Tool Bounds
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 0(q2(x1)) -> 0(q0(x1))
, 1(q2(x1)) -> q2(1(x1))
, 0(q1(x1)) -> q2(1(x1))
, 1(q1(0(x1))) -> 1(0(q1(x1)))
, 1(q1(1(x1))) -> 1(1(q1(x1)))
, 1(q0(0(x1))) -> 0(0(q1(x1)))
, 1(q0(1(x1))) -> 0(1(q1(x1)))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool CDI
stdout:
YES(?,O(n^2))
QUADRATIC upper bound on the derivational complexity
This TRS is terminating using the deltarestricted interpretation
q2(delta, X0) = + 1*X0 + 2 + 0*X0*delta + 1*delta
q0(delta, X0) = + 1*X0 + 2 + 0*X0*delta + 0*delta
q1(delta, X0) = + 1*X0 + 0 + 1*X0*delta + 0*delta
1(delta, X0) = + 1*X0 + 1 + 1*X0*delta + 0*delta
0(delta, X0) = + 1*X0 + 3 + 0*X0*delta + 2*delta
q2_tau_1(delta) = delta/(1 + 0 * delta)
q0_tau_1(delta) = delta/(1 + 0 * delta)
q1_tau_1(delta) = delta/(1 + 1 * delta)
1_tau_1(delta) = delta/(1 + 1 * delta)
0_tau_1(delta) = delta/(1 + 0 * delta)
Time: 14.069277 seconds
Statistics:
Number of monomials: 1339
Last formula building started for bound 3
Last SAT solving started for bound 3Tool EDA
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ 0(q2(x1)) -> 0(q0(x1))
, 1(q2(x1)) -> q2(1(x1))
, 0(q1(x1)) -> q2(1(x1))
, 1(q1(0(x1))) -> 1(0(q1(x1)))
, 1(q1(1(x1))) -> 1(1(q1(x1)))
, 1(q0(0(x1))) -> 0(0(q1(x1)))
, 1(q0(1(x1))) -> 0(1(q1(x1)))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following EDA-non-satisfying matrix interpretation:
Interpretation Functions:
1(x1) = [1 2] x1 + [0]
[0 1] [2]
q0(x1) = [1 0] x1 + [0]
[0 1] [1]
q1(x1) = [1 2] x1 + [0]
[0 1] [0]
0(x1) = [1 0] x1 + [2]
[0 1] [3]
q2(x1) = [1 0] x1 + [1]
[0 1] [1]
Hurray, we answered YES(?,O(n^2))Tool IDA
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ 0(q2(x1)) -> 0(q0(x1))
, 1(q2(x1)) -> q2(1(x1))
, 0(q1(x1)) -> q2(1(x1))
, 1(q1(0(x1))) -> 1(0(q1(x1)))
, 1(q1(1(x1))) -> 1(1(q1(x1)))
, 1(q0(0(x1))) -> 0(0(q1(x1)))
, 1(q0(1(x1))) -> 0(1(q1(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:
1(x1) = [1 2] x1 + [0]
[0 1] [2]
q0(x1) = [1 0] x1 + [0]
[0 1] [1]
q1(x1) = [1 1] x1 + [2]
[0 1] [0]
0(x1) = [1 1] x1 + [0]
[0 1] [3]
q2(x1) = [1 0] x1 + [1]
[0 1] [1]
Hurray, we answered YES(?,O(n^2))Tool TRI
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ 0(q2(x1)) -> 0(q0(x1))
, 1(q2(x1)) -> q2(1(x1))
, 0(q1(x1)) -> q2(1(x1))
, 1(q1(0(x1))) -> 1(0(q1(x1)))
, 1(q1(1(x1))) -> 1(1(q1(x1)))
, 1(q0(0(x1))) -> 0(0(q1(x1)))
, 1(q0(1(x1))) -> 0(1(q1(x1)))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
1(x1) = [1 2] x1 + [0]
[0 1] [1]
q0(x1) = [1 0] x1 + [0]
[0 1] [1]
q1(x1) = [1 2] x1 + [2]
[0 1] [0]
0(x1) = [1 0] x1 + [0]
[0 1] [2]
q2(x1) = [1 0] x1 + [1]
[0 1] [1]
Hurray, we answered YES(?,O(n^2))Tool TRI2
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ 0(q2(x1)) -> 0(q0(x1))
, 1(q2(x1)) -> q2(1(x1))
, 0(q1(x1)) -> q2(1(x1))
, 1(q1(0(x1))) -> 1(0(q1(x1)))
, 1(q1(1(x1))) -> 1(1(q1(x1)))
, 1(q0(0(x1))) -> 0(0(q1(x1)))
, 1(q0(1(x1))) -> 0(1(q1(x1)))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
1(x1) = [1 3] x1 + [0]
[0 1] [2]
q0(x1) = [1 0] x1 + [0]
[0 1] [1]
q1(x1) = [1 3] x1 + [2]
[0 1] [1]
0(x1) = [1 0] x1 + [0]
[0 1] [2]
q2(x1) = [1 0] x1 + [1]
[0 1] [1]
Hurray, we answered YES(?,O(n^2))