Problem SK90 4.48

Tool Bounds

Execution Time	60.034325ms
Answer	TIMEOUT
Input	SK90 4.48

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  f(g(x), x, y) -> y
     , f(x, x, y) -> x
     , f(x, y, g(y)) -> x
     , f(x, y, y) -> y
     , f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.13051796ms
Answer	YES(?,O(n^2))
Input	SK90 4.48

stdout:

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

This TRS is terminating using the deltarestricted interpretation
g(delta, X0) = + 1*X0 + 0 + 0*X0*delta + 0*delta
f(delta, X2, X1, X0) = + 1*X0 + 1*X1 + 1*X2 + 0 + 0*X0*delta + 0*X1*delta + 0*X2*delta + 2*delta
g_tau_1(delta) = delta/(1 + 0 * delta)
f_tau_1(delta) = delta/(1 + 0 * delta)
f_tau_2(delta) = delta/(1 + 0 * delta)
f_tau_3(delta) = delta/(1 + 0 * delta)

Time: 0.091488 seconds
Statistics:
Number of monomials: 221
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.13018084ms
Answer	YES(?,O(n^1))
Input	SK90 4.48

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(g(x), x, y) -> y
     , f(x, x, y) -> x
     , f(x, y, g(y)) -> x
     , f(x, y, y) -> y
     , f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [2]
   g(x1) = [1] x1 + [1]

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

Tool IDA

Execution Time	0.21844006ms
Answer	YES(?,O(n^1))
Input	SK90 4.48

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(g(x), x, y) -> y
     , f(x, x, y) -> x
     , f(x, y, g(y)) -> x
     , f(x, y, y) -> y
     , f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [2]
   g(x1) = [1] x1 + [1]

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

Tool TRI

Execution Time	8.1003904e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.48

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(g(x), x, y) -> y
     , f(x, x, y) -> x
     , f(x, y, g(y)) -> x
     , f(x, y, y) -> y
     , f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   f(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [2]
   g(x1) = [1] x1 + [1]

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

Tool TRI2

Execution Time	0.10314798ms
Answer	YES(?,O(n^2))
Input	SK90 4.48

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(g(x), x, y) -> y
     , f(x, x, y) -> x
     , f(x, y, g(y)) -> x
     , f(x, y, y) -> y
     , f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   f(x1, x2, x3) = [1 0] x1 + [1 3] x2 + [1 0] x3 + [1]
                   [0 1]      [0 1]      [0 1]      [0]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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