Problem SK90 2.48

Tool Bounds

Execution Time	3.813505e-2ms
Answer	YES(?,O(n^1))
Input	SK90 2.48

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  b(u(x)) -> a(e(x))
     , v(e(x)) -> x
     , c(u(x)) -> b(x)
     , d(u(x)) -> c(x)
     , d(x) -> e(u(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:
  {  d_0(1) -> 1
   , u_0(1) -> 1
   , u_1(1) -> 1
   , u_1(1) -> 3
   , e_0(1) -> 1
   , e_1(1) -> 2
   , e_1(3) -> 1
   , e_2(1) -> 4
   , c_0(1) -> 1
   , c_1(1) -> 1
   , b_0(1) -> 1
   , b_1(1) -> 1
   , b_2(1) -> 1
   , v_0(1) -> 1
   , a_0(1) -> 1
   , a_1(2) -> 1
   , a_2(4) -> 1}

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

Tool CDI

Execution Time	0.18952012ms
Answer	YES(?,O(n^2))
Input	SK90 2.48

stdout:

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

This TRS is terminating using the deltarestricted interpretation
a(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 0*delta
v(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 1*delta
b(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 1*delta
c(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 3*delta
d(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 3*delta
u(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 1*delta
e(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 0*delta
a_tau_1(delta) = delta/(1 + 0 * delta)
v_tau_1(delta) = delta/(1 + 0 * delta)
b_tau_1(delta) = delta/(1 + 0 * delta)
c_tau_1(delta) = delta/(1 + 0 * delta)
d_tau_1(delta) = delta/(1 + 0 * delta)
u_tau_1(delta) = delta/(1 + 0 * delta)
e_tau_1(delta) = delta/(1 + 0 * delta)

Time: 0.149439 seconds
Statistics:
Number of monomials: 196
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.14221692ms
Answer	YES(?,O(n^1))
Input	SK90 2.48

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  b(u(x)) -> a(e(x))
     , v(e(x)) -> x
     , c(u(x)) -> b(x)
     , d(u(x)) -> c(x)
     , d(x) -> e(u(x))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   d(x1) = [1] x1 + [3]
   u(x1) = [1] x1 + [1]
   e(x1) = [1] x1 + [1]
   c(x1) = [1] x1 + [3]
   b(x1) = [1] x1 + [3]
   v(x1) = [1] x1 + [1]
   a(x1) = [1] x1 + [1]

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

Tool IDA

Execution Time	0.24468994ms
Answer	YES(?,O(n^1))
Input	SK90 2.48

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  b(u(x)) -> a(e(x))
     , v(e(x)) -> x
     , c(u(x)) -> b(x)
     , d(u(x)) -> c(x)
     , d(x) -> e(u(x))}
  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:
   d(x1) = [1] x1 + [3]
   u(x1) = [1] x1 + [1]
   e(x1) = [1] x1 + [1]
   c(x1) = [1] x1 + [2]
   b(x1) = [1] x1 + [2]
   v(x1) = [1] x1 + [1]
   a(x1) = [1] x1 + [1]

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

Tool TRI

Execution Time	9.8722935e-2ms
Answer	YES(?,O(n^1))
Input	SK90 2.48

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  b(u(x)) -> a(e(x))
     , v(e(x)) -> x
     , c(u(x)) -> b(x)
     , d(u(x)) -> c(x)
     , d(x) -> e(u(x))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   d(x1) = [1] x1 + [3]
   u(x1) = [1] x1 + [1]
   e(x1) = [1] x1 + [1]
   c(x1) = [1] x1 + [3]
   b(x1) = [1] x1 + [3]
   v(x1) = [1] x1 + [1]
   a(x1) = [1] x1 + [1]

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

Tool TRI2

Execution Time	0.11404586ms
Answer	YES(?,O(n^2))
Input	SK90 2.48

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  b(u(x)) -> a(e(x))
     , v(e(x)) -> x
     , c(u(x)) -> b(x)
     , d(u(x)) -> c(x)
     , d(x) -> e(u(x))}
  StartTerms: all
  Strategy: none

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

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

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