Problem Transformed CSR 04 Ex23 Luc06 GM

Tool Bounds

Execution Time	60.03485ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex23 Luc06 GM

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , mark(g(X)) -> g(mark(X))
     , mark(c(X)) -> c(X)
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(mark(X))
     , a__f(f(a())) -> c(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	60.040684ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex23 Luc06 GM

stdout:

TIMEOUT

Statistics:
Number of monomials: 3167
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.7488141ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex23 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(c(X)) -> c(X)
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(mark(X))
     , a__f(f(a())) -> c(f(g(f(a()))))}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.9335971ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex23 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(c(X)) -> c(X)
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(mark(X))
     , a__f(f(a())) -> c(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() = [1]
         [1]
   f(x1) = [1 0] x1 + [2]
           [0 1]      [2]
   a__f(x1) = [1 0] x1 + [3]
              [0 1]      [2]
   g(x1) = [1 0] x1 + [0]
           [0 1]      [1]
   c(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   mark(x1) = [1 1] x1 + [0]
              [0 1]      [0]

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

Tool TRI

Execution Time	0.254081ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex23 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(c(X)) -> c(X)
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(mark(X))
     , a__f(f(a())) -> c(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]
         [1]
   f(x1) = [1 0] x1 + [1]
           [0 1]      [3]
   a__f(x1) = [1 0] x1 + [3]
              [0 1]      [3]
   g(x1) = [1 0] x1 + [0]
           [0 1]      [1]
   c(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   mark(x1) = [1 1] x1 + [0]
              [0 1]      [0]

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

Tool TRI2

Execution Time	0.23437285ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex23 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(c(X)) -> c(X)
     , mark(a()) -> a()
     , mark(f(X)) -> a__f(mark(X))
     , a__f(f(a())) -> c(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]
         [1]
   f(x1) = [1 0] x1 + [0]
           [0 1]      [2]
   a__f(x1) = [1 0] x1 + [1]
              [0 1]      [2]
   g(x1) = [1 0] x1 + [0]
           [0 1]      [1]
   c(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   mark(x1) = [1 1] x1 + [0]
              [0 1]      [0]

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