Tool CaT
stdout:
MAYBE
Problem:
quot(0(),s(y),s(z)) -> 0()
quot(s(x),s(y),z) -> quot(x,y,z)
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
quot(x,0(),s(z)) -> s(quot(x,plus(z,s(0())),s(z)))
Proof:
OpenTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ quot(0(), s(y), s(z)) -> 0()
, quot(s(x), s(y), z) -> quot(x, y, z)
, plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))
, quot(x, 0(), s(z)) -> s(quot(x, plus(z, s(0())), s(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: quot^#(0(), s(y), s(z)) -> c_0()
, 2: quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, 3: plus^#(0(), y) -> c_2()
, 4: plus^#(s(x), y) -> c_3(plus^#(x, y))
, 5: quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ YES(?,O(n^3)) ]
|
`->{3} [ YES(?,O(n^3)) ]
->{2,5} [ NA ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2,5}: NA
--------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
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 {2,5}->{1}: NA
-------------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(quot) = {}, Uargs(s) = {1}, Uargs(plus) = {},
Uargs(quot^#) = {2}, Uargs(c_1) = {1}, Uargs(plus^#) = {},
Uargs(c_3) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
s(x1) = [1 0 0] x1 + [2]
[0 0 0] [0]
[0 0 0] [0]
plus(x1, x2) = [2 0 0] x1 + [3 3 3] x2 + [2]
[0 0 0] [3 3 3] [0]
[0 0 0] [3 3 3] [0]
quot^#(x1, x2, x3) = [0 0 0] x1 + [3 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 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]
plus^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
* Path {4}: YES(?,O(n^3))
-----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
s(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
plus(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quot^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 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]
plus^#(x1, x2) = [0 0 0] x1 + [3 3 3] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_4(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: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 4 4] x1 + [2]
[0 1 2] [2]
[0 0 1] [2]
plus^#(x1, x2) = [0 1 2] x1 + [0 0 0] x2 + [2]
[2 2 2] [4 4 4] [0]
[2 0 2] [4 4 4] [0]
c_3(x1) = [1 0 0] x1 + [3]
[0 0 0] [6]
[2 0 0] [2]
* Path {4}->{3}: 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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
plus(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quot^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 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]
plus^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_4(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: {plus^#(0(), y) -> c_2()}
Weak Rules: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[2]
[2]
s(x1) = [1 4 0] x1 + [0]
[0 1 3] [2]
[0 0 1] [2]
plus^#(x1, x2) = [0 3 2] x1 + [0 0 0] x2 + [0]
[2 2 2] [4 4 0] [0]
[2 2 2] [4 4 0] [0]
c_2() = [1]
[0]
[0]
c_3(x1) = [1 0 0] x1 + [7]
[0 0 0] [7]
[0 0 0] [7]
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: quot^#(0(), s(y), s(z)) -> c_0()
, 2: quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, 3: plus^#(0(), y) -> c_2()
, 4: plus^#(s(x), y) -> c_3(plus^#(x, y))
, 5: quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ YES(?,O(n^1)) ]
|
`->{3} [ YES(?,O(n^1)) ]
->{2,5} [ MAYBE ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2,5}: MAYBE
-----------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
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 2'
--------------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))
, plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
Proof Output:
The input cannot be shown compatible
* Path {2,5}->{1}: NA
-------------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(quot) = {}, Uargs(s) = {1}, Uargs(plus) = {},
Uargs(quot^#) = {2}, Uargs(c_1) = {1}, Uargs(plus^#) = {},
Uargs(c_3) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
0() = [0]
[0]
s(x1) = [1 0] x1 + [2]
[0 0] [0]
plus(x1, x2) = [2 0] x1 + [3 3] x2 + [2]
[0 0] [3 3] [0]
quot^#(x1, x2, x3) = [0 0] x1 + [3 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [1 0] x1 + [0]
[0 1] [0]
plus^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [1 0] x1 + [0]
[0 1] [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
* Path {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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
plus(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quot^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
plus^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
[3 3] [3 3] [0]
c_2() = [0]
[0]
c_3(x1) = [1 0] x1 + [0]
[0 1] [0]
c_4(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: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 0] x1 + [0]
[0 1] [2]
plus^#(x1, x2) = [0 1] x1 + [0 0] x2 + [0]
[4 5] [4 4] [0]
c_3(x1) = [1 0] x1 + [1]
[0 0] [7]
* Path {4}->{3}: 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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
plus(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quot^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
plus^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1) = [1 0] x1 + [0]
[0 1] [0]
c_4(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: {plus^#(0(), y) -> c_2()}
Weak Rules: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[0]
s(x1) = [1 3] x1 + [2]
[0 0] [2]
plus^#(x1, x2) = [3 0] x1 + [0 0] x2 + [4]
[2 2] [0 4] [0]
c_2() = [1]
[0]
c_3(x1) = [1 0] x1 + [3]
[0 0] [7]
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: quot^#(0(), s(y), s(z)) -> c_0()
, 2: quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, 3: plus^#(0(), y) -> c_2()
, 4: plus^#(s(x), y) -> c_3(plus^#(x, y))
, 5: quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ YES(?,O(n^1)) ]
|
`->{3} [ YES(?,O(n^1)) ]
->{2,5} [ MAYBE ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2,5}: MAYBE
-----------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
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:
{ quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))
, plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
Proof Output:
The input cannot be shown compatible
* Path {2,5}->{1}: NA
-------------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(quot) = {}, Uargs(s) = {1}, Uargs(plus) = {},
Uargs(quot^#) = {2}, Uargs(c_1) = {1}, Uargs(plus^#) = {},
Uargs(c_3) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
0() = [3]
s(x1) = [1] x1 + [1]
plus(x1, x2) = [2] x1 + [3] x2 + [0]
quot^#(x1, x2, x3) = [0] x1 + [3] x2 + [0] x3 + [0]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
plus^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [1] x1 + [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
* Path {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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
plus(x1, x2) = [0] x1 + [0] x2 + [0]
quot^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
plus^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_2() = [0]
c_3(x1) = [1] x1 + [0]
c_4(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: innermost DP runtime-complexity with respect to
Strict Rules: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1] x1 + [4]
plus^#(x1, x2) = [2] x1 + [7] x2 + [0]
c_3(x1) = [1] x1 + [7]
* Path {4}->{3}: 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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
plus(x1, x2) = [0] x1 + [0] x2 + [0]
quot^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
plus^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1) = [1] x1 + [0]
c_4(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: innermost DP runtime-complexity with respect to
Strict Rules: {plus^#(0(), y) -> c_2()}
Weak Rules: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
s(x1) = [1] x1 + [2]
plus^#(x1, x2) = [2] x1 + [7] x2 + [4]
c_2() = [1]
c_3(x1) = [1] x1 + [4]
4) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
Tool RC1
stdout:
MAYBE
Tool RC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ quot(0(), s(y), s(z)) -> 0()
, quot(s(x), s(y), z) -> quot(x, y, z)
, plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))
, quot(x, 0(), s(z)) -> s(quot(x, plus(z, s(0())), s(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: quot^#(0(), s(y), s(z)) -> c_0()
, 2: quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, 3: plus^#(0(), y) -> c_2(y)
, 4: plus^#(s(x), y) -> c_3(plus^#(x, y))
, 5: quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ YES(?,O(n^3)) ]
|
`->{3} [ YES(?,O(n^2)) ]
->{2,5} [ NA ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2,5}: NA
--------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
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 {2,5}->{1}: NA
-------------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(quot) = {}, Uargs(s) = {1}, Uargs(plus) = {},
Uargs(quot^#) = {2}, Uargs(c_1) = {1}, Uargs(plus^#) = {},
Uargs(c_2) = {}, Uargs(c_3) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
s(x1) = [1 0 0] x1 + [2]
[0 0 0] [0]
[0 0 0] [0]
plus(x1, x2) = [2 0 0] x1 + [3 3 3] x2 + [2]
[0 0 0] [3 3 3] [0]
[0 0 0] [3 3 3] [0]
quot^#(x1, x2, x3) = [0 0 0] x1 + [3 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 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]
plus^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
* Path {4}: YES(?,O(n^3))
-----------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_2) = {}, Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
s(x1) = [1 3 0] x1 + [0]
[0 1 0] [0]
[0 0 0] [0]
plus(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quot^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 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]
plus^#(x1, x2) = [0 0 0] x1 + [3 3 3] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_2(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_3(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_4(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: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 4 4] x1 + [2]
[0 1 2] [2]
[0 0 1] [2]
plus^#(x1, x2) = [0 1 2] x1 + [0 0 0] x2 + [2]
[2 2 2] [4 4 4] [0]
[2 0 2] [4 4 4] [0]
c_3(x1) = [1 0 0] x1 + [3]
[0 0 0] [6]
[2 0 0] [2]
* Path {4}->{3}: 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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_2) = {}, Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
plus(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
quot^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 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]
plus^#(x1, x2) = [0 0 0] x1 + [3 3 3] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_2(x1) = [1 1 1] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_3(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_4(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: {plus^#(0(), y) -> c_2(y)}
Weak Rules: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_2) = {},
Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[0]
[0]
s(x1) = [1 2 3] x1 + [0]
[0 0 3] [2]
[0 0 1] [2]
plus^#(x1, x2) = [2 2 2] x1 + [0 0 0] x2 + [2]
[0 2 2] [0 0 0] [0]
[4 0 0] [4 0 4] [4]
c_2(x1) = [0 0 0] x1 + [1]
[0 0 0] [0]
[0 0 0] [0]
c_3(x1) = [1 0 0] x1 + [5]
[0 0 0] [7]
[2 2 0] [0]
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: quot^#(0(), s(y), s(z)) -> c_0()
, 2: quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, 3: plus^#(0(), y) -> c_2(y)
, 4: plus^#(s(x), y) -> c_3(plus^#(x, y))
, 5: quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ YES(?,O(n^1)) ]
|
`->{3} [ YES(?,O(n^1)) ]
->{2,5} [ MAYBE ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2,5}: MAYBE
-----------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
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 2'
--------------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))
, plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
Proof Output:
The input cannot be shown compatible
* Path {2,5}->{1}: NA
-------------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(quot) = {}, Uargs(s) = {1}, Uargs(plus) = {},
Uargs(quot^#) = {2}, Uargs(c_1) = {1}, Uargs(plus^#) = {},
Uargs(c_2) = {}, Uargs(c_3) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
0() = [0]
[0]
s(x1) = [1 0] x1 + [2]
[0 0] [0]
plus(x1, x2) = [2 0] x1 + [3 3] x2 + [2]
[0 0] [3 3] [0]
quot^#(x1, x2, x3) = [0 0] x1 + [3 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [1 0] x1 + [0]
[0 1] [0]
plus^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [1 0] x1 + [0]
[0 1] [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
* Path {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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_2) = {}, Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
0() = [0]
[0]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
plus(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quot^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
plus^#(x1, x2) = [3 3] x1 + [3 3] x2 + [0]
[3 3] [3 3] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
c_3(x1) = [1 0] x1 + [0]
[0 1] [0]
c_4(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: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1 0] x1 + [0]
[0 1] [2]
plus^#(x1, x2) = [0 1] x1 + [0 0] x2 + [0]
[4 5] [4 4] [0]
c_3(x1) = [1 0] x1 + [1]
[0 0] [7]
* Path {4}->{3}: 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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_2) = {}, Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
plus(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
quot^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
plus^#(x1, x2) = [0 0] x1 + [3 3] x2 + [0]
[0 0] [0 0] [0]
c_2(x1) = [1 1] x1 + [0]
[0 0] [0]
c_3(x1) = [1 0] x1 + [0]
[0 1] [0]
c_4(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: {plus^#(0(), y) -> c_2(y)}
Weak Rules: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_2) = {},
Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[2]
s(x1) = [1 0] x1 + [2]
[0 0] [0]
plus^#(x1, x2) = [2 0] x1 + [0 0] x2 + [4]
[2 2] [4 4] [0]
c_2(x1) = [0 0] x1 + [1]
[0 0] [0]
c_3(x1) = [1 0] x1 + [3]
[0 0] [4]
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: quot^#(0(), s(y), s(z)) -> c_0()
, 2: quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, 3: plus^#(0(), y) -> c_2(y)
, 4: plus^#(s(x), y) -> c_3(plus^#(x, y))
, 5: quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ YES(?,O(n^1)) ]
|
`->{3} [ YES(?,O(n^1)) ]
->{2,5} [ MAYBE ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2,5}: MAYBE
-----------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
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:
{ quot^#(s(x), s(y), z) -> c_1(quot^#(x, y, z))
, quot^#(x, 0(), s(z)) -> c_4(quot^#(x, plus(z, s(0())), s(z)))
, plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
Proof Output:
The input cannot be shown compatible
* Path {2,5}->{1}: NA
-------------------
The usable rules for this path are:
{ plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(quot) = {}, Uargs(s) = {1}, Uargs(plus) = {},
Uargs(quot^#) = {2}, Uargs(c_1) = {1}, Uargs(plus^#) = {},
Uargs(c_2) = {}, Uargs(c_3) = {}, Uargs(c_4) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
0() = [3]
s(x1) = [1] x1 + [1]
plus(x1, x2) = [2] x1 + [3] x2 + [0]
quot^#(x1, x2, x3) = [0] x1 + [3] x2 + [0] x3 + [0]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
plus^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [1] x1 + [0]
Complexity induced by the adequate RMI: YES(?,O(n^1))
We have not generated a proof for the resulting sub-problem.
* Path {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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_2) = {}, Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
plus(x1, x2) = [0] x1 + [0] x2 + [0]
quot^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
plus^#(x1, x2) = [3] x1 + [3] x2 + [0]
c_2(x1) = [0] x1 + [0]
c_3(x1) = [1] x1 + [0]
c_4(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: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
s(x1) = [1] x1 + [4]
plus^#(x1, x2) = [2] x1 + [7] x2 + [0]
c_3(x1) = [1] x1 + [7]
* Path {4}->{3}: 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(quot) = {}, Uargs(s) = {}, Uargs(plus) = {},
Uargs(quot^#) = {}, Uargs(c_1) = {}, Uargs(plus^#) = {},
Uargs(c_2) = {}, Uargs(c_3) = {1}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
quot(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
plus(x1, x2) = [0] x1 + [0] x2 + [0]
quot^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
plus^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [1] x1 + [0]
c_4(x1) = [0] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
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Answer: YES(?,O(n^1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {plus^#(0(), y) -> c_2(y)}
Weak Rules: {plus^#(s(x), y) -> c_3(plus^#(x, y))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(plus^#) = {}, Uargs(c_2) = {},
Uargs(c_3) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
s(x1) = [1] x1 + [2]
plus^#(x1, x2) = [3] x1 + [7] x2 + [2]
c_2(x1) = [1] x1 + [1]
c_3(x1) = [1] x1 + [5]
4) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.