Tool Bounds
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ c(c(c(x1))) -> b(x1)
, a(x1) -> c(b(x1))
, b(b(x1)) -> a(c(x1))
, b(c(x1)) -> a(x1)}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool CDI
stdout:
MAYBE
Statistics:
Number of monomials: 191
Last formula building started for bound 3
Last SAT solving started for bound 3Tool EDA
stdout:
YES(?,O(n^5))
We consider the following Problem:
Strict Trs:
{ c(c(c(x1))) -> b(x1)
, a(x1) -> c(b(x1))
, b(b(x1)) -> a(c(x1))
, b(c(x1)) -> a(x1)}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^5))
Proof:
We have the following EDA-non-satisfying matrix interpretation:
Interpretation Functions:
c(x1) = [1 0 0 1 0] x1 + [0]
[0 1 0 0 1] [0]
[0 0 0 0 0] [2]
[0 1 0 0 1] [1]
[0 0 1 0 0] [0]
b(x1) = [1 2 1 1 2] x1 + [1]
[0 1 1 0 1] [0]
[0 0 0 0 0] [2]
[0 1 1 0 1] [1]
[0 0 0 0 0] [2]
a(x1) = [1 3 2 1 3] x1 + [3]
[0 1 1 0 1] [2]
[0 0 0 0 0] [2]
[0 1 1 0 1] [3]
[0 0 0 0 0] [2]
Hurray, we answered YES(?,O(n^5))Tool IDA
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ c(c(c(x1))) -> b(x1)
, a(x1) -> c(b(x1))
, b(b(x1)) -> a(c(x1))
, b(c(x1)) -> a(x1)}
StartTerms: all
Strategy: none
Certificate: MAYBE
Proof:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'matrix-interpretation of dimension 4' failed due to the following reason:
The input cannot be shown compatible
2) 'matrix-interpretation of dimension 4' failed due to the following reason:
The input cannot be shown compatible
3) 'matrix-interpretation of dimension 4' failed due to the following reason:
The input cannot be shown compatible
4) 'matrix-interpretation of dimension 4' failed due to the following reason:
The input cannot be shown compatible
5) 'matrix-interpretation of dimension 3' failed due to the following reason:
The input cannot be shown compatible
6) 'matrix-interpretation of dimension 3' failed due to the following reason:
The input cannot be shown compatible
7) 'matrix-interpretation of dimension 3' failed due to the following reason:
The input cannot be shown compatible
8) 'matrix-interpretation of dimension 2' failed due to the following reason:
The input cannot be shown compatible
9) 'matrix-interpretation of dimension 2' failed due to the following reason:
The input cannot be shown compatible
10) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
Arrrr..Tool TRI
stdout:
YES(?,O(n^3))
We consider the following Problem:
Strict Trs:
{ c(c(c(x1))) -> b(x1)
, a(x1) -> c(b(x1))
, b(b(x1)) -> a(c(x1))
, b(c(x1)) -> a(x1)}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^3))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
c(x1) = [1 1 0 0 0] x1 + [0]
[0 0 1 1 0] [0]
[0 0 1 0 0] [1]
[0 0 0 1 1] [0]
[0 0 0 0 0] [1]
b(x1) = [1 1 2 2 1] x1 + [0]
[0 0 1 1 1] [1]
[0 0 1 0 0] [2]
[0 0 0 1 1] [1]
[0 0 0 0 0] [1]
a(x1) = [1 1 3 3 2] x1 + [2]
[0 0 1 1 1] [3]
[0 0 1 0 0] [3]
[0 0 0 1 1] [2]
[0 0 0 0 0] [1]
Hurray, we answered YES(?,O(n^3))Tool TRI2
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ c(c(c(x1))) -> b(x1)
, a(x1) -> c(b(x1))
, b(b(x1)) -> a(c(x1))
, b(c(x1)) -> a(x1)}
StartTerms: all
Strategy: none
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..