Problem Transformed CSR 04 Ex6 GM04 L

Tool Bounds

Execution Time	2.5295973e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 GM04 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f() -> g()
     , c() -> f()}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^1))

Proof:
  The problem is match-bounded by 2.
  The enriched problem is compatible with the following automaton:
  {  c_0() -> 1
   , f_0() -> 2
   , f_1() -> 1
   , g_0() -> 3
   , g_1() -> 2
   , g_2() -> 1}

Hurray, we answered YES(?,O(n^1))

Tool CDI

Execution Time	3.818512e-2ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex6 GM04 L

stdout:

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

This TRS is terminating using the deltarestricted interpretation
g(delta) =  + 0 + 0*delta
c(delta) =  + 0 + 2*delta
f(delta) =  + 0 + 1*delta

Time: 0.000583 seconds
Statistics:
Number of monomials: 10
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	8.7852e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 GM04 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f() -> g()
     , c() -> f()}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^1))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   c() = [3]
   f() = [2]
   g() = [1]

Hurray, we answered YES(?,O(n^1))

Tool IDA

Execution Time	0.1028471ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 GM04 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f() -> g()
     , c() -> f()}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^1))

Proof:
  We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
  Interpretation Functions:
   c() = [3]
   f() = [2]
   g() = [1]

Hurray, we answered YES(?,O(n^1))

Tool TRI

Execution Time	5.033183e-2ms
Answer	YES(?,O(1))
Input	Transformed CSR 04 Ex6 GM04 L

stdout:

YES(?,O(1))

We consider the following Problem:

  Strict Trs:
    {  f() -> g()
     , c() -> f()}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(1))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   c() = [3]
   f() = [2]
   g() = [1]

Hurray, we answered YES(?,O(1))

Tool TRI2

Execution Time	3.0875921e-2ms
Answer	YES(?,O(1))
Input	Transformed CSR 04 Ex6 GM04 L

stdout:

YES(?,O(1))

We consider the following Problem:

  Strict Trs:
    {  f() -> g()
     , c() -> f()}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(1))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   c() = [3]
         [3]
   f() = [1]
         [3]
   g() = [0]
         [3]

Hurray, we answered YES(?,O(1))