Problem Rubio 04 bintrees

Tool Bounds

Execution Time	60.085243ms
Answer	TIMEOUT
Input	Rubio 04 bintrees

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  lessleaves(cons(U, V), cons(W, Z)) ->
       lessleaves(concat(U, V), concat(W, Z))
     , lessleaves(leaf(), cons(W, Z)) -> true()
     , lessleaves(X, leaf()) -> false()
     , concat(cons(U, V), Y) -> cons(U, concat(V, Y))
     , concat(leaf(), Y) -> Y}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.37998414ms
Answer	YES(?,O(n^2))
Input	Rubio 04 bintrees

stdout:

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

This TRS is terminating using the deltarestricted interpretation
true(delta) =  + 0 + 0*delta
lessleaves(delta, X1, X0) =  + 0*X0 + 0*X1 + 0 + 2*X0*delta + 2*X1*delta + 0*delta
false(delta) =  + 0 + 0*delta
cons(delta, X1, X0) =  + 1*X0 + 0*X1 + 2 + 0*X0*delta + 3*X1*delta + 0*delta
leaf(delta) =  + 2 + 0*delta
concat(delta, X1, X0) =  + 1*X0 + 1*X1 + 0 + 0*X0*delta + 1*X1*delta + 0*delta
lessleaves_tau_1(delta) = delta/(0 + 2 * delta)
lessleaves_tau_2(delta) = delta/(0 + 2 * delta)
cons_tau_1(delta) = delta/(0 + 3 * delta)
cons_tau_2(delta) = delta/(1 + 0 * delta)
concat_tau_1(delta) = delta/(1 + 1 * delta)
concat_tau_2(delta) = delta/(1 + 0 * delta)

Time: 0.340823 seconds
Statistics:
Number of monomials: 325
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.37622786ms
Answer	YES(?,O(n^2))
Input	Rubio 04 bintrees

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  lessleaves(cons(U, V), cons(W, Z)) ->
       lessleaves(concat(U, V), concat(W, Z))
     , lessleaves(leaf(), cons(W, Z)) -> true()
     , lessleaves(X, leaf()) -> false()
     , concat(cons(U, V), Y) -> cons(U, concat(V, Y))
     , concat(leaf(), Y) -> Y}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   leaf() = [0]
            [2]
   concat(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                    [0 1]      [0 1]      [0]
   cons(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [2]
   lessleaves(x1, x2) = [1 2] x1 + [1 2] x2 + [0]
                        [0 1]      [0 1]      [0]
   false() = [3]
             [1]
   true() = [3]
            [0]

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

Tool IDA

Execution Time	0.664675ms
Answer	YES(?,O(n^2))
Input	Rubio 04 bintrees

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  lessleaves(cons(U, V), cons(W, Z)) ->
       lessleaves(concat(U, V), concat(W, Z))
     , lessleaves(leaf(), cons(W, Z)) -> true()
     , lessleaves(X, leaf()) -> false()
     , concat(cons(U, V), Y) -> cons(U, concat(V, Y))
     , concat(leaf(), Y) -> Y}
  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:
   leaf() = [0]
            [2]
   concat(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                    [0 1]      [0 1]      [0]
   cons(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [2]
   lessleaves(x1, x2) = [1 2] x1 + [1 2] x2 + [0]
                        [0 0]      [0 0]      [0]
   false() = [3]
             [0]
   true() = [3]
            [0]

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

Tool TRI

Execution Time	0.21028686ms
Answer	YES(?,O(n^2))
Input	Rubio 04 bintrees

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  lessleaves(cons(U, V), cons(W, Z)) ->
       lessleaves(concat(U, V), concat(W, Z))
     , lessleaves(leaf(), cons(W, Z)) -> true()
     , lessleaves(X, leaf()) -> false()
     , concat(cons(U, V), Y) -> cons(U, concat(V, Y))
     , concat(leaf(), Y) -> Y}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   leaf() = [1]
            [0]
   concat(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                    [0 1]      [0 1]      [0]
   cons(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [2]
   lessleaves(x1, x2) = [1 2] x1 + [1 2] x2 + [0]
                        [0 0]      [0 0]      [1]
   false() = [0]
             [1]
   true() = [0]
            [1]

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

Tool TRI2

Execution Time	0.17065096ms
Answer	YES(?,O(n^2))
Input	Rubio 04 bintrees

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  lessleaves(cons(U, V), cons(W, Z)) ->
       lessleaves(concat(U, V), concat(W, Z))
     , lessleaves(leaf(), cons(W, Z)) -> true()
     , lessleaves(X, leaf()) -> false()
     , concat(cons(U, V), Y) -> cons(U, concat(V, Y))
     , concat(leaf(), Y) -> Y}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   leaf() = [0]
            [2]
   concat(x1, x2) = [1 1] x1 + [1 0] x2 + [1]
                    [0 1]      [0 1]      [1]
   cons(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [3]
   lessleaves(x1, x2) = [1 0] x1 + [1 3] x2 + [0]
                        [0 0]      [0 0]      [1]
   false() = [1]
             [1]
   true() = [0]
            [1]

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