Problem AG01 3.33

Tool Bounds

Execution Time	3.0771017e-2ms
Answer	YES(?,O(n^1))
Input	AG01 3.33

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  q(g(g(x))) -> p(g(f(x)))
     , q(f(f(x))) -> p(f(g(x)))
     , p(g(g(x))) -> q(g(f(x)))
     , p(f(f(x))) -> q(f(g(x)))}
  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:
  {  f_0(1) -> 1
   , f_1(1) -> 3
   , f_1(4) -> 2
   , p_0(1) -> 1
   , p_1(2) -> 1
   , g_0(1) -> 1
   , g_1(1) -> 4
   , g_1(3) -> 2
   , q_0(1) -> 1
   , q_1(2) -> 1}

Hurray, we answered YES(?,O(n^1))

Tool CDI

Execution Time	60.038303ms
Answer	TIMEOUT
Input	AG01 3.33

stdout:

TIMEOUT

Statistics:
Number of monomials: 1872
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.930923ms
Answer	YES(?,O(n^2))
Input	AG01 3.33

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  q(g(g(x))) -> p(g(f(x)))
     , q(f(f(x))) -> p(f(g(x)))
     , p(g(g(x))) -> q(g(f(x)))
     , p(f(f(x))) -> q(f(g(x)))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1) = [1 0] x1 + [2]
           [0 0]      [0]
   p(x1) = [1 2] x1 + [0]
           [0 0]      [0]
   g(x1) = [1 0] x1 + [1]
           [0 1]      [1]
   q(x1) = [1 2] x1 + [0]
           [0 0]      [0]

Hurray, we answered YES(?,O(n^2))

Tool IDA

Execution Time	1.149215ms
Answer	YES(?,O(n^2))
Input	AG01 3.33

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  q(g(g(x))) -> p(g(f(x)))
     , q(f(f(x))) -> p(f(g(x)))
     , p(g(g(x))) -> q(g(f(x)))
     , p(f(f(x))) -> q(f(g(x)))}
  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:
   f(x1) = [1 0] x1 + [1]
           [0 0]      [0]
   p(x1) = [1 2] x1 + [2]
           [0 0]      [0]
   g(x1) = [1 0] x1 + [0]
           [0 1]      [1]
   q(x1) = [1 2] x1 + [2]
           [0 0]      [0]

Hurray, we answered YES(?,O(n^2))

Tool TRI

Execution Time	0.32942295ms
Answer	YES(?,O(n^2))
Input	AG01 3.33

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  q(g(g(x))) -> p(g(f(x)))
     , q(f(f(x))) -> p(f(g(x)))
     , p(g(g(x))) -> q(g(f(x)))
     , p(f(f(x))) -> q(f(g(x)))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   f(x1) = [1 0] x1 + [1]
           [0 0]      [0]
   p(x1) = [1 1] x1 + [0]
           [0 1]      [0]
   g(x1) = [1 0] x1 + [0]
           [0 1]      [2]
   q(x1) = [1 1] x1 + [0]
           [0 1]      [0]

Hurray, we answered YES(?,O(n^2))

Tool TRI2

Execution Time	0.33089495ms
Answer	YES(?,O(n^1))
Input	AG01 3.33

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  q(g(g(x))) -> p(g(f(x)))
     , q(f(f(x))) -> p(f(g(x)))
     , p(g(g(x))) -> q(g(f(x)))
     , p(f(f(x))) -> q(f(g(x)))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^1))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   f(x1) = [1 0] x1 + [2]
           [0 0]      [0]
   p(x1) = [1 2] x1 + [0]
           [0 0]      [0]
   g(x1) = [1 0] x1 + [0]
           [0 1]      [3]
   q(x1) = [1 2] x1 + [0]
           [0 0]      [0]

Hurray, we answered YES(?,O(n^1))