Tool Bounds
| Execution Time | 6.715584e-2ms |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.49 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(c(x)) -> b(x)
, w(a(c(x))) -> u(b(d(x)))
, w(a(a(x))) -> u(w(x))
, v(c(x)) -> b(x)
, v(a(c(x))) -> u(b(d(x)))
, v(a(a(x))) -> u(v(x))
, u(b(d(d(x)))) -> b(x)
, a(c(d(x))) -> c(x)}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ d_0(1) -> 1
, d_0(2) -> 1
, d_0(3) -> 1
, d_0(4) -> 1
, d_0(5) -> 1
, d_0(6) -> 1
, d_0(7) -> 1
, d_1(1) -> 9
, d_1(2) -> 9
, d_1(3) -> 9
, d_1(4) -> 9
, d_1(5) -> 9
, d_1(6) -> 9
, d_1(7) -> 9
, c_0(1) -> 2
, c_0(2) -> 2
, c_0(3) -> 2
, c_0(4) -> 2
, c_0(5) -> 2
, c_0(6) -> 2
, c_0(7) -> 2
, c_1(1) -> 3
, c_1(2) -> 3
, c_1(3) -> 3
, c_1(4) -> 3
, c_1(5) -> 3
, c_1(6) -> 3
, c_1(7) -> 3
, a_0(1) -> 3
, a_0(2) -> 3
, a_0(3) -> 3
, a_0(4) -> 3
, a_0(5) -> 3
, a_0(6) -> 3
, a_0(7) -> 3
, b_0(1) -> 4
, b_0(2) -> 4
, b_0(3) -> 4
, b_0(4) -> 4
, b_0(5) -> 4
, b_0(6) -> 4
, b_0(7) -> 4
, b_1(1) -> 5
, b_1(1) -> 6
, b_1(1) -> 7
, b_1(1) -> 8
, b_1(2) -> 5
, b_1(2) -> 6
, b_1(2) -> 7
, b_1(2) -> 8
, b_1(3) -> 5
, b_1(3) -> 6
, b_1(3) -> 7
, b_1(3) -> 8
, b_1(4) -> 5
, b_1(4) -> 6
, b_1(4) -> 7
, b_1(4) -> 8
, b_1(5) -> 5
, b_1(5) -> 6
, b_1(5) -> 7
, b_1(5) -> 8
, b_1(6) -> 5
, b_1(6) -> 6
, b_1(6) -> 7
, b_1(6) -> 8
, b_1(7) -> 5
, b_1(7) -> 6
, b_1(7) -> 7
, b_1(7) -> 8
, b_1(9) -> 8
, b_2(1) -> 8
, b_2(2) -> 8
, b_2(3) -> 8
, b_2(4) -> 8
, b_2(5) -> 8
, b_2(6) -> 8
, b_2(7) -> 8
, u_0(1) -> 5
, u_0(2) -> 5
, u_0(3) -> 5
, u_0(4) -> 5
, u_0(5) -> 5
, u_0(6) -> 5
, u_0(7) -> 5
, u_1(8) -> 6
, u_1(8) -> 7
, u_1(8) -> 8
, v_0(1) -> 6
, v_0(2) -> 6
, v_0(3) -> 6
, v_0(4) -> 6
, v_0(5) -> 6
, v_0(6) -> 6
, v_0(7) -> 6
, v_1(1) -> 8
, v_1(2) -> 8
, v_1(3) -> 8
, v_1(4) -> 8
, v_1(5) -> 8
, v_1(6) -> 8
, v_1(7) -> 8
, w_0(1) -> 7
, w_0(2) -> 7
, w_0(3) -> 7
, w_0(4) -> 7
, w_0(5) -> 7
, w_0(6) -> 7
, w_0(7) -> 7
, w_1(1) -> 8
, w_1(2) -> 8
, w_1(3) -> 8
, w_1(4) -> 8
, w_1(5) -> 8
, w_1(6) -> 8
, w_1(7) -> 8}
Hurray, we answered YES(?,O(n^1))Tool CDI
| Execution Time | 13.276927ms |
|---|
| Answer | YES(?,O(n^2)) |
|---|
| Input | SK90 2.49 |
|---|
stdout:
YES(?,O(n^2))
QUADRATIC upper bound on the derivational complexity
This TRS is terminating using the deltarestricted interpretation
w(delta, X0) = + 1*X0 + 0 + 2*X0*delta + 0*delta
v(delta, X0) = + 1*X0 + 0 + 2*X0*delta + 0*delta
u(delta, X0) = + 1*X0 + 0 + 0*X0*delta + 0*delta
b(delta, X0) = + 1*X0 + 0 + 2*X0*delta + 0*delta
d(delta, X0) = + 1*X0 + 0 + 0*X0*delta + 2*delta
a(delta, X0) = + 1*X0 + 2 + 0*X0*delta + 0*delta
c(delta, X0) = + 1*X0 + 2 + 0*X0*delta + 0*delta
w_tau_1(delta) = delta/(1 + 2 * delta)
v_tau_1(delta) = delta/(1 + 2 * delta)
u_tau_1(delta) = delta/(1 + 0 * delta)
b_tau_1(delta) = delta/(1 + 2 * delta)
d_tau_1(delta) = delta/(1 + 0 * delta)
a_tau_1(delta) = delta/(1 + 0 * delta)
c_tau_1(delta) = delta/(1 + 0 * delta)
Time: 13.237700 seconds
Statistics:
Number of monomials: 1747
Last formula building started for bound 3
Last SAT solving started for bound 3Tool EDA
| Execution Time | 0.11839414ms |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.49 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(c(x)) -> b(x)
, w(a(c(x))) -> u(b(d(x)))
, w(a(a(x))) -> u(w(x))
, v(c(x)) -> b(x)
, v(a(c(x))) -> u(b(d(x)))
, v(a(a(x))) -> u(v(x))
, u(b(d(d(x)))) -> b(x)
, a(c(d(x))) -> c(x)}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
We have the following EDA-non-satisfying matrix interpretation:
Interpretation Functions:
d(x1) = [1] x1 + [1]
c(x1) = [1] x1 + [0]
a(x1) = [1] x1 + [3]
b(x1) = [1] x1 + [0]
u(x1) = [1] x1 + [0]
v(x1) = [1] x1 + [1]
w(x1) = [1] x1 + [1]
Hurray, we answered YES(?,O(n^1))Tool IDA
| Execution Time | 0.41465712ms |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.49 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(c(x)) -> b(x)
, w(a(c(x))) -> u(b(d(x)))
, w(a(a(x))) -> u(w(x))
, v(c(x)) -> b(x)
, v(a(c(x))) -> u(b(d(x)))
, v(a(a(x))) -> u(v(x))
, u(b(d(d(x)))) -> b(x)
, a(c(d(x))) -> c(x)}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
d(x1) = [1] x1 + [1]
c(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [3]
b(x1) = [1] x1 + [0]
u(x1) = [1] x1 + [0]
v(x1) = [1] x1 + [0]
w(x1) = [1] x1 + [0]
Hurray, we answered YES(?,O(n^1))Tool TRI
| Execution Time | 0.11403608ms |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.49 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(c(x)) -> b(x)
, w(a(c(x))) -> u(b(d(x)))
, w(a(a(x))) -> u(w(x))
, v(c(x)) -> b(x)
, v(a(c(x))) -> u(b(d(x)))
, v(a(a(x))) -> u(v(x))
, u(b(d(d(x)))) -> b(x)
, a(c(d(x))) -> c(x)}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
d(x1) = [1] x1 + [1]
c(x1) = [1] x1 + [0]
a(x1) = [1] x1 + [3]
b(x1) = [1] x1 + [0]
u(x1) = [1] x1 + [0]
v(x1) = [1] x1 + [2]
w(x1) = [1] x1 + [1]
Hurray, we answered YES(?,O(n^1))Tool TRI2
| Execution Time | 0.30385804ms |
|---|
| Answer | YES(?,O(n^2)) |
|---|
| Input | SK90 2.49 |
|---|
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ w(c(x)) -> b(x)
, w(a(c(x))) -> u(b(d(x)))
, w(a(a(x))) -> u(w(x))
, v(c(x)) -> b(x)
, v(a(c(x))) -> u(b(d(x)))
, v(a(a(x))) -> u(v(x))
, u(b(d(d(x)))) -> b(x)
, a(c(d(x))) -> c(x)}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
d(x1) = [1 0] x1 + [2]
[0 0] [0]
c(x1) = [1 0] x1 + [1]
[0 0] [2]
a(x1) = [1 2] x1 + [0]
[0 1] [2]
b(x1) = [1 0] x1 + [0]
[0 0] [0]
u(x1) = [1 0] x1 + [0]
[0 0] [0]
v(x1) = [1 1] x1 + [0]
[0 0] [0]
w(x1) = [1 0] x1 + [0]
[0 0] [0]
Hurray, we answered YES(?,O(n^2))