Tool CaT
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.43 |
|---|
stdout:
MAYBE
Problem:
merge(nil(),y) -> y
merge(x,nil()) -> x
merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
++(nil(),y) -> y
++(.(x,y),z) -> .(x,++(y,z))
if(true(),x,y) -> x
if(false(),x,y) -> x
Proof:
OpenTool IRC1
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.43 |
|---|
stdout:
MAYBE
Tool IRC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.43 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, ++(nil(), y) -> y
, ++(.(x, y), z) -> .(x, ++(y, z))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
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: merge^#(nil(), y) -> c_0()
, 2: merge^#(x, nil()) -> c_1()
, 3: merge^#(.(x, y), .(u, v)) ->
c_2(if^#(<(x, u),
.(x, merge(y, .(u, v))),
.(u, merge(.(x, y), v))))
, 4: ++^#(nil(), y) -> c_3()
, 5: ++^#(.(x, y), z) -> c_4(++^#(y, z))
, 6: if^#(true(), x, y) -> c_5()
, 7: if^#(false(), x, y) -> c_6()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ YES(?,O(1)) ]
->{6} [ YES(?,O(1)) ]
->{5} [ YES(?,O(n^2)) ]
|
`->{4} [ YES(?,O(n^2)) ]
->{3} [ NA ]
->{2} [ YES(?,O(1)) ]
->{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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0() = [0]
[0]
c_1() = [0]
[0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3() = [0]
[0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5() = [0]
[0]
c_6() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {merge^#(nil(), y) -> c_0()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(merge^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [2]
[2]
merge^#(x1, x2) = [2 0] x1 + [0 0] x2 + [7]
[2 2] [0 0] [7]
c_0() = [0]
[1]
* Path {2}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0() = [0]
[0]
c_1() = [0]
[0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3() = [0]
[0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5() = [0]
[0]
c_6() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {merge^#(x, nil()) -> c_1()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(merge^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [2]
[2]
merge^#(x1, x2) = [0 0] x1 + [2 0] x2 + [7]
[0 0] [2 2] [7]
c_1() = [0]
[1]
* Path {3}: NA
------------
The usable rules for this path are:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
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 {5}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [1 1] x1 + [1 2] x2 + [0]
[0 1] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0() = [0]
[0]
c_1() = [0]
[0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [3 3] x1 + [1 0] x2 + [0]
[3 3] [3 3] [0]
c_3() = [0]
[0]
c_4(x1) = [1 0] x1 + [0]
[0 1] [0]
c_5() = [0]
[0]
c_6() = [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: {++^#(.(x, y), z) -> c_4(++^#(y, z))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(++^#) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
.(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [1]
++^#(x1, x2) = [0 1] x1 + [0 0] x2 + [0]
[0 0] [0 4] [4]
c_4(x1) = [1 0] x1 + [0]
[0 0] [3]
* Path {5}->{4}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0() = [0]
[0]
c_1() = [0]
[0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3() = [0]
[0]
c_4(x1) = [1 0] x1 + [0]
[0 1] [0]
c_5() = [0]
[0]
c_6() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(n^2))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {++^#(nil(), y) -> c_3()}
Weak Rules: {++^#(.(x, y), z) -> c_4(++^#(y, z))}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(++^#) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [2]
[2]
.(x1, x2) = [0 0] x1 + [1 2] x2 + [4]
[0 0] [0 1] [0]
++^#(x1, x2) = [1 3] x1 + [0 0] x2 + [4]
[2 2] [4 4] [0]
c_3() = [1]
[0]
c_4(x1) = [1 0] x1 + [3]
[0 0] [7]
* 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0() = [0]
[0]
c_1() = [0]
[0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3() = [0]
[0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5() = [0]
[0]
c_6() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {if^#(true(), x, y) -> c_5()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(if^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
true() = [2]
[2]
if^#(x1, x2, x3) = [2 0] x1 + [0 0] x2 + [0 0] x3 + [7]
[2 2] [0 0] [0 0] [7]
c_5() = [0]
[1]
* Path {7}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0() = [0]
[0]
c_1() = [0]
[0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3() = [0]
[0]
c_4(x1) = [0 0] x1 + [0]
[0 0] [0]
c_5() = [0]
[0]
c_6() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {if^#(false(), x, y) -> c_6()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(if^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
false() = [2]
[2]
if^#(x1, x2, x3) = [2 0] x1 + [0 0] x2 + [0 0] x3 + [7]
[2 2] [0 0] [0 0] [7]
c_6() = [0]
[1]
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: merge^#(nil(), y) -> c_0()
, 2: merge^#(x, nil()) -> c_1()
, 3: merge^#(.(x, y), .(u, v)) ->
c_2(if^#(<(x, u),
.(x, merge(y, .(u, v))),
.(u, merge(.(x, y), v))))
, 4: ++^#(nil(), y) -> c_3()
, 5: ++^#(.(x, y), z) -> c_4(++^#(y, z))
, 6: if^#(true(), x, y) -> c_5()
, 7: if^#(false(), x, y) -> c_6()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ YES(?,O(1)) ]
->{6} [ YES(?,O(1)) ]
->{5} [ YES(?,O(n^1)) ]
|
`->{4} [ YES(?,O(n^1)) ]
->{3} [ MAYBE ]
->{2} [ YES(?,O(1)) ]
->{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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3() = [0]
c_4(x1) = [0] x1 + [0]
c_5() = [0]
c_6() = [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: {merge^#(nil(), y) -> c_0()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(merge^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
merge^#(x1, x2) = [1] x1 + [0] x2 + [7]
c_0() = [1]
* Path {2}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3() = [0]
c_4(x1) = [0] x1 + [0]
c_5() = [0]
c_6() = [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: {merge^#(x, nil()) -> c_1()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(merge^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [7]
merge^#(x1, x2) = [0] x1 + [1] x2 + [7]
c_1() = [1]
* Path {3}: MAYBE
---------------
The usable rules for this path are:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ merge^#(.(x, y), .(u, v)) ->
c_2(if^#(<(x, u),
.(x, merge(y, .(u, v))),
.(u, merge(.(x, y), v))))
, merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
Proof Output:
The input cannot be shown compatible
* Path {5}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [1] x1 + [1] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [3] x1 + [1] x2 + [0]
c_3() = [0]
c_4(x1) = [1] x1 + [0]
c_5() = [0]
c_6() = [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: {++^#(.(x, y), z) -> c_4(++^#(y, z))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(++^#) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
.(x1, x2) = [0] x1 + [1] x2 + [4]
++^#(x1, x2) = [2] x1 + [7] x2 + [0]
c_4(x1) = [1] x1 + [7]
* Path {5}->{4}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3() = [0]
c_4(x1) = [1] x1 + [0]
c_5() = [0]
c_6() = [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: {++^#(nil(), y) -> c_3()}
Weak Rules: {++^#(.(x, y), z) -> c_4(++^#(y, z))}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(++^#) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [2]
.(x1, x2) = [0] x1 + [1] x2 + [2]
++^#(x1, x2) = [6] x1 + [7] x2 + [0]
c_3() = [1]
c_4(x1) = [1] x1 + [7]
* 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3() = [0]
c_4(x1) = [0] x1 + [0]
c_5() = [0]
c_6() = [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: {if^#(true(), x, y) -> c_5()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(if^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
true() = [7]
if^#(x1, x2, x3) = [1] x1 + [0] x2 + [0] x3 + [7]
c_5() = [1]
* Path {7}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_2) = {},
Uargs(if^#) = {}, Uargs(++^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3() = [0]
c_4(x1) = [0] x1 + [0]
c_5() = [0]
c_6() = [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: {if^#(false(), x, y) -> c_6()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(if^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
false() = [7]
if^#(x1, x2, x3) = [1] x1 + [0] x2 + [0] x3 + [7]
c_6() = [1]
3) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
4) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
5) '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 2.43 |
|---|
stdout:
MAYBE
Tool RC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.43 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, ++(nil(), y) -> y
, ++(.(x, y), z) -> .(x, ++(y, z))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
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: merge^#(nil(), y) -> c_0(y)
, 2: merge^#(x, nil()) -> c_1(x)
, 3: merge^#(.(x, y), .(u, v)) ->
c_2(if^#(<(x, u),
.(x, merge(y, .(u, v))),
.(u, merge(.(x, y), v))))
, 4: ++^#(nil(), y) -> c_3(y)
, 5: ++^#(.(x, y), z) -> c_4(x, ++^#(y, z))
, 6: if^#(true(), x, y) -> c_5(x)
, 7: if^#(false(), x, y) -> c_6(x)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ YES(?,O(1)) ]
->{6} [ YES(?,O(1)) ]
->{5} [ YES(?,O(n^2)) ]
|
`->{4} [ YES(?,O(n^2)) ]
->{3} [ NA ]
->{2} [ YES(?,O(1)) ]
->{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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [3 3] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [1 1] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {merge^#(nil(), y) -> c_0(y)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(merge^#) = {}, Uargs(c_0) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [2]
[2]
merge^#(x1, x2) = [2 2] x1 + [7 7] x2 + [7]
[2 2] [7 7] [3]
c_0(x1) = [1 3] x1 + [0]
[1 1] [1]
* Path {2}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [3 3] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [1 1] x1 + [0]
[0 0] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {merge^#(x, nil()) -> c_1(x)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(merge^#) = {}, Uargs(c_1) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [2]
[2]
merge^#(x1, x2) = [7 7] x1 + [2 2] x2 + [7]
[7 7] [2 2] [3]
c_1(x1) = [1 3] x1 + [0]
[1 1] [1]
* Path {3}: NA
------------
The usable rules for this path are:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
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 {5}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [1 1] x1 + [1 2] x2 + [0]
[0 1] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
[3 3] [3 3] [0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(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: {++^#(.(x, y), z) -> c_4(x, ++^#(y, z))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(++^#) = {}, Uargs(c_4) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
.(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [1]
++^#(x1, x2) = [0 1] x1 + [0 0] x2 + [0]
[4 0] [0 0] [0]
c_4(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
* Path {5}->{4}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [3 3] x2 + [0]
[0 0] [0 0] [0]
c_3(x1) = [1 1] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(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^2))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {++^#(nil(), y) -> c_3(y)}
Weak Rules: {++^#(.(x, y), z) -> c_4(x, ++^#(y, z))}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [2]
[2]
.(x1, x2) = [1 7] x1 + [1 2] x2 + [2]
[0 1] [0 1] [4]
++^#(x1, x2) = [2 1] x1 + [0 0] x2 + [0]
[0 2] [0 0] [0]
c_3(x1) = [0 0] x1 + [1]
[0 0] [0]
c_4(x1, x2) = [0 1] x1 + [1 0] x2 + [6]
[0 0] [0 0] [7]
* 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [3 3] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [1 1] x1 + [0]
[0 0] [0]
c_6(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(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {if^#(true(), x, y) -> c_5(x)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(if^#) = {}, Uargs(c_5) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
true() = [2]
[2]
if^#(x1, x2, x3) = [2 2] x1 + [7 7] x2 + [0 0] x3 + [7]
[2 2] [7 7] [0 0] [3]
c_5(x1) = [1 3] x1 + [0]
[1 1] [1]
* Path {7}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
<(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
++(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
true() = [0]
[0]
false() = [0]
[0]
merge^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
if^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [3 3] x3 + [0]
[0 0] [0 0] [0 0] [0]
++^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_5(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [1 1] x1 + [0]
[0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {if^#(false(), x, y) -> c_6(x)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(if^#) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
false() = [2]
[2]
if^#(x1, x2, x3) = [2 2] x1 + [7 7] x2 + [0 0] x3 + [7]
[2 2] [7 7] [0 0] [3]
c_6(x1) = [1 3] x1 + [0]
[1 1] [1]
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: merge^#(nil(), y) -> c_0(y)
, 2: merge^#(x, nil()) -> c_1(x)
, 3: merge^#(.(x, y), .(u, v)) ->
c_2(if^#(<(x, u),
.(x, merge(y, .(u, v))),
.(u, merge(.(x, y), v))))
, 4: ++^#(nil(), y) -> c_3(y)
, 5: ++^#(.(x, y), z) -> c_4(x, ++^#(y, z))
, 6: if^#(true(), x, y) -> c_5(x)
, 7: if^#(false(), x, y) -> c_6(x)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ YES(?,O(1)) ]
->{6} [ YES(?,O(1)) ]
->{5} [ YES(?,O(n^1)) ]
|
`->{4} [ YES(?,O(n^1)) ]
->{3} [ MAYBE ]
->{2} [ YES(?,O(1)) ]
->{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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_0(x1) = [1] x1 + [0]
c_1(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(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: DP runtime-complexity with respect to
Strict Rules: {merge^#(nil(), y) -> c_0(y)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(merge^#) = {}, Uargs(c_0) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [5]
merge^#(x1, x2) = [3] x1 + [7] x2 + [0]
c_0(x1) = [1] x1 + [0]
* Path {2}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [3] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(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: DP runtime-complexity with respect to
Strict Rules: {merge^#(x, nil()) -> c_1(x)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(merge^#) = {}, Uargs(c_1) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [5]
merge^#(x1, x2) = [7] x1 + [3] x2 + [0]
c_1(x1) = [1] x1 + [0]
* Path {3}: MAYBE
---------------
The usable rules for this path are:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ merge^#(.(x, y), .(u, v)) ->
c_2(if^#(<(x, u),
.(x, merge(y, .(u, v))),
.(u, merge(.(x, y), v))))
, merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
Proof Output:
The input cannot be shown compatible
* Path {5}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [1] x1 + [1] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2) = [1] x1 + [1] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(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: {++^#(.(x, y), z) -> c_4(x, ++^#(y, z))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(++^#) = {}, Uargs(c_4) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
.(x1, x2) = [1] x1 + [1] x2 + [4]
++^#(x1, x2) = [2] x1 + [7] x2 + [0]
c_4(x1, x2) = [0] x1 + [1] x2 + [7]
* Path {5}->{4}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
++^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_3(x1) = [1] x1 + [0]
c_4(x1, x2) = [0] x1 + [1] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(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: {++^#(nil(), y) -> c_3(y)}
Weak Rules: {++^#(.(x, y), z) -> c_4(x, ++^#(y, z))}
Proof Output:
The following argument positions are usable:
Uargs(.) = {}, Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
nil() = [2]
.(x1, x2) = [1] x1 + [1] x2 + [2]
++^#(x1, x2) = [2] x1 + [7] x2 + [0]
c_3(x1) = [1] x1 + [1]
c_4(x1, x2) = [0] x1 + [1] x2 + [3]
* 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [3] x3 + [0]
++^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [1] x1 + [0]
c_6(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: DP runtime-complexity with respect to
Strict Rules: {if^#(true(), x, y) -> c_5(x)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(if^#) = {}, Uargs(c_5) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
true() = [5]
if^#(x1, x2, x3) = [3] x1 + [7] x2 + [0] x3 + [0]
c_5(x1) = [1] x1 + [0]
* Path {7}: 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(merge) = {}, Uargs(.) = {}, Uargs(if) = {}, Uargs(<) = {},
Uargs(++) = {}, Uargs(merge^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(if^#) = {},
Uargs(++^#) = {}, Uargs(c_3) = {}, Uargs(c_4) = {},
Uargs(c_5) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
merge(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
<(x1, x2) = [0] x1 + [0] x2 + [0]
++(x1, x2) = [0] x1 + [0] x2 + [0]
true() = [0]
false() = [0]
merge^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
if^#(x1, x2, x3) = [0] x1 + [0] x2 + [3] x3 + [0]
++^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1, x2) = [0] x1 + [0] x2 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [1] x1 + [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: {if^#(false(), x, y) -> c_6(x)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(if^#) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
false() = [5]
if^#(x1, x2, x3) = [3] x1 + [7] x2 + [0] x3 + [0]
c_6(x1) = [1] x1 + [0]
3) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
4) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
5) '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 2.43 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, ++(nil(), y) -> y
, ++(.(x, y), z) -> .(x, ++(y, z))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
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 2.43 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, ++(nil(), y) -> y
, ++(.(x, y), z) -> .(x, ++(y, z))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
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 2.43 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, ++(nil(), y) -> y
, ++(.(x, y), z) -> .(x, ++(y, z))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
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 2.43 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, ++(nil(), y) -> y
, ++(.(x, y), z) -> .(x, ++(y, z))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
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..Tool rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 2.43 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, ++(nil(), y) -> y
, ++(.(x, y), z) -> .(x, ++(y, z))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool tup3irc
| Execution Time | 60.06129ms |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 2.43 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ merge(nil(), y) -> y
, merge(x, nil()) -> x
, merge(.(x, y), .(u, v)) ->
if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
, ++(nil(), y) -> y
, ++(.(x, y), z) -> .(x, ++(y, z))
, if(true(), x, y) -> x
, if(false(), x, y) -> x}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..