Problem TCT 09 ma3

Tool Bounds

Execution Time	4.084301e-2ms
Answer	YES(?,O(n^1))
Input	TCT 09 ma3

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(x, s(y)) -> minus(p(x), y)
     , minus(x, 0()) -> x
     , p(s(x)) -> x
     , p(0()) -> 0()}
  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:
  {  0_0() -> 1
   , 0_0() -> 2
   , 0_1() -> 1
   , 0_1() -> 2
   , 0_2() -> 1
   , 0_2() -> 2
   , p_0(1) -> 1
   , p_0(1) -> 2
   , p_1(1) -> 1
   , p_1(1) -> 2
   , p_1(2) -> 1
   , p_1(2) -> 2
   , s_0(1) -> 1
   , s_0(1) -> 2
   , minus_0(1, 1) -> 1
   , minus_0(1, 1) -> 2
   , minus_1(2, 1) -> 1
   , minus_1(2, 1) -> 2}

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

Tool CDI

Execution Time	0.124840975ms
Answer	YES(?,O(n^2))
Input	TCT 09 ma3

stdout:

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

This TRS is terminating using the deltarestricted interpretation
minus(delta, X1, X0) =  + 1*X0 + 1*X1 + 0 + 1*X0*delta + 0*X1*delta + 0*delta
s(delta, X0) =  + 1*X0 + 3 + 0*X0*delta + 1*delta
p(delta, X0) =  + 1*X0 + 2 + 0*X0*delta + 3*delta
0(delta) =  + 2 + 0*delta
minus_tau_1(delta) = delta/(1 + 0 * delta)
minus_tau_2(delta) = delta/(1 + 1 * delta)
s_tau_1(delta) = delta/(1 + 0 * delta)
p_tau_1(delta) = delta/(1 + 0 * delta)

Time: 0.087808 seconds
Statistics:
Number of monomials: 131
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.14672494ms
Answer	YES(?,O(n^1))
Input	TCT 09 ma3

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(x, s(y)) -> minus(p(x), y)
     , minus(x, 0()) -> x
     , p(s(x)) -> x
     , p(0()) -> 0()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   0() = [3]
   p(x1) = [1] x1 + [2]
   s(x1) = [1] x1 + [3]
   minus(x1, x2) = [1] x1 + [1] x2 + [3]

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

Tool IDA

Execution Time	0.19321203ms
Answer	YES(?,O(n^1))
Input	TCT 09 ma3

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(x, s(y)) -> minus(p(x), y)
     , minus(x, 0()) -> x
     , p(s(x)) -> x
     , p(0()) -> 0()}
  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:
   0() = [3]
   p(x1) = [1] x1 + [1]
   s(x1) = [1] x1 + [3]
   minus(x1, x2) = [1] x1 + [1] x2 + [3]

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

Tool TRI

Execution Time	0.10466981ms
Answer	YES(?,O(n^1))
Input	TCT 09 ma3

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(x, s(y)) -> minus(p(x), y)
     , minus(x, 0()) -> x
     , p(s(x)) -> x
     , p(0()) -> 0()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   0() = [3]
   p(x1) = [1] x1 + [1]
   s(x1) = [1] x1 + [3]
   minus(x1, x2) = [1] x1 + [1] x2 + [3]

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

Tool TRI2

Execution Time	0.11269903ms
Answer	YES(?,O(n^2))
Input	TCT 09 ma3

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  minus(x, s(y)) -> minus(p(x), y)
     , minus(x, 0()) -> x
     , p(s(x)) -> x
     , p(0()) -> 0()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   0() = [0]
         [3]
   p(x1) = [1 0] x1 + [2]
           [0 1]      [1]
   s(x1) = [1 3] x1 + [0]
           [0 1]      [3]
   minus(x1, x2) = [1 2] x1 + [1 3] x2 + [0]
                   [0 1]      [0 1]      [0]

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