Problem SK90 4.56

Tool Bounds

Execution Time	2.9001951e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.56

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  The problem is match-bounded by 1.
  The enriched problem is compatible with the following automaton:
  {  a_0() -> 1
   , a_1() -> 2
   , b_0() -> 1
   , b_1() -> 2
   , f_0(1, 1) -> 1
   , f_1(2, 3) -> 1
   , c_0() -> 1
   , c_1() -> 3
   , d_0() -> 1
   , d_1() -> 3}

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

Tool CDI

Execution Time	6.1939955e-2ms
Answer	YES(?,O(n^2))
Input	SK90 4.56

stdout:

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

This TRS is terminating using the deltarestricted interpretation
d(delta) =  + 0 + 0*delta
b(delta) =  + 0 + 3*delta
c(delta) =  + 2 + 0*delta
a(delta) =  + 0 + 0*delta
f(delta, X1, X0) =  + 0*X0 + 0*X1 + 0 + 1*X0*delta + 2*X1*delta + 0*delta
f_tau_1(delta) = delta/(0 + 2 * delta)
f_tau_2(delta) = delta/(0 + 1 * delta)

Time: 0.023346 seconds
Statistics:
Number of monomials: 30
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.36096ms
Answer	YES(?,O(n^2))
Input	SK90 4.56

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   a() = [1]
         [0]
   b() = [1]
         [0]
   f(x1, x2) = [1 2] x1 + [1 0] x2 + [2]
               [0 0]      [0 0]      [0]
   c() = [0]
         [2]
   d() = [0]
         [3]

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

Tool IDA

Execution Time	0.39866996ms
Answer	YES(?,O(n^2))
Input	SK90 4.56

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(c(), d()) -> f(b(), d())
     , f(a(), b()) -> f(a(), c())}
  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() = [0]
         [0]
   b() = [1]
         [0]
   f(x1, x2) = [1 2] x1 + [1 0] x2 + [2]
               [0 0]      [0 0]      [0]
   c() = [0]
         [3]
   d() = [0]
         [3]

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

Tool TRI

Execution Time	0.13676596ms
Answer	YES(?,O(n^1))
Input	SK90 4.56

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [0]
         [3]
   b() = [1]
         [3]
   f(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
               [0 0]      [0 0]      [0]
   c() = [2]
         [0]
   d() = [3]
         [0]

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

Tool TRI2

Execution Time	0.10763097ms
Answer	YES(?,O(n^1))
Input	SK90 4.56

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [2]
         [3]
   b() = [1]
         [2]
   f(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
               [0 0]      [0 0]      [0]
   c() = [2]
         [0]
   d() = [3]
         [0]

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