Problem Mixed TRS jones4

Tool Bounds

Execution Time	5.7348967e-2ms
Answer	YES(?,O(n^1))
Input	Mixed TRS jones4

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  p(m, 0(), 0()) -> m
     , p(m, s(n), 0()) -> p(0(), n, m)
     , p(m, n, s(r)) -> p(m, r, n)}
  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:
  {  s_0(1) -> 1
   , p_0(1, 1, 1) -> 1
   , p_1(1, 1, 1) -> 1
   , p_1(2, 1, 1) -> 1
   , p_1(2, 1, 2) -> 1
   , 0_0() -> 1
   , 0_1() -> 1
   , 0_1() -> 2}

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

Tool CDI

Execution Time	0.31872702ms
Answer	YES(?,O(n^2))
Input	Mixed TRS jones4

stdout:

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

This TRS is terminating using the deltarestricted interpretation
0(delta) =  + 0 + 0*delta
s(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 2*delta
p(delta, X2, X1, X0) =  + 1*X0 + 1*X1 + 1*X2 + 0 + 0*X0*delta + 0*X1*delta + 0*X2*delta + 2*delta
s_tau_1(delta) = delta/(1 + 0 * delta)
p_tau_1(delta) = delta/(1 + 0 * delta)
p_tau_2(delta) = delta/(1 + 0 * delta)
p_tau_3(delta) = delta/(1 + 0 * delta)

Time: 0.280491 seconds
Statistics:
Number of monomials: 204
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.14414907ms
Answer	YES(?,O(n^1))
Input	Mixed TRS jones4

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  p(m, 0(), 0()) -> m
     , p(m, s(n), 0()) -> p(0(), n, m)
     , p(m, n, s(r)) -> p(m, r, n)}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   s(x1) = [1] x1 + [1]
   p(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [2]
   0() = [2]

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

Tool IDA

Execution Time	0.20736599ms
Answer	YES(?,O(n^1))
Input	Mixed TRS jones4

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  p(m, 0(), 0()) -> m
     , p(m, s(n), 0()) -> p(0(), n, m)
     , p(m, n, s(r)) -> p(m, r, n)}
  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:
   s(x1) = [1] x1 + [3]
   p(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [1]
   0() = [0]

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

Tool TRI

Execution Time	6.431794e-2ms
Answer	YES(?,O(n^1))
Input	Mixed TRS jones4

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  p(m, 0(), 0()) -> m
     , p(m, s(n), 0()) -> p(0(), n, m)
     , p(m, n, s(r)) -> p(m, r, n)}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   s(x1) = [1] x1 + [1]
   p(x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [2]
   0() = [2]

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

Tool TRI2

Execution Time	0.11130905ms
Answer	YES(?,O(n^2))
Input	Mixed TRS jones4

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  p(m, 0(), 0()) -> m
     , p(m, s(n), 0()) -> p(0(), n, m)
     , p(m, n, s(r)) -> p(m, r, n)}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   s(x1) = [1 1] x1 + [2]
           [0 0]      [2]
   p(x1, x2, x3) = [1 2] x1 + [1 1] x2 + [1 0] x3 + [1]
                   [0 1]      [0 0]      [0 0]      [1]
   0() = [0]
         [0]

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