Problem TCT 09 append

Tool Bounds

Execution Time	60.03137ms
Answer	TIMEOUT
Input	TCT 09 append

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  app(cons(x, xs), ys) -> cons(x, app(xs, ys))
     , app(nil(), xs) -> nil()}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.104563ms
Answer	YES(?,O(n^2))
Input	TCT 09 append

stdout:

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

This TRS is terminating using the deltarestricted interpretation
cons(delta, X1, X0) =  + 1*X0 + 0*X1 + 2 + 0*X0*delta + 1*X1*delta + 0*delta
app(delta, X1, X0) =  + 0*X0 + 1*X1 + 0 + 1*X0*delta + 1*X1*delta + 3*delta
nil(delta) =  + 1 + 0*delta
cons_tau_1(delta) = delta/(0 + 1 * delta)
cons_tau_2(delta) = delta/(1 + 0 * delta)
app_tau_1(delta) = delta/(1 + 1 * delta)
app_tau_2(delta) = delta/(0 + 1 * delta)

Time: 0.066458 seconds
Statistics:
Number of monomials: 95
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.25545406ms
Answer	YES(?,O(n^2))
Input	TCT 09 append

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  app(cons(x, xs), ys) -> cons(x, app(xs, ys))
     , app(nil(), xs) -> nil()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   nil() = [1]
           [1]
   app(x1, x2) = [1 3] x1 + [1 0] x2 + [0]
                 [0 1]      [0 0]      [2]
   cons(x1, x2) = [1 0] x1 + [1 2] x2 + [0]
                  [0 0]      [0 1]      [3]

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

Tool IDA

Execution Time	0.34442306ms
Answer	YES(?,O(n^2))
Input	TCT 09 append

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  app(cons(x, xs), ys) -> cons(x, app(xs, ys))
     , app(nil(), xs) -> nil()}
  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:
   nil() = [2]
           [0]
   app(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
                 [0 1]      [0 1]      [0]
   cons(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [2]

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

Tool TRI

Execution Time	0.12590694ms
Answer	YES(?,O(n^2))
Input	TCT 09 append

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  app(cons(x, xs), ys) -> cons(x, app(xs, ys))
     , app(nil(), xs) -> nil()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   nil() = [0]
           [1]
   app(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
                 [0 1]      [0 1]      [0]
   cons(x1, x2) = [1 1] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [1]

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

Tool TRI2

Execution Time	6.994796e-2ms
Answer	YES(?,O(n^2))
Input	TCT 09 append

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  app(cons(x, xs), ys) -> cons(x, app(xs, ys))
     , app(nil(), xs) -> nil()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   nil() = [0]
           [1]
   app(x1, x2) = [1 1] x1 + [1 3] x2 + [0]
                 [0 1]      [0 1]      [0]
   cons(x1, x2) = [1 1] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [1]

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