Problem AotoYamada 05 023

Tool Bounds

Execution Time	60.028324ms
Answer	TIMEOUT
Input	AotoYamada 05 023

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	60.040024ms
Answer	TIMEOUT
Input	AotoYamada 05 023

stdout:

TIMEOUT

Statistics:
Number of monomials: 2435
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.6349089ms
Answer	YES(?,O(n^2))
Input	AotoYamada 05 023

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.841089ms
Answer	YES(?,O(n^2))
Input	AotoYamada 05 023

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.25314403ms
Answer	YES(?,O(n^2))
Input	AotoYamada 05 023

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	0.19947791ms
Answer	YES(?,O(n^2))
Input	AotoYamada 05 023

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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