Tool CaT
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 4.61 |
|---|
stdout:
MAYBE
Problem:
bsort(nil()) -> nil()
bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
bubble(nil()) -> nil()
bubble(.(x,nil())) -> .(x,nil())
bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
last(nil()) -> 0()
last(.(x,nil())) -> x
last(.(x,.(y,z))) -> last(.(y,z))
butlast(nil()) -> nil()
butlast(.(x,nil())) -> nil()
butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
Proof:
OpenTool IRC1
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 4.61 |
|---|
stdout:
MAYBE
Tool IRC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 4.61 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))}
Proof Output:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: bsort^#(nil()) -> c_0()
, 2: bsort^#(.(x, y)) ->
c_1(last^#(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y)))))))
, 3: bubble^#(nil()) -> c_2()
, 4: bubble^#(.(x, nil())) -> c_3()
, 5: bubble^#(.(x, .(y, z))) ->
c_4(bubble^#(.(x, z)), bubble^#(.(y, z)))
, 6: last^#(nil()) -> c_5()
, 7: last^#(.(x, nil())) -> c_6()
, 8: last^#(.(x, .(y, z))) -> c_7(last^#(.(y, z)))
, 9: butlast^#(nil()) -> c_8()
, 10: butlast^#(.(x, nil())) -> c_9()
, 11: butlast^#(.(x, .(y, z))) -> c_10(butlast^#(.(y, z)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{11} [ YES(?,O(n^1)) ]
|
`->{10} [ YES(?,O(n^1)) ]
->{9} [ YES(?,O(1)) ]
->{6} [ YES(?,O(1)) ]
->{5} [ MAYBE ]
|
`->{4} [ NA ]
->{3} [ YES(?,O(1)) ]
->{2} [ inherited ]
|
|->{7} [ NA ]
|
`->{8} [ inherited ]
|
`->{7} [ NA ]
->{1} [ YES(?,O(1)) ]
Sub-problems:
-------------
* Path {1}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_4) = {},
Uargs(c_7) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3() = [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5() = [0]
c_6() = [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {bsort^#(nil()) -> c_0()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(bsort^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
bsort^#(x1) = [1] x1 + [7]
c_0() = [1]
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{8}->{7}.
* Path {2}->{7}: NA
-----------------
The usable rules for this path are:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {2}->{8}: inherited
------------------------
This path is subsumed by the proof of path {2}->{8}->{7}.
* Path {2}->{8}->{7}: NA
----------------------
The usable rules for this path are:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {3}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_4) = {},
Uargs(c_7) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3() = [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5() = [0]
c_6() = [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {bubble^#(nil()) -> c_2()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(bubble^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
bubble^#(x1) = [1] x1 + [7]
c_2() = [1]
* Path {5}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_4) = {1, 2},
Uargs(c_7) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [3] x1 + [0]
c_2() = [0]
c_3() = [0]
c_4(x1, x2) = [1] x1 + [1] x2 + [0]
c_5() = [0]
c_6() = [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(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:
{bubble^#(.(x, .(y, z))) ->
c_4(bubble^#(.(x, z)), bubble^#(.(y, z)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {5}->{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(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_4) = {1, 2},
Uargs(c_7) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3() = [0]
c_4(x1, x2) = [1] x1 + [1] x2 + [0]
c_5() = [0]
c_6() = [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {6}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_4) = {},
Uargs(c_7) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3() = [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5() = [0]
c_6() = [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {last^#(nil()) -> c_5()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(last^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
last^#(x1) = [1] x1 + [7]
c_5() = [1]
* Path {9}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_4) = {},
Uargs(c_7) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3() = [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5() = [0]
c_6() = [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1) = [0] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {butlast^#(nil()) -> c_8()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(butlast^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
butlast^#(x1) = [1] x1 + [7]
c_8() = [1]
* Path {11}: 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(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_4) = {},
Uargs(c_7) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [1] x1 + [1] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3() = [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5() = [0]
c_6() = [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [3] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1) = [1] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules:
{butlast^#(.(x, .(y, z))) -> c_10(butlast^#(.(y, z)))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
.(x1, x2) = [1] x1 + [1] x2 + [2]
butlast^#(x1) = [2] x1 + [0]
c_10(x1) = [1] x1 + [3]
* Path {11}->{10}: 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(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_4) = {},
Uargs(c_7) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3() = [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5() = [0]
c_6() = [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1) = [1] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {butlast^#(.(x, nil())) -> c_9()}
Weak Rules: {butlast^#(.(x, .(y, z))) -> c_10(butlast^#(.(y, z)))}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [0]
.(x1, x2) = [1] x1 + [0] x2 + [0]
butlast^#(x1) = [0] x1 + [1]
c_9() = [0]
c_10(x1) = [1] x1 + [0]
2) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
3) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
4) '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
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 4.61 |
|---|
stdout:
MAYBE
Tool RC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 4.61 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))}
Proof Output:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: bsort^#(nil()) -> c_0()
, 2: bsort^#(.(x, y)) ->
c_1(last^#(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y)))))))
, 3: bubble^#(nil()) -> c_2()
, 4: bubble^#(.(x, nil())) -> c_3(x)
, 5: bubble^#(.(x, .(y, z))) ->
c_4(x, y, y, bubble^#(.(x, z)), x, bubble^#(.(y, z)))
, 6: last^#(nil()) -> c_5()
, 7: last^#(.(x, nil())) -> c_6(x)
, 8: last^#(.(x, .(y, z))) -> c_7(last^#(.(y, z)))
, 9: butlast^#(nil()) -> c_8()
, 10: butlast^#(.(x, nil())) -> c_9()
, 11: butlast^#(.(x, .(y, z))) -> c_10(x, butlast^#(.(y, z)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{11} [ YES(?,O(n^1)) ]
|
`->{10} [ YES(?,O(n^1)) ]
->{9} [ YES(?,O(1)) ]
->{6} [ YES(?,O(1)) ]
->{5} [ MAYBE ]
|
`->{4} [ NA ]
->{3} [ YES(?,O(1)) ]
->{2} [ inherited ]
|
|->{7} [ NA ]
|
`->{8} [ inherited ]
|
`->{7} [ NA ]
->{1} [ YES(?,O(1)) ]
Sub-problems:
-------------
* Path {1}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_3) = {},
Uargs(c_4) = {}, Uargs(c_6) = {}, Uargs(c_7) = {},
Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2, x3, x4, x5, x6) = [0] x1 + [0] x2 + [0] x3 + [0] x4 + [0] x5 + [0] x6 + [0]
c_5() = [0]
c_6(x1) = [0] x1 + [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {bsort^#(nil()) -> c_0()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(bsort^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
bsort^#(x1) = [1] x1 + [7]
c_0() = [1]
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{8}->{7}.
* Path {2}->{7}: NA
-----------------
The usable rules for this path are:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {2}->{8}: inherited
------------------------
This path is subsumed by the proof of path {2}->{8}->{7}.
* Path {2}->{8}->{7}: NA
----------------------
The usable rules for this path are:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {3}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_3) = {},
Uargs(c_4) = {}, Uargs(c_6) = {}, Uargs(c_7) = {},
Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2, x3, x4, x5, x6) = [0] x1 + [0] x2 + [0] x3 + [0] x4 + [0] x5 + [0] x6 + [0]
c_5() = [0]
c_6(x1) = [0] x1 + [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {bubble^#(nil()) -> c_2()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(bubble^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
bubble^#(x1) = [1] x1 + [7]
c_2() = [1]
* Path {5}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_3) = {},
Uargs(c_4) = {4, 6}, Uargs(c_6) = {}, Uargs(c_7) = {},
Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [3] x1 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2, x3, x4, x5, x6) = [0] x1 + [0] x2 + [0] x3 + [1] x4 + [0] x5 + [1] x6 + [0]
c_5() = [0]
c_6(x1) = [0] x1 + [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules:
{bubble^#(.(x, .(y, z))) ->
c_4(x, y, y, bubble^#(.(x, z)), x, bubble^#(.(y, z)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {5}->{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(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_3) = {},
Uargs(c_4) = {4, 6}, Uargs(c_6) = {}, Uargs(c_7) = {},
Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [1] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [3] x1 + [0]
c_2() = [0]
c_3(x1) = [1] x1 + [0]
c_4(x1, x2, x3, x4, x5, x6) = [0] x1 + [0] x2 + [0] x3 + [1] x4 + [0] x5 + [1] x6 + [0]
c_5() = [0]
c_6(x1) = [0] x1 + [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
We have not generated a proof for the resulting sub-problem.
* Path {6}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_3) = {},
Uargs(c_4) = {}, Uargs(c_6) = {}, Uargs(c_7) = {},
Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2, x3, x4, x5, x6) = [0] x1 + [0] x2 + [0] x3 + [0] x4 + [0] x5 + [0] x6 + [0]
c_5() = [0]
c_6(x1) = [0] x1 + [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {last^#(nil()) -> c_5()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(last^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
last^#(x1) = [1] x1 + [7]
c_5() = [1]
* Path {9}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_3) = {},
Uargs(c_4) = {}, Uargs(c_6) = {}, Uargs(c_7) = {},
Uargs(butlast^#) = {}, Uargs(c_10) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2, x3, x4, x5, x6) = [0] x1 + [0] x2 + [0] x3 + [0] x4 + [0] x5 + [0] x6 + [0]
c_5() = [0]
c_6(x1) = [0] x1 + [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1, x2) = [0] x1 + [0] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {butlast^#(nil()) -> c_8()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(butlast^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
butlast^#(x1) = [1] x1 + [7]
c_8() = [1]
* Path {11}: 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(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_3) = {},
Uargs(c_4) = {}, Uargs(c_6) = {}, Uargs(c_7) = {},
Uargs(butlast^#) = {}, Uargs(c_10) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [1] x1 + [1] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2, x3, x4, x5, x6) = [0] x1 + [0] x2 + [0] x3 + [0] x4 + [0] x5 + [0] x6 + [0]
c_5() = [0]
c_6(x1) = [0] x1 + [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [3] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: DP runtime-complexity with respect to
Strict Rules:
{butlast^#(.(x, .(y, z))) -> c_10(x, butlast^#(.(y, z)))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
.(x1, x2) = [1] x1 + [1] x2 + [1]
butlast^#(x1) = [1] x1 + [0]
c_10(x1, x2) = [1] x1 + [1] x2 + [0]
* Path {11}->{10}: 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(bsort) = {}, Uargs(.) = {}, Uargs(last) = {},
Uargs(bubble) = {}, Uargs(butlast) = {}, Uargs(if) = {},
Uargs(<=) = {}, Uargs(bsort^#) = {}, Uargs(c_1) = {},
Uargs(last^#) = {}, Uargs(bubble^#) = {}, Uargs(c_3) = {},
Uargs(c_4) = {}, Uargs(c_6) = {}, Uargs(c_7) = {},
Uargs(butlast^#) = {}, Uargs(c_10) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
bsort(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
last(x1) = [0] x1 + [0]
bubble(x1) = [0] x1 + [0]
butlast(x1) = [0] x1 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<=(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
bsort^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
last^#(x1) = [0] x1 + [0]
bubble^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2, x3, x4, x5, x6) = [0] x1 + [0] x2 + [0] x3 + [0] x4 + [0] x5 + [0] x6 + [0]
c_5() = [0]
c_6(x1) = [0] x1 + [0]
c_7(x1) = [0] x1 + [0]
butlast^#(x1) = [0] x1 + [0]
c_8() = [0]
c_9() = [0]
c_10(x1, x2) = [0] x1 + [1] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {butlast^#(.(x, nil())) -> c_9()}
Weak Rules:
{butlast^#(.(x, .(y, z))) -> c_10(x, butlast^#(.(y, z)))}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(butlast^#) = {}, Uargs(c_10) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [0]
.(x1, x2) = [1] x1 + [1] x2 + [2]
butlast^#(x1) = [2] x1 + [0]
c_9() = [1]
c_10(x1, x2) = [0] x1 + [1] x2 + [2]
2) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
3) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
4) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
Tool pair1rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 4.61 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair2rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 4.61 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3irc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 4.61 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 4.61 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ bsort(nil()) -> nil()
, bsort(.(x, y)) ->
last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y))))))
, bubble(nil()) -> nil()
, bubble(.(x, nil())) -> .(x, nil())
, bubble(.(x, .(y, z))) ->
if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z))))
, last(nil()) -> 0()
, last(.(x, nil())) -> x
, last(.(x, .(y, z))) -> last(.(y, z))
, butlast(nil()) -> nil()
, butlast(.(x, nil())) -> nil()
, butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z)))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..