Problem Zantema 05 z26

Tool Bounds

Execution Time	20.708214ms
Answer	MAYBE
Input	Zantema 05 z26

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  f(b(x), b(y)) -> b(f(x, y))
     , f(a(x), a(y)) -> a(f(x, y))
     , a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y))))))}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  None of the processors succeeded.


Arrrr..

Tool CDI

Execution Time	60.037144ms
Answer	TIMEOUT
Input	Zantema 05 z26

stdout:

TIMEOUT

Statistics:
Number of monomials: 0
Last formula building started for bound 0
Last SAT solving started for bound 0

Tool EDA

Execution Time	60.041798ms
Answer	TIMEOUT
Input	Zantema 05 z26

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  f(b(x), b(y)) -> b(f(x, y))
     , f(a(x), a(y)) -> a(f(x, y))
     , a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y))))))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool IDA

Execution Time	60.03964ms
Answer	TIMEOUT
Input	Zantema 05 z26

stdout:

Tool TRI

Execution Time	0.5439122ms
Answer	YES(?,O(n^2))
Input	Zantema 05 z26

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(b(x), b(y)) -> b(f(x, y))
     , f(a(x), a(y)) -> a(f(x, y))
     , a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y))))))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   f(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 1]      [0 1]      [0]
   a(x1) = [1 3] x1 + [1]
           [0 1]      [3]
   b(x1) = [1 0] x1 + [1]
           [0 0]      [0]

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

Tool TRI2

Execution Time	0.5825212ms
Answer	YES(?,O(n^2))
Input	Zantema 05 z26