Problem Transformed CSR 04 Ex15 Luc06 GM

Tool Bounds

Execution Time	60.032146ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex15 Luc06 GM

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(mark(X))
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(X)
     , a__f(f(a())) -> a__f(g(f(a())))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	8.46718ms
Answer	MAYBE
Input	Transformed CSR 04 Ex15 Luc06 GM

stdout:

MAYBE

Statistics:
Number of monomials: 360
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	1.621489ms
Answer	YES(?,O(n^3))
Input	Transformed CSR 04 Ex15 Luc06 GM

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(mark(X))
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(X)
     , a__f(f(a())) -> a__f(g(f(a())))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^3))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   a() = [3]
         [1]
         [1]
   f(x1) = [1 0 1] x1 + [0]
           [0 0 0]      [0]
           [0 1 1]      [1]
   a__f(x1) = [1 0 1] x1 + [1]
              [0 0 0]      [0]
              [0 1 1]      [1]
   g(x1) = [1 0 0] x1 + [1]
           [0 1 0]      [2]
           [0 0 0]      [0]
   mark(x1) = [1 2 0] x1 + [3]
              [0 1 0]      [0]
              [0 0 1]      [0]

Hurray, we answered YES(?,O(n^3))

Tool IDA

Execution Time	3.645978ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex15 Luc06 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(mark(X))
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(X)
     , a__f(f(a())) -> a__f(g(f(a())))}
  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:
   a() = [2]
         [2]
         [0]
   f(x1) = [1 0 2] x1 + [0]
           [0 0 1]      [1]
           [0 0 0]      [2]
   a__f(x1) = [1 0 3] x1 + [2]
              [0 0 1]      [1]
              [0 0 0]      [2]
   g(x1) = [1 2 0] x1 + [0]
           [0 1 0]      [3]
           [0 0 0]      [0]
   mark(x1) = [1 3 0] x1 + [0]
              [0 1 0]      [2]
              [0 1 0]      [2]

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

Tool TRI

Execution Time	0.442492ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex15 Luc06 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(mark(X))
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(X)
     , a__f(f(a())) -> a__f(g(f(a())))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.19656515ms
Answer	MAYBE
Input	Transformed CSR 04 Ex15 Luc06 GM

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(mark(X))
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(X)
     , a__f(f(a())) -> a__f(g(f(a())))}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..