Problem AG01 3.56

Tool Bounds

Execution Time	60.02881ms
Answer	TIMEOUT
Input	AG01 3.56

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  f(x) -> x
     , f(f(x)) -> f(d(f(x)))
     , f(c(s(x), y)) -> f(c(x, s(y)))
     , g(c(x, s(y))) -> g(c(s(x), y))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	1.450129ms
Answer	MAYBE
Input	AG01 3.56

stdout:

MAYBE

Statistics:
Number of monomials: 433
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.74355507ms
Answer	YES(?,O(n^2))
Input	AG01 3.56

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(x) -> x
     , f(f(x)) -> f(d(f(x)))
     , f(c(s(x), y)) -> f(c(x, s(y)))
     , g(c(x, s(y))) -> g(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 + [2]
           [0 1]      [2]
   c(x1, x2) = [1 0] x1 + [1 2] x2 + [2]
               [0 1]      [0 0]      [0]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   f(x1) = [1 3] x1 + [1]
           [0 1]      [2]
   d(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool IDA

Execution Time	1.1956ms
Answer	YES(?,O(n^2))
Input	AG01 3.56

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(x) -> x
     , f(f(x)) -> f(d(f(x)))
     , f(c(s(x), y)) -> f(c(x, s(y)))
     , g(c(x, s(y))) -> g(c(s(x), y))}
  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:
   s(x1) = [1 0] x1 + [0]
           [0 1]      [2]
   c(x1, x2) = [1 0] x1 + [1 2] x2 + [0]
               [0 1]      [0 0]      [0]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   f(x1) = [1 3] x1 + [2]
           [0 1]      [2]
   d(x1) = [1 1] x1 + [0]
           [0 0]      [0]

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

Tool TRI

Execution Time	0.27544212ms
Answer	YES(?,O(n^2))
Input	AG01 3.56

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(x) -> x
     , f(f(x)) -> f(d(f(x)))
     , f(c(s(x), y)) -> f(c(x, s(y)))
     , g(c(x, s(y))) -> g(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]      [2]
   c(x1, x2) = [1 0] x1 + [1 2] x2 + [1]
               [0 1]      [0 0]      [0]
   g(x1) = [1 0] x1 + [3]
           [0 0]      [1]
   f(x1) = [1 3] x1 + [1]
           [0 1]      [1]
   d(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool TRI2

Execution Time	0.23303604ms
Answer	YES(?,O(n^2))
Input	AG01 3.56

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(x) -> x
     , f(f(x)) -> f(d(f(x)))
     , f(c(s(x), y)) -> f(c(x, s(y)))
     , g(c(x, s(y))) -> g(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 + [1]
           [0 1]      [2]
   c(x1, x2) = [1 0] x1 + [1 2] x2 + [0]
               [0 1]      [0 0]      [1]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   f(x1) = [1 3] x1 + [1]
           [0 1]      [1]
   d(x1) = [1 0] x1 + [2]
           [0 0]      [0]

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