Problem Der95 01

Tool Bounds

Execution Time	6.635499e-2ms
Answer	YES(?,O(n^1))
Input	Der95 01

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  \(/(x, y), x) -> y
     , /(x, \(y, x)) -> y
     , /(.(y, x), x) -> y
     , \(x, .(x, y)) -> y
     , .(/(y, x), x) -> y
     , .(x, \(x, y)) -> y
     , /(x, e()) -> x
     , \(e(), x) -> x
     , .(x, e()) -> x
     , .(e(), x) -> x
     , /(x, x) -> e()
     , \(x, x) -> e()}
  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:
  {  \_0(1, 1) -> 1
   , e_0() -> 1
   , e_1() -> 1
   , /_0(1, 1) -> 1
   , ._0(1, 1) -> 1}

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

Tool EDA

Execution Time	0.15875101ms
Answer	YES(?,O(n^1))
Input	Der95 01

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  \(/(x, y), x) -> y
     , /(x, \(y, x)) -> y
     , /(.(y, x), x) -> y
     , \(x, .(x, y)) -> y
     , .(/(y, x), x) -> y
     , .(x, \(x, y)) -> y
     , /(x, e()) -> x
     , \(e(), x) -> x
     , .(x, e()) -> x
     , .(e(), x) -> x
     , /(x, x) -> e()
     , \(x, x) -> e()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   \(x1, x2) = [1] x1 + [1] x2 + [3]
   e() = [0]
   /(x1, x2) = [1] x1 + [1] x2 + [3]
   .(x1, x2) = [1] x1 + [1] x2 + [3]

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

Tool IDA

Execution Time	0.2666309ms
Answer	YES(?,O(n^1))
Input	Der95 01

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  \(/(x, y), x) -> y
     , /(x, \(y, x)) -> y
     , /(.(y, x), x) -> y
     , \(x, .(x, y)) -> y
     , .(/(y, x), x) -> y
     , .(x, \(x, y)) -> y
     , /(x, e()) -> x
     , \(e(), x) -> x
     , .(x, e()) -> x
     , .(e(), x) -> x
     , /(x, x) -> e()
     , \(x, x) -> e()}
  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:
   \(x1, x2) = [1] x1 + [1] x2 + [3]
   e() = [0]
   /(x1, x2) = [1] x1 + [1] x2 + [3]
   .(x1, x2) = [1] x1 + [1] x2 + [3]

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

Tool TRI

Execution Time	6.667304e-2ms
Answer	YES(?,O(n^1))
Input	Der95 01

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  \(/(x, y), x) -> y
     , /(x, \(y, x)) -> y
     , /(.(y, x), x) -> y
     , \(x, .(x, y)) -> y
     , .(/(y, x), x) -> y
     , .(x, \(x, y)) -> y
     , /(x, e()) -> x
     , \(e(), x) -> x
     , .(x, e()) -> x
     , .(e(), x) -> x
     , /(x, x) -> e()
     , \(x, x) -> e()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   \(x1, x2) = [1] x1 + [1] x2 + [3]
   e() = [2]
   /(x1, x2) = [1] x1 + [1] x2 + [3]
   .(x1, x2) = [1] x1 + [1] x2 + [3]

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

Tool TRI2

Execution Time	0.14037585ms
Answer	YES(?,O(n^2))
Input	Der95 01

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  \(/(x, y), x) -> y
     , /(x, \(y, x)) -> y
     , /(.(y, x), x) -> y
     , \(x, .(x, y)) -> y
     , .(/(y, x), x) -> y
     , .(x, \(x, y)) -> y
     , /(x, e()) -> x
     , \(e(), x) -> x
     , .(x, e()) -> x
     , .(e(), x) -> x
     , /(x, x) -> e()
     , \(x, x) -> e()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   \(x1, x2) = [1 0] x1 + [1 3] x2 + [3]
               [0 1]      [0 1]      [1]
   e() = [0]
         [1]
   /(x1, x2) = [1 2] x1 + [1 0] x2 + [2]
               [0 1]      [0 1]      [2]
   .(x1, x2) = [1 1] x1 + [1 1] x2 + [0]
               [0 1]      [0 1]      [3]

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