Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(c(s(X), Y)) -> f(c(X, s(Y)))
, f(c(X, s(Y))) -> f(c(s(X), Y))}
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:
{ s_0(1) -> 1
, s_0(2) -> 1
, s_0(3) -> 1
, s_0(4) -> 1
, s_1(1) -> 6
, s_1(2) -> 6
, s_1(3) -> 6
, s_1(4) -> 6
, s_1(6) -> 6
, s_1(9) -> 10
, s_1(10) -> 10
, s_2(1) -> 9
, s_2(2) -> 9
, s_2(3) -> 9
, s_2(4) -> 9
, s_2(9) -> 9
, c_0(1, 1) -> 2
, c_0(1, 2) -> 2
, c_0(1, 3) -> 2
, c_0(1, 4) -> 2
, c_0(2, 1) -> 2
, c_0(2, 2) -> 2
, c_0(2, 3) -> 2
, c_0(2, 4) -> 2
, c_0(3, 1) -> 2
, c_0(3, 2) -> 2
, c_0(3, 3) -> 2
, c_0(3, 4) -> 2
, c_0(4, 1) -> 2
, c_0(4, 2) -> 2
, c_0(4, 3) -> 2
, c_0(4, 4) -> 2
, c_1(1, 6) -> 5
, c_1(2, 6) -> 5
, c_1(3, 6) -> 5
, c_1(4, 6) -> 5
, c_1(6, 1) -> 7
, c_1(6, 2) -> 7
, c_1(6, 3) -> 7
, c_1(6, 4) -> 7
, c_1(10, 1) -> 5
, c_1(10, 2) -> 5
, c_1(10, 3) -> 5
, c_1(10, 4) -> 5
, c_2(9, 1) -> 8
, c_2(9, 2) -> 8
, c_2(9, 3) -> 8
, c_2(9, 4) -> 8
, c_2(9, 6) -> 8
, f_0(1) -> 3
, f_0(2) -> 3
, f_0(3) -> 3
, f_0(4) -> 3
, f_1(5) -> 4
, f_1(7) -> 3
, f_2(8) -> 4
, g_0(1) -> 4
, g_0(2) -> 4
, g_0(3) -> 4
, g_0(4) -> 4}
Hurray, we answered YES(?,O(n^1))Tool CDI
stdout:
YES(?,O(n^2))
QUADRATIC upper bound on the derivational complexity
This TRS is terminating using the deltarestricted interpretation
g(delta, X0) = + 0*X0 + 0 + 3*X0*delta + 3*delta
s(delta, X0) = + 1*X0 + 1 + 0*X0*delta + 0*delta
c(delta, X1, X0) = + 1*X0 + 0*X1 + 0 + 0*X0*delta + 2*X1*delta + 0*delta
f(delta, X0) = + 0*X0 + 0 + 3*X0*delta + 0*delta
g_tau_1(delta) = delta/(0 + 3 * delta)
s_tau_1(delta) = delta/(1 + 0 * delta)
c_tau_1(delta) = delta/(0 + 2 * delta)
c_tau_2(delta) = delta/(1 + 0 * delta)
f_tau_1(delta) = delta/(0 + 3 * delta)
Time: 5.723208 seconds
Statistics:
Number of monomials: 750
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:
{ g(c(s(X), Y)) -> f(c(X, s(Y)))
, f(c(X, s(Y))) -> f(c(s(X), Y))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following EDA-non-satisfying matrix interpretation:
Interpretation Functions:
s(x1) = [1 0] x1 + [0]
[0 1] [2]
c(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
f(x1) = [1 1] x1 + [0]
[0 0] [0]
g(x1) = [1 2] x1 + [3]
[0 0] [3]
Hurray, we answered YES(?,O(n^2))Tool IDA
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(c(s(X), Y)) -> f(c(X, s(Y)))
, f(c(X, s(Y))) -> f(c(s(X), Y))}
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:
s(x1) = [1 0] x1 + [0]
[0 1] [3]
c(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
[0 1] [0 0] [0]
f(x1) = [1 0] x1 + [1]
[0 0] [0]
g(x1) = [1 1] x1 + [3]
[0 0] [3]
Hurray, we answered YES(?,O(n^1))Tool TRI
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(c(s(X), Y)) -> f(c(X, s(Y)))
, f(c(X, s(Y))) -> f(c(s(X), Y))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
s(x1) = [1 0] x1 + [0]
[0 1] [2]
c(x1, x2) = [1 0] x1 + [1 2] x2 + [0]
[0 0] [0 0] [2]
f(x1) = [1 0] x1 + [0]
[0 0] [0]
g(x1) = [1 2] x1 + [3]
[0 0] [3]
Hurray, we answered YES(?,O(n^1))Tool TRI2
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ g(c(s(X), Y)) -> f(c(X, s(Y)))
, f(c(X, s(Y))) -> f(c(s(X), Y))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
s(x1) = [1 0] x1 + [0]
[0 1] [3]
c(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
[0 1] [0 1] [1]
f(x1) = [1 0] x1 + [0]
[0 0] [0]
g(x1) = [1 1] x1 + [3]
[0 0] [3]
Hurray, we answered YES(?,O(n^2))