Problem SK90 2.09

Tool Bounds

Execution Time	60.031734ms
Answer	TIMEOUT
Input	SK90 2.09

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.15515709ms
Answer	YES(?,O(n^2))
Input	SK90 2.09

stdout:

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

This TRS is terminating using the deltarestricted interpretation
s(delta, X0) =  + 1*X0 + 2 + 0*X0*delta + 0*delta
0(delta) =  + 0 + 0*delta
+(delta, X1, X0) =  + 1*X0 + 1*X1 + 0 + 0*X0*delta + 1*X1*delta + 1*delta
s_tau_1(delta) = delta/(1 + 0 * delta)
+_tau_1(delta) = delta/(1 + 1 * delta)
+_tau_2(delta) = delta/(1 + 0 * delta)

Time: 0.113869 seconds
Statistics:
Number of monomials: 142
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.261796ms
Answer	YES(?,O(n^2))
Input	SK90 2.09

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.465657ms
Answer	YES(?,O(n^2))
Input	SK90 2.09

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(s(x), y) -> +(x, s(y))
     , +(s(x), y) -> s(+(x, y))
     , +(0(), 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:
   0() = [3]
         [3]
   +(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
               [0 1]      [0 1]      [2]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [2]

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

Tool TRI

Execution Time	0.122430086ms
Answer	YES(?,O(n^2))
Input	SK90 2.09

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	9.317207e-2ms
Answer	YES(?,O(n^2))
Input	SK90 2.09

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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