Problem Der95 07

Tool Bounds

Execution Time	60.02836ms
Answer	TIMEOUT
Input	Der95 07

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  b(w(x)) -> w(b(x))
     , b(r(x)) -> r(b(x))
     , w(r(x)) -> r(w(x))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.18484116ms
Answer	YES(?,O(n^2))
Input	Der95 07

stdout:

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

This TRS is terminating using the deltarestricted interpretation
b(delta, X0) =  + 1*X0 + 0 + 2*X0*delta + 0*delta
w(delta, X0) =  + 1*X0 + 2 + 1*X0*delta + 0*delta
r(delta, X0) =  + 1*X0 + 3 + 1*X0*delta + 0*delta
b_tau_1(delta) = delta/(1 + 2 * delta)
w_tau_1(delta) = delta/(1 + 1 * delta)
r_tau_1(delta) = delta/(1 + 1 * delta)

Time: 0.147255 seconds
Statistics:
Number of monomials: 135
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.32633305ms
Answer	YES(?,O(n^2))
Input	Der95 07

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  b(w(x)) -> w(b(x))
     , b(r(x)) -> r(b(x))
     , w(r(x)) -> r(w(x))}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.43265486ms
Answer	YES(?,O(n^2))
Input	Der95 07

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.14889503ms
Answer	YES(?,O(n^2))
Input	Der95 07

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  b(w(x)) -> w(b(x))
     , b(r(x)) -> r(b(x))
     , w(r(x)) -> r(w(x))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.14183593ms
Answer	YES(?,O(n^2))
Input	Der95 07

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  b(w(x)) -> w(b(x))
     , b(r(x)) -> r(b(x))
     , w(r(x)) -> r(w(x))}
  StartTerms: all
  Strategy: none

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

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

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