Problem SK90 2.11

Tool Bounds

Execution Time	60.046097ms
Answer	TIMEOUT
Input	SK90 2.11

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  -(s(x), s(y)) -> -(x, y)
     , -(x, 0()) -> x
     , -(0(), y) -> 0()
     , +(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	0.18600917ms
Answer	YES(?,O(n^2))
Input	SK90 2.11

stdout:

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

This TRS is terminating using the deltarestricted interpretation
-(delta, X1, X0) =  + 1*X0 + 1*X1 + 0 + 3*X0*delta + 0*X1*delta + 2*delta
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
-_tau_1(delta) = delta/(1 + 0 * delta)
-_tau_2(delta) = delta/(1 + 3 * delta)
s_tau_1(delta) = delta/(1 + 0 * delta)
+_tau_1(delta) = delta/(1 + 1 * delta)
+_tau_2(delta) = delta/(1 + 0 * delta)

Time: 0.145503 seconds
Statistics:
Number of monomials: 187
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.39732814ms
Answer	YES(?,O(n^2))
Input	SK90 2.11

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool IDA

Execution Time	0.5759928ms
Answer	YES(?,O(n^2))
Input	SK90 2.11

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.16571093ms
Answer	YES(?,O(n^2))
Input	SK90 2.11

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI2

Execution Time	0.11468387ms
Answer	YES(?,O(n^2))
Input	SK90 2.11

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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