Problem SK90 4.35

Tool Bounds

Execution Time	2.500987e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.35

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {a(b(x)) -> a(c(b(x)))}
  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:
  {  b_0(1) -> 1
   , b_1(1) -> 3
   , a_0(1) -> 1
   , a_1(2) -> 1
   , c_0(1) -> 1
   , c_1(3) -> 2}

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

Tool CDI

Execution Time	0.14741611ms
Answer	YES(?,O(n^2))
Input	SK90 4.35

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 + 2 + 1*X0*delta + 0*delta
c(delta, X0) =  + 0*X0 + 0 + 2*X0*delta + 0*delta
a(delta, X0) =  + 1*X0 + 0 + 3*X0*delta + 0*delta
b_tau_1(delta) = delta/(0 + 1 * delta)
c_tau_1(delta) = delta/(0 + 2 * delta)
a_tau_1(delta) = delta/(1 + 3 * delta)

Time: 0.109393 seconds
Statistics:
Number of monomials: 63
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.32973194ms
Answer	YES(?,O(n^2))
Input	SK90 4.35

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.40237117ms
Answer	YES(?,O(n^2))
Input	SK90 4.35

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {a(b(x)) -> a(c(b(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:
   b(x1) = [1 0] x1 + [0]
           [0 0]      [2]
   a(x1) = [1 2] x1 + [0]
           [0 0]      [1]
   c(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool TRI

Execution Time	0.10412884ms
Answer	YES(?,O(n^2))
Input	SK90 4.35

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	9.159207e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.35

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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