Problem SK90 4.36

Tool Bounds

Execution Time	2.7698994e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.36

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {a(a(x)) -> a(b(a(x)))}
  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:
  {  a_0(1) -> 1
   , a_0(2) -> 1
   , a_1(1) -> 4
   , a_1(2) -> 4
   , a_1(3) -> 1
   , a_1(3) -> 4
   , a_2(3) -> 6
   , a_2(5) -> 4
   , b_0(1) -> 2
   , b_0(2) -> 2
   , b_1(4) -> 3
   , b_2(6) -> 5}

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

Tool CDI

Execution Time	0.1455059ms
Answer	YES(?,O(n^2))
Input	SK90 4.36

stdout:

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

This TRS is terminating using the deltarestricted interpretation
b(delta, X0) = + 0*X0 + 0 + 2*X0*delta + 0*delta
a(delta, X0) = + 0*X0 + 2 + 3*X0*delta + 0*delta
b_tau_1(delta) = delta/(0 + 2 * delta)
a_tau_1(delta) = delta/(0 + 3 * delta)

Time: 0.108087 seconds
Statistics:
Number of monomials: 60
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.2710619ms
Answer	YES(?,O(n^2))
Input	SK90 4.36

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {a(a(x)) -> a(b(a(x)))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   a(x1) = [1 1] x1 + [0]
           [0 0]      [1]
   b(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool IDA

Execution Time	0.3573532ms
Answer	YES(?,O(n^2))
Input	SK90 4.36

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {a(a(x)) -> a(b(a(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:
   a(x1) = [1 1] x1 + [0]
           [0 0]      [1]
   b(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool TRI

Execution Time	0.118331194ms
Answer	YES(?,O(n^2))
Input	SK90 4.36

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {a(a(x)) -> a(b(a(x)))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	7.321215e-2ms
Answer	YES(?,O(n^2))
Input	SK90 4.36

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {a(a(x)) -> a(b(a(x)))}
  StartTerms: all
  Strategy: none

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

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

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