Problem Zantema 04 z085

Tool Bounds

Execution Time	60.02791ms
Answer	TIMEOUT
Input	Zantema 04 z085

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.16987514ms
Answer	YES(?,O(n^2))
Input	Zantema 04 z085

stdout:

YES(?,O(n^2))
QUADRATIC upper bound on the derivational complexity

This TRS is terminating using the deltarestricted interpretation
a(delta, X0) = + 0*X0 + 2 + 1*X0*delta + 3*delta
b(delta, X0) = + 0*X0 + 2 + 1*X0*delta + 0*delta
a_tau_1(delta) = delta/(0 + 1 * delta)
b_tau_1(delta) = delta/(0 + 1 * delta)

Time: 0.133363 seconds
Statistics:
Number of monomials: 95
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.26920295ms
Answer	YES(?,O(n^2))
Input	Zantema 04 z085

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.43832707ms
Answer	YES(?,O(n^2))
Input	Zantema 04 z085

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  b(b(b(x1))) -> a(x1)
     , a(x1) -> b(b(x1))}
  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:
   a(x1) = [1 2] x1 + [3]
           [0 0]      [1]
   b(x1) = [1 2] x1 + [0]
           [0 0]      [1]

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

Tool TRI

Execution Time	0.108655214ms
Answer	YES(?,O(n^2))
Input	Zantema 04 z085

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  b(b(b(x1))) -> a(x1)
     , a(x1) -> 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 1] x1 + [0]
           [0 1]      [1]

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

Tool TRI2

Execution Time	7.587814e-2ms
Answer	YES(?,O(n^1))
Input	Zantema 04 z085

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  b(b(b(x1))) -> a(x1)
     , a(x1) -> 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 2] x1 + [3]
           [0 0]      [1]
   b(x1) = [1 2] x1 + [0]
           [0 0]      [1]

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