote(x1) = [0 0] x1 + [0]
[0 0] [0]
first1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil1() = [0]
[0]
cons1(x1, x2) = [1 2] x1 + [1 2] x2 + [2]
[0 1] [0 0] [3]
01() = [0]
[0]
quote1(x1) = [0 0] x1 + [0]
[0 0] [0]
s1(x1) = [1 0] x1 + [2]
[0 0] [0]
unquote(x1) = [1 0] x1 + [1]
[0 0] [0]
unquote1(x1) = [2 1] x1 + [1]
[2 0] [0]
fcons(x1, x2) = [2 0] x1 + [1 0] x2 + [1]
[0 0] [0 0] [2]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
first^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
first1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_7() = [0]
[0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_9() = [0]
[0]
quote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_10(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13(x1) = [0 0] x1 + [0]
[0 0] [0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15() = [0]
[0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
unquote1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_17() = [0]
[0]
c_18(x1) = [1 0] x1 + [0]
[0 1] [0]
fcons^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
[0 0] [0 0] [0]
c_19(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
Complexity induced by the adequate RMI: YES(?,O(n^2))
We have not generated a proof for the resulting sub-problem.
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: sel^#(s(X), cons(Y, Z)) -> c_0(sel^#(X, Z))
, 2: sel^#(0(), cons(X, Z)) -> c_1(X)
, 3: first^#(0(), Z) -> c_2()
, 4: first^#(s(X), cons(Y, Z)) -> c_3(Y, first^#(X, Z))
, 5: from^#(X) -> c_4(X, from^#(s(X)))
, 6: sel1^#(s(X), cons(Y, Z)) -> c_5(sel1^#(X, Z))
, 7: sel1^#(0(), cons(X, Z)) -> c_6(quote^#(X))
, 8: first1^#(0(), Z) -> c_7()
, 9: first1^#(s(X), cons(Y, Z)) -> c_8(quote^#(Y), first1^#(X, Z))
, 10: quote^#(0()) -> c_9()
, 11: quote1^#(cons(X, Z)) -> c_10(quote^#(X), quote1^#(Z))
, 12: quote1^#(nil()) -> c_11()
, 13: quote^#(s(X)) -> c_12(quote^#(X))
, 14: quote^#(sel(X, Z)) -> c_13(sel1^#(X, Z))
, 15: quote1^#(first(X, Z)) -> c_14(first1^#(X, Z))
, 16: unquote^#(01()) -> c_15()
, 17: unquote^#(s1(X)) -> c_16(unquote^#(X))
, 18: unquote1^#(nil1()) -> c_17()
, 19: unquote1^#(cons1(X, Z)) ->
c_18(fcons^#(unquote(X), unquote1(Z)))
, 20: fcons^#(X, Z) -> c_19(X, Z)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{19} [ NA ]
|
`->{20} [ NA ]
->{18} [ YES(?,O(1)) ]
->{17} [ YES(?,O(n^1)) ]
|
`->{16} [ NA ]
->{11} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{10} [ NA ]
|
|->{12} [ NA ]
|
`->{15} [ NA ]
|
|->{8} [ NA ]
|
`->{9} [ NA ]
|
|->{6,14,13,7} [ NA ]
| |
| `->{10} [ NA ]
|
|->{8} [ NA ]
|
`->{10} [ NA ]
->{5} [ MAYBE ]
->{4} [ NA ]
|
`->{3} [ NA ]
->{1} [ NA ]
|
`->{2} [ NA ]
Sub-problems:
-------------
* Path {1}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_0(x1) = [1] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {1}->{2}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {1}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_0(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}: NA
------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {2}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {5}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {2},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [3] x1 + [0]
c_4(x1, x2) = [2] x1 + [1] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules: {from^#(X) -> c_4(X, from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {11}: NA
-------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [1] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [3] x1 + [0]
c_10(x1, x2) = [3] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}: NA
--------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [3] x1 + [3] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [2] x2 + [0]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [1] x1 + [0]
quote^#(x1) = [2] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
c_13(x1) = [1] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{6,14,13,7}->{10}: NA
--------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [1] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
c_13(x1) = [1] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{10}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{12}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [3] x1 + [3] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [1] x1 + [1] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [1] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [3] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{8}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}: NA
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [1] x1 + [0]
first1^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [3] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}: NA
-------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [2] x1 + [2] x2 + [0]
s(x1) = [1] x1 + [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [1] x1 + [0]
quote^#(x1) = [3] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [1] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
c_13(x1) = [1] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{6,14,13,7}->{10}: NA
-------------------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {1}, Uargs(c_6) = {1},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {1},
Uargs(c_13) = {1}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [1] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [1] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
c_13(x1) = [1] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{8}: NA
-----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {2},
Uargs(quote1^#) = {}, Uargs(c_10) = {2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {11}->{15}->{9}->{10}: NA
------------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {1, 2},
Uargs(quote1^#) = {}, Uargs(c_10) = {1, 2}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {1}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [1] x1 + [1] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [1] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {17}: YES(?,O(n^1))
------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [1] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [3] x1 + [0]
c_15() = [0]
c_16(x1) = [1] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {unquote^#(s1(X)) -> c_16(unquote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s1) = {}, Uargs(unquote^#) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s1(x1) = [1] x1 + [4]
unquote^#(x1) = [2] x1 + [0]
c_16(x1) = [1] x1 + [7]
* Path {17}->{16}: NA
-------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {1}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [1] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {18}: YES(?,O(1))
----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {}, Uargs(cons) = {},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {},
Uargs(fcons^#) = {}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [0] x1 + [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [0]
cons1(x1, x2) = [0] x1 + [0] x2 + [0]
01() = [0]
quote1(x1) = [0] x1 + [0]
s1(x1) = [0] x1 + [0]
unquote(x1) = [0] x1 + [0]
unquote1(x1) = [0] x1 + [0]
fcons(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [0] x1 + [0]
fcons^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {unquote1^#(nil1()) -> c_17()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(unquote1^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil1() = [7]
unquote1^#(x1) = [1] x1 + [7]
c_17() = [1]
* Path {19}: NA
-------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [2]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [1]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [3]
cons1(x1, x2) = [1] x1 + [1] x2 + [2]
01() = [3]
quote1(x1) = [0] x1 + [0]
s1(x1) = [1] x1 + [3]
unquote(x1) = [1] x1 + [0]
unquote1(x1) = [2] x1 + [0]
fcons(x1, x2) = [1] x1 + [1] x2 + [1]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [3] x1 + [0]
c_17() = [0]
c_18(x1) = [1] x1 + [0]
fcons^#(x1, x2) = [3] x1 + [1] x2 + [0]
c_19(x1, x2) = [0] x1 + [0] x2 + [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
* Path {19}->{20}: NA
-------------------
The usable rules for this path are:
{ unquote(01()) -> 0()
, unquote(s1(X)) -> s(unquote(X))
, unquote1(nil1()) -> nil()
, unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
, fcons(X, Z) -> cons(X, Z)}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(sel) = {}, Uargs(s) = {1}, Uargs(cons) = {1, 2},
Uargs(first) = {}, Uargs(from) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(first1) = {}, Uargs(cons1) = {},
Uargs(quote1) = {}, Uargs(s1) = {}, Uargs(unquote) = {},
Uargs(unquote1) = {}, Uargs(fcons) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(first^#) = {},
Uargs(c_3) = {}, Uargs(from^#) = {}, Uargs(c_4) = {},
Uargs(sel1^#) = {}, Uargs(c_5) = {}, Uargs(c_6) = {},
Uargs(quote^#) = {}, Uargs(first1^#) = {}, Uargs(c_8) = {},
Uargs(quote1^#) = {}, Uargs(c_10) = {}, Uargs(c_12) = {},
Uargs(c_13) = {}, Uargs(c_14) = {}, Uargs(unquote^#) = {},
Uargs(c_16) = {}, Uargs(unquote1^#) = {}, Uargs(c_18) = {1},
Uargs(fcons^#) = {1, 2}, Uargs(c_19) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
sel(x1, x2) = [0] x1 + [0] x2 + [0]
s(x1) = [1] x1 + [2]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
first(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [1]
from(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
first1(x1, x2) = [0] x1 + [0] x2 + [0]
nil1() = [3]
cons1(x1, x2) = [1] x1 + [1] x2 + [2]
01() = [3]
quote1(x1) = [0] x1 + [0]
s1(x1) = [1] x1 + [3]
unquote(x1) = [1] x1 + [0]
unquote1(x1) = [2] x1 + [0]
fcons(x1, x2) = [1] x1 + [1] x2 + [1]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
first^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
first1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_7() = [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
c_9() = [0]
quote1^#(x1) = [0] x1 + [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
c_13(x1) = [0] x1 + [0]
c_14(x1) = [0] x1 + [0]
unquote^#(x1) = [0] x1 + [0]
c_15() = [0]
c_16(x1) = [0] x1 + [0]
unquote1^#(x1) = [0] x1 + [0]
c_17() = [0]
c_18(x1) = [1] x1 + [0]
fcons^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_19(x1, x2) = [1] x1 + [1] x2 + [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
4) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.