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:
{ dbl(0()) -> 0()
, dbl(s(X)) -> s(s(dbl(X)))
, dbls(nil()) -> nil()
, dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y))
, sel(0(), cons(X, Y)) -> X
, sel(s(X), cons(Y, Z)) -> sel(X, Z)
, indx(nil(), X) -> nil()
, indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z))
, from(X) -> cons(X, from(s(X)))
, dbl1(0()) -> 01()
, dbl1(s(X)) -> s1(s1(dbl1(X)))
, sel1(0(), cons(X, Y)) -> X
, sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
, quote(0()) -> 01()
, quote(s(X)) -> s1(quote(X))
, quote(dbl(X)) -> dbl1(X)
, quote(sel(X, Y)) -> sel1(X, Y)}
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: dbl^#(0()) -> c_0()
, 2: dbl^#(s(X)) -> c_1(dbl^#(X))
, 3: dbls^#(nil()) -> c_2()
, 4: dbls^#(cons(X, Y)) -> c_3(dbl^#(X), dbls^#(Y))
, 5: sel^#(0(), cons(X, Y)) -> c_4()
, 6: sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z))
, 7: indx^#(nil(), X) -> c_6()
, 8: indx^#(cons(X, Y), Z) -> c_7(sel^#(X, Z), indx^#(Y, Z))
, 9: from^#(X) -> c_8(from^#(s(X)))
, 10: dbl1^#(0()) -> c_9()
, 11: dbl1^#(s(X)) -> c_10(dbl1^#(X))
, 12: sel1^#(0(), cons(X, Y)) -> c_11()
, 13: sel1^#(s(X), cons(Y, Z)) -> c_12(sel1^#(X, Z))
, 14: quote^#(0()) -> c_13()
, 15: quote^#(s(X)) -> c_14(quote^#(X))
, 16: quote^#(dbl(X)) -> c_15(dbl1^#(X))
, 17: quote^#(sel(X, Y)) -> c_16(sel1^#(X, Y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{15} [ YES(?,O(n^2)) ]
|
|->{14} [ YES(?,O(n^2)) ]
|
|->{16} [ NA ]
| |
| |->{10} [ NA ]
| |
| `->{11} [ NA ]
| |
| `->{10} [ NA ]
|
`->{17} [ NA ]
|
|->{12} [ NA ]
|
`->{13} [ NA ]
|
`->{12} [ NA ]
->{9} [ MAYBE ]
->{8} [ NA ]
|
|->{5} [ NA ]
|
|->{6} [ NA ]
| |
| `->{5} [ NA ]
|
`->{7} [ NA ]
->{4} [ YES(?,O(n^3)) ]
|
|->{1} [ NA ]
|
|->{2} [ NA ]
| |
| `->{1} [ NA ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [3 0 0] x1 + [0]
[3 0 0] [0]
[3 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 1 0] x1 + [0]
[3 3 3] [0]
[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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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: innermost DP runtime-complexity with respect to
Strict Rules: {dbls^#(cons(X, Y)) -> c_3(dbl^#(X), dbls^#(Y))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(cons) = {}, Uargs(dbl^#) = {}, Uargs(dbls^#) = {},
Uargs(c_3) = {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]
dbl^#(x1) = [0 0 2] x1 + [0]
[0 0 0] [2]
[0 0 2] [2]
dbls^#(x1) = [2 4 0] x1 + [0]
[2 0 2] [0]
[0 0 4] [2]
c_3(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 {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
dbls^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{2}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
dbls^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
[0 0 0] [0 1 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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
sel^#(x1, x2) = [3 0 0] x1 + [3 3 3] x2 + [0]
[3 0 0] [3 3 3] [0]
[3 0 0] [3 3 3] [0]
c_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 3] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_6() = [0]
[0]
[0]
c_7(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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {1, 2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(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]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {1}, Uargs(indx^#) = {}, Uargs(c_7) = {1, 2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(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]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {1}, Uargs(indx^#) = {}, Uargs(c_7) = {1, 2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(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]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {9}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {1}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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) = [3 3 3] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_8(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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: innermost DP runtime-complexity with respect to
Strict Rules: {from^#(X) -> c_8(from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {15}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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: innermost DP runtime-complexity with respect to
Strict Rules: {quote^#(s(X)) -> c_14(quote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(quote^#) = {}, Uargs(c_14) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 2 2] x1 + [2]
[0 1 2] [2]
[0 0 0] [0]
quote^#(x1) = [0 1 0] x1 + [2]
[6 0 0] [0]
[2 3 0] [2]
c_14(x1) = [1 0 0] x1 + [1]
[2 0 2] [0]
[0 0 0] [0]
* Path {15}->{14}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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: innermost DP runtime-complexity with respect to
Strict Rules: {quote^#(0()) -> c_13()}
Weak Rules: {quote^#(s(X)) -> c_14(quote^#(X))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(quote^#) = {}, Uargs(c_14) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[2]
[2]
s(x1) = [1 1 0] x1 + [0]
[0 1 1] [1]
[0 0 0] [0]
quote^#(x1) = [2 2 2] x1 + [0]
[0 6 0] [0]
[0 0 2] [0]
c_13() = [1]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [2]
[0 0 0] [3]
[0 0 0] [0]
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {1},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {1}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {1},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {1}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {1},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {1},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {1},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4() = [0]
[0]
[0]
c_5(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11() = [0]
[0]
[0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
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: dbl^#(0()) -> c_0()
, 2: dbl^#(s(X)) -> c_1(dbl^#(X))
, 3: dbls^#(nil()) -> c_2()
, 4: dbls^#(cons(X, Y)) -> c_3(dbl^#(X), dbls^#(Y))
, 5: sel^#(0(), cons(X, Y)) -> c_4()
, 6: sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z))
, 7: indx^#(nil(), X) -> c_6()
, 8: indx^#(cons(X, Y), Z) -> c_7(sel^#(X, Z), indx^#(Y, Z))
, 9: from^#(X) -> c_8(from^#(s(X)))
, 10: dbl1^#(0()) -> c_9()
, 11: dbl1^#(s(X)) -> c_10(dbl1^#(X))
, 12: sel1^#(0(), cons(X, Y)) -> c_11()
, 13: sel1^#(s(X), cons(Y, Z)) -> c_12(sel1^#(X, Z))
, 14: quote^#(0()) -> c_13()
, 15: quote^#(s(X)) -> c_14(quote^#(X))
, 16: quote^#(dbl(X)) -> c_15(dbl1^#(X))
, 17: quote^#(sel(X, Y)) -> c_16(sel1^#(X, Y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{15} [ YES(?,O(n^1)) ]
|
|->{14} [ YES(?,O(n^1)) ]
|
|->{16} [ NA ]
| |
| |->{10} [ NA ]
| |
| `->{11} [ NA ]
| |
| `->{10} [ NA ]
|
`->{17} [ NA ]
|
|->{12} [ NA ]
|
`->{13} [ NA ]
|
`->{12} [ NA ]
->{9} [ MAYBE ]
->{8} [ NA ]
|
|->{5} [ NA ]
|
|->{6} [ NA ]
| |
| `->{5} [ NA ]
|
`->{7} [ NA ]
->{4} [ NA ]
|
|->{1} [ NA ]
|
|->{2} [ NA ]
| |
| `->{1} [ NA ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [3 0] x1 + [0]
[3 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [1 3] x1 + [0]
[3 3] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_0() = [0]
[0]
c_1(x1) = [1 0] x1 + [0]
[0 1] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{2}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [1 0] x1 + [0]
[0 1] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [3 0] x1 + [3 3] x2 + [0]
[3 0] [3 3] [0]
c_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [1 3] x1 + [3 3] x2 + [0]
[3 3] [3 3] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {1, 2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {1}, Uargs(indx^#) = {}, Uargs(c_7) = {1, 2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 2] 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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
[3 3] [3 3] [0]
c_4() = [0]
[0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {1}, Uargs(indx^#) = {}, Uargs(c_7) = {1, 2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {9}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {1}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 0] x1 + [0]
[0 1] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_8(x1) = [1 0] x1 + [0]
[0 1] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 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_8(from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {15}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [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: innermost DP runtime-complexity with respect to
Strict Rules: {quote^#(s(X)) -> c_14(quote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(quote^#) = {}, Uargs(c_14) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 0] x1 + [0]
[0 1] [1]
quote^#(x1) = [0 1] x1 + [1]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 0] [0]
* Path {15}->{14}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [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: innermost DP runtime-complexity with respect to
Strict Rules: {quote^#(0()) -> c_13()}
Weak Rules: {quote^#(s(X)) -> c_14(quote^#(X))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(quote^#) = {}, Uargs(c_14) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[2]
s(x1) = [1 2] x1 + [1]
[0 0] [3]
quote^#(x1) = [1 2] x1 + [2]
[6 1] [0]
c_13() = [1]
[0]
c_14(x1) = [1 0] x1 + [5]
[2 0] [3]
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {1},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [1 0] x1 + [0]
[0 1] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {1}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {1},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_9() = [0]
[0]
c_10(x1) = [1 0] x1 + [0]
[0 1] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [1 0] x1 + [0]
[0 1] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {1}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {1},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [1 0] x1 + [0]
[0 1] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [1 0] x1 + [0]
[0 1] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(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]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {1},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 2] 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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
[3 3] [3 3] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {1},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4() = [0]
[0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11() = [0]
[0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
We have not generated a proof for the resulting sub-problem.
3) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
4) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: dbl^#(0()) -> c_0()
, 2: dbl^#(s(X)) -> c_1(dbl^#(X))
, 3: dbls^#(nil()) -> c_2()
, 4: dbls^#(cons(X, Y)) -> c_3(dbl^#(X), dbls^#(Y))
, 5: sel^#(0(), cons(X, Y)) -> c_4()
, 6: sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z))
, 7: indx^#(nil(), X) -> c_6()
, 8: indx^#(cons(X, Y), Z) -> c_7(sel^#(X, Z), indx^#(Y, Z))
, 9: from^#(X) -> c_8(from^#(s(X)))
, 10: dbl1^#(0()) -> c_9()
, 11: dbl1^#(s(X)) -> c_10(dbl1^#(X))
, 12: sel1^#(0(), cons(X, Y)) -> c_11()
, 13: sel1^#(s(X), cons(Y, Z)) -> c_12(sel1^#(X, Z))
, 14: quote^#(0()) -> c_13()
, 15: quote^#(s(X)) -> c_14(quote^#(X))
, 16: quote^#(dbl(X)) -> c_15(dbl1^#(X))
, 17: quote^#(sel(X, Y)) -> c_16(sel1^#(X, Y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{15} [ NA ]
|
|->{14} [ NA ]
|
|->{16} [ NA ]
| |
| |->{10} [ NA ]
| |
| `->{11} [ NA ]
| |
| `->{10} [ NA ]
|
`->{17} [ NA ]
|
|->{12} [ NA ]
|
`->{13} [ NA ]
|
`->{12} [ NA ]
->{9} [ MAYBE ]
->{8} [ NA ]
|
|->{5} [ NA ]
|
|->{6} [ NA ]
| |
| `->{5} [ NA ]
|
`->{7} [ NA ]
->{4} [ NA ]
|
|->{1} [ NA ]
|
|->{2} [ NA ]
| |
| `->{1} [ NA ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [1] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [3] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [3] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [3] x1 + [0]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{2}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [3] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [1] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {1, 2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [1] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {1}, Uargs(indx^#) = {}, Uargs(c_7) = {1, 2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_4() = [0]
c_5(x1) = [1] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [1] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {1}, Uargs(indx^#) = {}, Uargs(c_7) = {1, 2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [1] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [1] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {2},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {9}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {1}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [3] x1 + [0]
c_8(x1) = [1] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [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_8(from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [3] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{14}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {1},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [1] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {1}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {1},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [3] x1 + [0]
c_9() = [0]
c_10(x1) = [1] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [1] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {1}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {1},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [1] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [1] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [3] x1 + [3] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [1] x1 + [1] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [1] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [3] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [1] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {1},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [1] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_5) = {}, Uargs(indx^#) = {}, Uargs(c_7) = {},
Uargs(from^#) = {}, Uargs(c_8) = {}, Uargs(dbl1^#) = {},
Uargs(c_10) = {}, Uargs(sel1^#) = {}, Uargs(c_12) = {1},
Uargs(quote^#) = {}, Uargs(c_14) = {1}, Uargs(c_15) = {},
Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4() = [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1) = [0] x1 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11() = [0]
c_12(x1) = [1] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [1] x1 + [0]
We have not generated a proof for the resulting sub-problem.
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:
{ dbl(0()) -> 0()
, dbl(s(X)) -> s(s(dbl(X)))
, dbls(nil()) -> nil()
, dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y))
, sel(0(), cons(X, Y)) -> X
, sel(s(X), cons(Y, Z)) -> sel(X, Z)
, indx(nil(), X) -> nil()
, indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z))
, from(X) -> cons(X, from(s(X)))
, dbl1(0()) -> 01()
, dbl1(s(X)) -> s1(s1(dbl1(X)))
, sel1(0(), cons(X, Y)) -> X
, sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
, quote(0()) -> 01()
, quote(s(X)) -> s1(quote(X))
, quote(dbl(X)) -> dbl1(X)
, quote(sel(X, Y)) -> sel1(X, Y)}
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: dbl^#(0()) -> c_0()
, 2: dbl^#(s(X)) -> c_1(dbl^#(X))
, 3: dbls^#(nil()) -> c_2()
, 4: dbls^#(cons(X, Y)) -> c_3(dbl^#(X), dbls^#(Y))
, 5: sel^#(0(), cons(X, Y)) -> c_4(X)
, 6: sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z))
, 7: indx^#(nil(), X) -> c_6()
, 8: indx^#(cons(X, Y), Z) -> c_7(sel^#(X, Z), indx^#(Y, Z))
, 9: from^#(X) -> c_8(X, from^#(s(X)))
, 10: dbl1^#(0()) -> c_9()
, 11: dbl1^#(s(X)) -> c_10(dbl1^#(X))
, 12: sel1^#(0(), cons(X, Y)) -> c_11(X)
, 13: sel1^#(s(X), cons(Y, Z)) -> c_12(sel1^#(X, Z))
, 14: quote^#(0()) -> c_13()
, 15: quote^#(s(X)) -> c_14(quote^#(X))
, 16: quote^#(dbl(X)) -> c_15(dbl1^#(X))
, 17: quote^#(sel(X, Y)) -> c_16(sel1^#(X, Y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{15} [ YES(?,O(n^2)) ]
|
|->{14} [ YES(?,O(n^2)) ]
|
|->{16} [ NA ]
| |
| |->{10} [ NA ]
| |
| `->{11} [ NA ]
| |
| `->{10} [ NA ]
|
`->{17} [ NA ]
|
|->{12} [ NA ]
|
`->{13} [ NA ]
|
`->{12} [ NA ]
->{9} [ MAYBE ]
->{8} [ NA ]
|
|->{5} [ NA ]
|
|->{6} [ NA ]
| |
| `->{5} [ NA ]
|
`->{7} [ NA ]
->{4} [ YES(?,O(n^3)) ]
|
|->{1} [ NA ]
|
|->{2} [ NA ]
| |
| `->{1} [ NA ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [3 0 0] x1 + [0]
[3 0 0] [0]
[3 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 1 0] x1 + [0]
[3 3 3] [0]
[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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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: {dbls^#(cons(X, Y)) -> c_3(dbl^#(X), dbls^#(Y))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(cons) = {}, Uargs(dbl^#) = {}, Uargs(dbls^#) = {},
Uargs(c_3) = {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]
dbl^#(x1) = [0 0 2] x1 + [0]
[0 0 0] [2]
[0 0 2] [2]
dbls^#(x1) = [2 4 0] x1 + [0]
[2 0 2] [0]
[0 0 4] [2]
c_3(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 {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
dbls^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{2}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
dbls^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
cons(x1, x2) = [1 0 0] x1 + [1 3 0] x2 + [0]
[0 0 0] [0 1 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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
sel^#(x1, x2) = [3 0 0] x1 + [3 3 3] x2 + [0]
[3 0 0] [3 3 3] [0]
[3 0 0] [3 3 3] [0]
c_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 3] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_6() = [0]
[0]
[0]
c_7(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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {1, 2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
cons(x1, x2) = [1 1 1] x1 + [0 0 0] x2 + [0]
[0 0 3] [0 0 0] [0]
[0 0 1] [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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
sel^#(x1, x2) = [0 0 0] x1 + [3 2 1] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_4(x1) = [1 1 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(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]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {1}, Uargs(indx^#) = {},
Uargs(c_7) = {1, 2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(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]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {1}, Uargs(indx^#) = {},
Uargs(c_7) = {1, 2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
cons(x1, x2) = [1 3 3] x1 + [0 0 0] x2 + [0]
[0 0 3] [0 0 0] [0]
[0 0 1] [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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
sel^#(x1, x2) = [0 0 0] x1 + [1 2 1] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_4(x1) = [1 1 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(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]
from^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {9}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {2},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_8(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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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_8(X, from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {15}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
quote^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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: {quote^#(s(X)) -> c_14(quote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(quote^#) = {}, Uargs(c_14) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 2 2] x1 + [2]
[0 1 2] [2]
[0 0 0] [0]
quote^#(x1) = [0 1 0] x1 + [2]
[6 0 0] [0]
[2 3 0] [2]
c_14(x1) = [1 0 0] x1 + [1]
[2 0 2] [0]
[0 0 0] [0]
* Path {15}->{14}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [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: {quote^#(0()) -> c_13()}
Weak Rules: {quote^#(s(X)) -> c_14(quote^#(X))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(quote^#) = {}, Uargs(c_14) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[2]
[2]
s(x1) = [1 1 0] x1 + [0]
[0 1 1] [1]
[0 0 0] [0]
quote^#(x1) = [2 2 2] x1 + [0]
[0 6 0] [0]
[0 0 2] [0]
c_13() = [1]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [2]
[0 0 0] [3]
[0 0 0] [0]
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {1}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {1}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {1}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {1}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {1}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
cons(x1, x2) = [1 1 1] x1 + [0 0 0] x2 + [0]
[0 0 3] [0 0 0] [0]
[0 0 1] [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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [3 2 1] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11(x1) = [1 1 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {1}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [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]
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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(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_11(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {1}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0 0] x1 + [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]
dbls(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
cons(x1, x2) = [1 3 3] x1 + [0 0 0] x2 + [0]
[0 0 3] [0 0 0] [0]
[0 0 1] [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]
indx(x1, 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]
dbl1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
01() = [0]
[0]
[0]
s1(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]
dbl^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
dbls^#(x1) = [0 0 0] x1 + [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]
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_4(x1) = [0 0 0] x1 + [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]
indx^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_6() = [0]
[0]
[0]
c_7(x1, 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_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]
dbl1^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_9() = [0]
[0]
[0]
c_10(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
sel1^#(x1, x2) = [0 0 0] x1 + [1 2 1] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_11(x1) = [1 1 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_12(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]
c_13() = [0]
[0]
[0]
c_14(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_15(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_16(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
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: dbl^#(0()) -> c_0()
, 2: dbl^#(s(X)) -> c_1(dbl^#(X))
, 3: dbls^#(nil()) -> c_2()
, 4: dbls^#(cons(X, Y)) -> c_3(dbl^#(X), dbls^#(Y))
, 5: sel^#(0(), cons(X, Y)) -> c_4(X)
, 6: sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z))
, 7: indx^#(nil(), X) -> c_6()
, 8: indx^#(cons(X, Y), Z) -> c_7(sel^#(X, Z), indx^#(Y, Z))
, 9: from^#(X) -> c_8(X, from^#(s(X)))
, 10: dbl1^#(0()) -> c_9()
, 11: dbl1^#(s(X)) -> c_10(dbl1^#(X))
, 12: sel1^#(0(), cons(X, Y)) -> c_11(X)
, 13: sel1^#(s(X), cons(Y, Z)) -> c_12(sel1^#(X, Z))
, 14: quote^#(0()) -> c_13()
, 15: quote^#(s(X)) -> c_14(quote^#(X))
, 16: quote^#(dbl(X)) -> c_15(dbl1^#(X))
, 17: quote^#(sel(X, Y)) -> c_16(sel1^#(X, Y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{15} [ YES(?,O(n^1)) ]
|
|->{14} [ YES(?,O(n^1)) ]
|
|->{16} [ NA ]
| |
| |->{10} [ NA ]
| |
| `->{11} [ NA ]
| |
| `->{10} [ NA ]
|
`->{17} [ NA ]
|
|->{12} [ NA ]
|
`->{13} [ NA ]
|
`->{12} [ NA ]
->{9} [ MAYBE ]
->{8} [ NA ]
|
|->{5} [ NA ]
|
|->{6} [ NA ]
| |
| `->{5} [ NA ]
|
`->{7} [ NA ]
->{4} [ NA ]
|
|->{1} [ NA ]
|
|->{2} [ NA ]
| |
| `->{1} [ NA ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [3 0] x1 + [0]
[3 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [1 3] x1 + [0]
[3 3] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_0() = [0]
[0]
c_1(x1) = [1 0] x1 + [0]
[0 1] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{2}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [1 0] x1 + [0]
[0 1] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
sel^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [3 0] x1 + [3 3] x2 + [0]
[3 0] [3 3] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [1 3] x1 + [3 3] x2 + [0]
[3 3] [3 3] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {1, 2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 1] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [3 3] x2 + [0]
[0 0] [0 0] [0]
c_4(x1) = [1 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {1}, Uargs(indx^#) = {},
Uargs(c_7) = {1, 2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 2] 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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
[3 3] [3 3] [0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {1}, Uargs(indx^#) = {},
Uargs(c_7) = {1, 2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 1] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
sel^#(x1, x2) = [0 0] x1 + [3 3] x2 + [0]
[0 0] [0 0] [0]
c_4(x1) = [1 0] x1 + [0]
[0 0] [0]
c_5(x1) = [1 0] x1 + [0]
[0 1] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {9}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {2},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 1] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [1 3] x1 + [0]
[3 3] [0]
c_8(x1, x2) = [0 1] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [0 0] x1 + [0]
[0 0] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [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_8(X, from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {15}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [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: {quote^#(s(X)) -> c_14(quote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(quote^#) = {}, Uargs(c_14) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 0] x1 + [0]
[0 1] [1]
quote^#(x1) = [0 1] x1 + [1]
[0 0] [0]
c_14(x1) = [1 0] x1 + [0]
[0 0] [0]
* Path {15}->{14}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [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: {quote^#(0()) -> c_13()}
Weak Rules: {quote^#(s(X)) -> c_14(quote^#(X))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(quote^#) = {}, Uargs(c_14) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[2]
s(x1) = [1 2] x1 + [1]
[0 0] [3]
quote^#(x1) = [1 2] x1 + [2]
[6 1] [0]
c_13() = [1]
[0]
c_14(x1) = [1 0] x1 + [5]
[2 0] [3]
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {1}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [1 0] x1 + [0]
[0 1] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {1}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {1}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_9() = [0]
[0]
c_10(x1) = [1 0] x1 + [0]
[0 1] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [1 0] x1 + [0]
[0 1] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {1}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {1}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [1 0] x1 + [0]
[0 1] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [1 0] x1 + [0]
[0 1] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [0 0] x1 + [0]
[0 0] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 1] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [3 3] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [1 0] x1 + [0]
[0 0] [0]
c_12(x1) = [0 0] x1 + [0]
[0 0] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {1}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 2] 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]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
[3 3] [3 3] [0]
c_11(x1) = [0 0] x1 + [0]
[0 0] [0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {1}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [1 1] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
sel(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
indx(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
dbl1(x1) = [0 0] x1 + [0]
[0 0] [0]
01() = [0]
[0]
s1(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]
dbl^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
dbls^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(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_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
indx^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_6() = [0]
[0]
c_7(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_8(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
dbl1^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_9() = [0]
[0]
c_10(x1) = [0 0] x1 + [0]
[0 0] [0]
sel1^#(x1, x2) = [0 0] x1 + [3 3] x2 + [0]
[0 0] [0 0] [0]
c_11(x1) = [1 0] x1 + [0]
[0 0] [0]
c_12(x1) = [1 0] x1 + [0]
[0 1] [0]
quote^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_13() = [0]
[0]
c_14(x1) = [1 0] x1 + [0]
[0 1] [0]
c_15(x1) = [0 0] x1 + [0]
[0 0] [0]
c_16(x1) = [1 0] x1 + [0]
[0 1] [0]
We have not generated a proof for the resulting sub-problem.
3) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
4) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: dbl^#(0()) -> c_0()
, 2: dbl^#(s(X)) -> c_1(dbl^#(X))
, 3: dbls^#(nil()) -> c_2()
, 4: dbls^#(cons(X, Y)) -> c_3(dbl^#(X), dbls^#(Y))
, 5: sel^#(0(), cons(X, Y)) -> c_4(X)
, 6: sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z))
, 7: indx^#(nil(), X) -> c_6()
, 8: indx^#(cons(X, Y), Z) -> c_7(sel^#(X, Z), indx^#(Y, Z))
, 9: from^#(X) -> c_8(X, from^#(s(X)))
, 10: dbl1^#(0()) -> c_9()
, 11: dbl1^#(s(X)) -> c_10(dbl1^#(X))
, 12: sel1^#(0(), cons(X, Y)) -> c_11(X)
, 13: sel1^#(s(X), cons(Y, Z)) -> c_12(sel1^#(X, Z))
, 14: quote^#(0()) -> c_13()
, 15: quote^#(s(X)) -> c_14(quote^#(X))
, 16: quote^#(dbl(X)) -> c_15(dbl1^#(X))
, 17: quote^#(sel(X, Y)) -> c_16(sel1^#(X, Y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{15} [ YES(?,O(n^1)) ]
|
|->{14} [ NA ]
|
|->{16} [ NA ]
| |
| |->{10} [ NA ]
| |
| `->{11} [ NA ]
| |
| `->{10} [ NA ]
|
`->{17} [ NA ]
|
|->{12} [ NA ]
|
`->{13} [ NA ]
|
`->{12} [ NA ]
->{9} [ MAYBE ]
->{8} [ NA ]
|
|->{5} [ NA ]
|
|->{6} [ NA ]
| |
| `->{5} [ NA ]
|
`->{7} [ NA ]
->{4} [ NA ]
|
|->{1} [ NA ]
|
|->{2} [ NA ]
| |
| `->{1} [ NA ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [1] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [3] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [3] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [3] x1 + [0]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {4}->{2}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {1},
Uargs(dbls^#) = {}, Uargs(c_3) = {1, 2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {2}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [1] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [1] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [3] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [1] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {1, 2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_4(x1) = [1] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [1] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {1}, Uargs(indx^#) = {},
Uargs(c_7) = {1, 2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [1] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [1] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{6}->{5}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {1}, Uargs(indx^#) = {},
Uargs(c_7) = {1, 2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_4(x1) = [1] x1 + [0]
c_5(x1) = [1] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [1] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {8}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {2}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [1] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {9}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {2},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [3] x1 + [0]
c_8(x1, x2) = [2] x1 + [1] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [0] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [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_8(X, from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {15}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [3] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [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: {quote^#(s(X)) -> c_14(quote^#(X))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(quote^#) = {}, Uargs(c_14) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1] x1 + [4]
quote^#(x1) = [2] x1 + [0]
c_14(x1) = [1] x1 + [7]
* Path {15}->{14}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {1}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [1] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {1}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {1}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [3] x1 + [0]
c_9() = [0]
c_10(x1) = [1] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [1] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{16}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {1}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {1}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [1] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [1] x1 + [0]
c_16(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
sel(x1, x2) = [3] x1 + [3] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [1] x1 + [1] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [1] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [3] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_11(x1) = [1] x1 + [0]
c_12(x1) = [0] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [1] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}: 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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {1}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_11(x1) = [0] x1 + [0]
c_12(x1) = [1] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [1] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {15}->{17}->{13}->{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(dbl) = {}, Uargs(s) = {}, Uargs(dbls) = {}, Uargs(cons) = {},
Uargs(sel) = {}, Uargs(indx) = {}, Uargs(from) = {},
Uargs(dbl1) = {}, Uargs(s1) = {}, Uargs(sel1) = {},
Uargs(quote) = {}, Uargs(dbl^#) = {}, Uargs(c_1) = {},
Uargs(dbls^#) = {}, Uargs(c_3) = {}, Uargs(sel^#) = {},
Uargs(c_4) = {}, Uargs(c_5) = {}, Uargs(indx^#) = {},
Uargs(c_7) = {}, Uargs(from^#) = {}, Uargs(c_8) = {},
Uargs(dbl1^#) = {}, Uargs(c_10) = {}, Uargs(sel1^#) = {},
Uargs(c_11) = {}, Uargs(c_12) = {1}, Uargs(quote^#) = {},
Uargs(c_14) = {1}, Uargs(c_15) = {}, Uargs(c_16) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
dbl(x1) = [0] x1 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
dbls(x1) = [0] x1 + [0]
nil() = [0]
cons(x1, x2) = [1] x1 + [0] x2 + [0]
sel(x1, x2) = [0] x1 + [0] x2 + [0]
indx(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
dbl1(x1) = [0] x1 + [0]
01() = [0]
s1(x1) = [0] x1 + [0]
sel1(x1, x2) = [0] x1 + [0] x2 + [0]
quote(x1) = [0] x1 + [0]
dbl^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
dbls^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [0] x1 + [0] x2 + [0]
sel^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_4(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
indx^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_6() = [0]
c_7(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [0] x1 + [0]
c_8(x1, x2) = [0] x1 + [0] x2 + [0]
dbl1^#(x1) = [0] x1 + [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
sel1^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_11(x1) = [1] x1 + [0]
c_12(x1) = [1] x1 + [0]
quote^#(x1) = [0] x1 + [0]
c_13() = [0]
c_14(x1) = [1] x1 + [0]
c_15(x1) = [0] x1 + [0]
c_16(x1) = [1] x1 + [0]
We have not generated a proof for the resulting sub-problem.
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.