Problem TCT 09 add

Tool Bounds

Execution Time	60.027615ms
Answer	TIMEOUT
Input	TCT 09 add

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	9.44469e-2ms
Answer	YES(?,O(n^2))
Input	TCT 09 add

stdout:

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

This TRS is terminating using the deltarestricted interpretation
s(delta, X0) =  + 1*X0 + 2 + 0*X0*delta + 0*delta
0(delta) =  + 0 + 0*delta
add(delta, X1, X0) =  + 1*X0 + 1*X1 + 0 + 0*X0*delta + 1*X1*delta + 1*delta
s_tau_1(delta) = delta/(1 + 0 * delta)
add_tau_1(delta) = delta/(1 + 1 * delta)
add_tau_2(delta) = delta/(1 + 0 * delta)

Time: 0.056676 seconds
Statistics:
Number of monomials: 84
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.259063ms
Answer	YES(?,O(n^2))
Input	TCT 09 add

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.37610197ms
Answer	YES(?,O(n^2))
Input	TCT 09 add

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  add(s(x), y) -> s(add(x, y))
     , add(0(), x) -> 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:
   0() = [3]
         [3]
   add(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                 [0 1]      [0 1]      [2]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [2]

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

Tool TRI

Execution Time	8.3265066e-2ms
Answer	YES(?,O(n^2))
Input	TCT 09 add

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   0() = [3]
         [3]
   add(x1, x2) = [1 2] x1 + [1 3] x2 + [0]
                 [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [2]

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

Tool TRI2

Execution Time	6.6088915e-2ms
Answer	YES(?,O(n^2))
Input	TCT 09 add

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   0() = [3]
         [3]
   add(x1, x2) = [1 2] x1 + [1 3] x2 + [0]
                 [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [2]

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