Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ b(a(a(b(x1)))) -> b(a(b(x1)))
, a(b(a(x1))) -> a(a(b(b(a(a(x1))))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 4.
The enriched problem is compatible with the following automaton:
{ a_0(1) -> 1
, a_1(1) -> 8
, a_1(2) -> 7
, a_1(3) -> 2
, a_1(4) -> 1
, a_1(4) -> 2
, a_1(4) -> 8
, a_1(4) -> 9
, a_1(4) -> 10
, a_1(4) -> 17
, a_1(5) -> 4
, a_1(8) -> 7
, a_1(12) -> 2
, a_1(13) -> 2
, a_1(14) -> 2
, a_2(1) -> 10
, a_2(3) -> 17
, a_2(4) -> 17
, a_2(5) -> 17
, a_2(10) -> 9
, a_2(11) -> 16
, a_2(12) -> 11
, a_2(13) -> 2
, a_2(13) -> 8
, a_2(13) -> 9
, a_2(13) -> 10
, a_2(13) -> 17
, a_2(14) -> 13
, a_2(17) -> 16
, a_3(12) -> 26
, a_3(13) -> 26
, a_3(14) -> 26
, a_3(19) -> 18
, a_3(20) -> 25
, a_3(21) -> 20
, a_3(22) -> 9
, a_3(22) -> 10
, a_3(22) -> 17
, a_3(22) -> 18
, a_3(23) -> 22
, a_3(26) -> 25
, a_4(29) -> 28
, a_4(31) -> 30
, b_0(1) -> 1
, b_1(1) -> 3
, b_1(2) -> 1
, b_1(2) -> 3
, b_1(2) -> 6
, b_1(2) -> 10
, b_1(2) -> 15
, b_1(4) -> 1
, b_1(6) -> 5
, b_1(7) -> 6
, b_1(8) -> 1
, b_1(8) -> 3
, b_1(8) -> 10
, b_1(11) -> 1
, b_1(13) -> 1
, b_2(1) -> 10
, b_2(2) -> 10
, b_2(4) -> 10
, b_2(6) -> 12
, b_2(8) -> 10
, b_2(9) -> 6
, b_2(9) -> 15
, b_2(11) -> 1
, b_2(11) -> 3
, b_2(11) -> 6
, b_2(11) -> 10
, b_2(11) -> 15
, b_2(13) -> 1
, b_2(13) -> 3
, b_2(13) -> 6
, b_2(13) -> 10
, b_2(13) -> 15
, b_2(15) -> 14
, b_2(16) -> 15
, b_2(17) -> 6
, b_3(6) -> 19
, b_3(11) -> 19
, b_3(13) -> 19
, b_3(15) -> 21
, b_3(18) -> 6
, b_3(18) -> 15
, b_3(18) -> 24
, b_3(20) -> 6
, b_3(20) -> 10
, b_3(20) -> 15
, b_3(20) -> 24
, b_3(22) -> 6
, b_3(22) -> 15
, b_3(24) -> 23
, b_3(25) -> 24
, b_4(15) -> 29
, b_4(24) -> 31
, b_4(28) -> 24
, b_4(30) -> 6
, b_4(30) -> 15
, b_4(30) -> 24}
Hurray, we answered YES(?,O(n^1))Tool CDI
stdout:
TIMEOUT
Statistics:
Number of monomials: 2668
Last formula building started for bound 3
Last SAT solving started for bound 0Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ b(a(a(b(x1)))) -> b(a(b(x1)))
, a(b(a(x1))) -> a(a(b(b(a(a(x1))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool IDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ b(a(a(b(x1)))) -> b(a(b(x1)))
, a(b(a(x1))) -> a(a(b(b(a(a(x1))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ b(a(a(b(x1)))) -> b(a(b(x1)))
, a(b(a(x1))) -> a(a(b(b(a(a(x1))))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
a(x1) = [1 2 1] x1 + [0]
[0 0 0] [0]
[0 0 0] [2]
b(x1) = [1 0 0] x1 + [0]
[0 0 2] [0]
[0 0 0] [0]
Hurray, we answered YES(?,O(n^1))Tool TRI2
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ b(a(a(b(x1)))) -> b(a(b(x1)))
, a(b(a(x1))) -> a(a(b(b(a(a(x1))))))}
StartTerms: all
Strategy: none
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..