Tool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(X, g(X), Y) -> f(Y, Y, Y)
, g(b()) -> c()
, b() -> c()}
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: f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))
, 2: g^#(b()) -> c_1()
, 3: b^#() -> c_2()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ YES(?,O(1)) ]
->{2} [ YES(?,O(1)) ]
->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(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]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
b() = [0]
[0]
[0]
c() = [0]
[0]
[0]
f^#(x1, x2, x3) = [1 1 1] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[3 3 3] [3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [3 3 3] [0]
c_0(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
g^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
b^#() = [0]
[0]
[0]
c_2() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(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]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
b() = [0]
[0]
[0]
c() = [0]
[0]
[0]
f^#(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(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
g^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
b^#() = [0]
[0]
[0]
c_2() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {g^#(b()) -> c_1()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b() = [2]
[2]
[2]
g^#(x1) = [0 2 0] x1 + [7]
[2 2 0] [3]
[2 2 2] [3]
c_1() = [0]
[1]
[1]
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(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]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
b() = [0]
[0]
[0]
c() = [0]
[0]
[0]
f^#(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(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
g^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
b^#() = [0]
[0]
[0]
c_2() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {b^#() -> c_2()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b^#() = [7]
[7]
[7]
c_2() = [0]
[3]
[3]
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))
, 2: g^#(b()) -> c_1()
, 3: b^#() -> c_2()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ YES(?,O(1)) ]
->{2} [ YES(?,O(1)) ]
->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
b() = [0]
[0]
c() = [0]
[0]
f^#(x1, x2, x3) = [1 1] x1 + [0 0] x2 + [0 0] x3 + [0]
[3 3] [3 3] [3 3] [0]
c_0(x1) = [1 0] x1 + [0]
[0 1] [0]
g^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
b^#() = [0]
[0]
c_2() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
b() = [0]
[0]
c() = [0]
[0]
f^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
g^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
b^#() = [0]
[0]
c_2() = [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: {g^#(b()) -> c_1()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b() = [2]
[2]
g^#(x1) = [2 0] x1 + [7]
[2 2] [7]
c_1() = [0]
[1]
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
b() = [0]
[0]
c() = [0]
[0]
f^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
g^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
b^#() = [0]
[0]
c_2() = [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: {b^#() -> c_2()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b^#() = [7]
[7]
c_2() = [0]
[1]
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))
, 2: g^#(b()) -> c_1()
, 3: b^#() -> c_2()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ YES(?,O(1)) ]
->{2} [ YES(?,O(1)) ]
->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
g(x1) = [0] x1 + [0]
b() = [0]
c() = [0]
f^#(x1, x2, x3) = [1] x1 + [0] x2 + [0] x3 + [0]
c_0(x1) = [1] x1 + [0]
g^#(x1) = [0] x1 + [0]
c_1() = [0]
b^#() = [0]
c_2() = [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: {f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
g(x1) = [0] x1 + [0]
b() = [0]
c() = [0]
f^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
c_0(x1) = [0] x1 + [0]
g^#(x1) = [0] x1 + [0]
c_1() = [0]
b^#() = [0]
c_2() = [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: {g^#(b()) -> c_1()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b() = [7]
g^#(x1) = [1] x1 + [7]
c_1() = [1]
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
g(x1) = [0] x1 + [0]
b() = [0]
c() = [0]
f^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
c_0(x1) = [0] x1 + [0]
g^#(x1) = [0] x1 + [0]
c_1() = [0]
b^#() = [0]
c_2() = [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: {b^#() -> c_2()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b^#() = [7]
c_2() = [0]
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:
{ f(X, g(X), Y) -> f(Y, Y, Y)
, g(b()) -> c()
, b() -> c()}
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: f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))
, 2: g^#(b()) -> c_1()
, 3: b^#() -> c_2()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ YES(?,O(1)) ]
->{2} [ YES(?,O(1)) ]
->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(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]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
b() = [0]
[0]
[0]
c() = [0]
[0]
[0]
f^#(x1, x2, x3) = [1 1 1] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[3 3 3] [3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [3 3 3] [0]
c_0(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
g^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
b^#() = [0]
[0]
[0]
c_2() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules: {f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(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]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
b() = [0]
[0]
[0]
c() = [0]
[0]
[0]
f^#(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(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
g^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
b^#() = [0]
[0]
[0]
c_2() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {g^#(b()) -> c_1()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b() = [2]
[2]
[2]
g^#(x1) = [0 2 0] x1 + [7]
[2 2 0] [3]
[2 2 2] [3]
c_1() = [0]
[1]
[1]
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(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]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
b() = [0]
[0]
[0]
c() = [0]
[0]
[0]
f^#(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(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
g^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1() = [0]
[0]
[0]
b^#() = [0]
[0]
[0]
c_2() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {b^#() -> c_2()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b^#() = [7]
[7]
[7]
c_2() = [0]
[3]
[3]
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))
, 2: g^#(b()) -> c_1()
, 3: b^#() -> c_2()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ YES(?,O(1)) ]
->{2} [ YES(?,O(1)) ]
->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
b() = [0]
[0]
c() = [0]
[0]
f^#(x1, x2, x3) = [1 1] x1 + [0 0] x2 + [0 0] x3 + [0]
[3 3] [3 3] [3 3] [0]
c_0(x1) = [1 0] x1 + [0]
[0 1] [0]
g^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
b^#() = [0]
[0]
c_2() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules: {f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
b() = [0]
[0]
c() = [0]
[0]
f^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
g^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
b^#() = [0]
[0]
c_2() = [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: {g^#(b()) -> c_1()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b() = [2]
[2]
g^#(x1) = [2 0] x1 + [7]
[2 2] [7]
c_1() = [0]
[1]
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
b() = [0]
[0]
c() = [0]
[0]
f^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
g^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1() = [0]
[0]
b^#() = [0]
[0]
c_2() = [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: {b^#() -> c_2()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b^#() = [7]
[7]
c_2() = [0]
[1]
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))
, 2: g^#(b()) -> c_1()
, 3: b^#() -> c_2()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ YES(?,O(1)) ]
->{2} [ YES(?,O(1)) ]
->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
g(x1) = [0] x1 + [0]
b() = [0]
c() = [0]
f^#(x1, x2, x3) = [1] x1 + [0] x2 + [0] x3 + [0]
c_0(x1) = [1] x1 + [0]
g^#(x1) = [0] x1 + [0]
c_1() = [0]
b^#() = [0]
c_2() = [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: {f^#(X, g(X), Y) -> c_0(f^#(Y, Y, Y))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
g(x1) = [0] x1 + [0]
b() = [0]
c() = [0]
f^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
c_0(x1) = [0] x1 + [0]
g^#(x1) = [0] x1 + [0]
c_1() = [0]
b^#() = [0]
c_2() = [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: {g^#(b()) -> c_1()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b() = [7]
g^#(x1) = [1] x1 + [7]
c_1() = [1]
* 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(f) = {}, Uargs(g) = {}, Uargs(f^#) = {}, Uargs(c_0) = {},
Uargs(g^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
g(x1) = [0] x1 + [0]
b() = [0]
c() = [0]
f^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
c_0(x1) = [0] x1 + [0]
g^#(x1) = [0] x1 + [0]
c_1() = [0]
b^#() = [0]
c_2() = [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: {b^#() -> c_2()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
b^#() = [7]
c_2() = [0]
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.