Problem AG01 3.35

Tool Bounds

Execution Time	60.033443ms
Answer	TIMEOUT
Input	AG01 3.35

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  g(0()) -> 0()
     , f(s(x)) -> s(s(g(x)))
     , f(0()) -> s(0())
     , g(s(x)) -> f(x)}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	1.6663878ms
Answer	YES(?,O(n^2))
Input	AG01 3.35

stdout:

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

This TRS is terminating using the deltarestricted interpretation
0(delta) =  + 2 + 0*delta
s(delta, X0) =  + 1*X0 + 1 + 0*X0*delta + 0*delta
g(delta, X0) =  + 1*X0 + 0 + 1*X0*delta + 0*delta
f(delta, X0) =  + 1*X0 + 1 + 1*X0*delta + 0*delta
s_tau_1(delta) = delta/(1 + 0 * delta)
g_tau_1(delta) = delta/(1 + 1 * delta)
f_tau_1(delta) = delta/(1 + 1 * delta)

Time: 1.628786 seconds
Statistics:
Number of monomials: 244
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.35455298ms
Answer	YES(?,O(n^2))
Input	AG01 3.35

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(0()) -> 0()
     , f(s(x)) -> s(s(g(x)))
     , f(0()) -> s(0())
     , g(s(x)) -> f(x)}
  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 + [0]
           [0 1]      [1]
   g(x1) = [1 1] x1 + [0]
           [0 1]      [0]
   f(x1) = [1 1] x1 + [0]
           [0 1]      [1]
   0() = [0]
         [1]

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

Tool IDA

Execution Time	0.51830506ms
Answer	YES(?,O(n^2))
Input	AG01 3.35

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.18090606ms
Answer	YES(?,O(n^2))
Input	AG01 3.35

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(0()) -> 0()
     , f(s(x)) -> s(s(g(x)))
     , f(0()) -> s(0())
     , g(s(x)) -> f(x)}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.13794398ms
Answer	YES(?,O(n^2))
Input	AG01 3.35

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(0()) -> 0()
     , f(s(x)) -> s(s(g(x)))
     , f(0()) -> s(0())
     , g(s(x)) -> f(x)}
  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]      [1]
   g(x1) = [1 1] x1 + [0]
           [0 1]      [0]
   f(x1) = [1 1] x1 + [0]
           [0 1]      [1]
   0() = [0]
         [1]

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