Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ 4_0(1) -> 1
, 4_1(1) -> 6
, 3_0(1) -> 1
, 3_1(6) -> 5
, 3_1(10) -> 9
, 2_0(1) -> 1
, 2_1(5) -> 4
, 2_1(9) -> 8
, 2_1(12) -> 11
, 2_1(13) -> 3
, 1_0(1) -> 1
, 1_1(3) -> 2
, 1_1(5) -> 12
, 1_1(6) -> 10
, 0_0(1) -> 1
, 0_1(2) -> 1
, 0_1(8) -> 1
, 0_1(8) -> 7
, 5_0(1) -> 1
, 5_1(4) -> 3
, 5_1(5) -> 13
, 5_1(7) -> 1
, 5_1(11) -> 2}
Hurray, we answered YES(?,O(n^1))Tool CDI
stdout:
TIMEOUT
Statistics:
Number of monomials: 0
Last formula building started for bound 0
Last SAT solving started for bound 0Tool EDA
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following EDA-non-satisfying matrix interpretation:
Interpretation Functions:
4(x1) = [1 0] x1 + [0]
[0 0] [0]
3(x1) = [1 1] x1 + [0]
[0 0] [2]
2(x1) = [1 1] x1 + [0]
[0 0] [0]
1(x1) = [1 0] x1 + [0]
[0 0] [1]
0(x1) = [1 2] x1 + [0]
[0 0] [1]
5(x1) = [1 0] x1 + [1]
[0 0] [1]
Hurray, we answered YES(?,O(n^2))Tool IDA
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following EDA-non-satisfying and IDA(2)-non-satisfying matrix interpretation:
Interpretation Functions:
4(x1) = [1 0] x1 + [0]
[0 0] [2]
3(x1) = [1 2] x1 + [0]
[0 0] [1]
2(x1) = [1 0] x1 + [0]
[0 1] [3]
1(x1) = [1 2] x1 + [0]
[0 1] [0]
0(x1) = [1 0] x1 + [0]
[0 0] [0]
5(x1) = [1 0] x1 + [0]
[0 0] [0]
Hurray, we answered YES(?,O(n^2))Tool TRI
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
4(x1) = [1 0] x1 + [0]
[0 0] [1]
3(x1) = [1 0] x1 + [0]
[0 1] [0]
2(x1) = [1 1] x1 + [0]
[0 0] [0]
1(x1) = [1 0] x1 + [0]
[0 0] [0]
0(x1) = [1 2] x1 + [0]
[0 1] [0]
5(x1) = [1 0] x1 + [0]
[0 0] [2]
Hurray, we answered YES(?,O(n^2))Tool TRI2
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
, 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
, 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
4(x1) = [1 0] x1 + [0]
[0 0] [0]
3(x1) = [1 1] x1 + [0]
[0 0] [0]
2(x1) = [1 0] x1 + [0]
[0 0] [3]
1(x1) = [1 3] x1 + [0]
[0 0] [1]
0(x1) = [1 0] x1 + [0]
[0 0] [0]
5(x1) = [1 1] x1 + [0]
[0 0] [0]
Hurray, we answered YES(?,O(n^1))