Problem Zantema 04 z101

Tool Bounds

Execution Time	60.03423ms
Answer	TIMEOUT
Input	Zantema 04 z101

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  b(b(b(b(b(x1))))) -> a(a(a(x1)))
     , a(a(x1)) -> b(b(b(x1)))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	60.040096ms
Answer	TIMEOUT
Input	Zantema 04 z101

stdout:

TIMEOUT

Statistics:
Number of monomials: 1670
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	60.03691ms
Answer	TIMEOUT
Input	Zantema 04 z101

stdout:

Tool IDA

Execution Time	60.04763ms
Answer	TIMEOUT
Input	Zantema 04 z101

stdout:

Tool TRI

Execution Time	2.9169118ms
Answer	YES(?,O(n^1))
Input	Zantema 04 z101

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  b(b(b(b(b(x1))))) -> a(a(a(x1)))
     , a(a(x1)) -> b(b(b(x1)))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a(x1) = [1 1 0 1] x1 + [2]
           [0 0 2 0]      [1]
           [0 0 0 0]      [2]
           [0 0 0 0]      [1]
   b(x1) = [1 1 0 0] x1 + [0]
           [0 0 2 1]      [0]
           [0 0 0 0]      [2]
           [0 0 0 0]      [1]

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

Tool TRI2

Execution Time	0.1962471ms
Answer	YES(?,O(n^2))
Input	Zantema 04 z101

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  b(b(b(b(b(x1))))) -> a(a(a(x1)))
     , a(a(x1)) -> b(b(b(x1)))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a(x1) = [1 3] x1 + [2]
           [0 1]      [3]
   b(x1) = [1 2] x1 + [0]
           [0 1]      [2]

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