Problem Secret 06 TRS 6

Tool Bounds

Execution Time	60.0299ms
Answer	TIMEOUT
Input	Secret 06 TRS 6

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  a(y, c(b(a(0(), x), 0()))) -> b(a(c(b(0(), y)), x), 0())
     , a(y, x) -> y
     , b(x, y) -> c(a(c(y), a(0(), x)))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	60.04317ms
Answer	TIMEOUT
Input	Secret 06 TRS 6

stdout:

TIMEOUT

Statistics:
Number of monomials: 0
Last formula building started for bound 0
Last SAT solving started for bound 0

Tool EDA

Execution Time	20.362816ms
Answer	YES(?,O(n^3))
Input	Secret 06 TRS 6

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  a(y, c(b(a(0(), x), 0()))) -> b(a(c(b(0(), y)), x), 0())
     , a(y, x) -> y
     , b(x, y) -> c(a(c(y), a(0(), x)))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^3))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   b(x1, x2) = [1 0 0] x1 + [1 1 0] x2 + [3]
               [0 1 0]      [0 0 0]      [0]
               [0 0 0]      [0 0 0]      [0]
   c(x1) = [1 1 0] x1 + [0]
           [0 0 0]      [0]
           [0 0 0]      [0]
   0() = [0]
         [0]
         [1]
   a(x1, x2) = [1 1 0] x1 + [1 0 0] x2 + [1]
               [0 1 3]      [0 0 0]      [0]
               [0 0 1]      [0 0 0]      [0]

Hurray, we answered YES(?,O(n^3))

Tool IDA

Execution Time	23.762033ms
Answer	YES(?,O(n^3))
Input	Secret 06 TRS 6

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  a(y, c(b(a(0(), x), 0()))) -> b(a(c(b(0(), y)), x), 0())
     , a(y, x) -> y
     , b(x, y) -> c(a(c(y), a(0(), x)))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^3))

Proof:
  We have the following EDA-non-satisfying and IDA(3)-non-satisfying matrix interpretation:
  Interpretation Functions:
   b(x1, x2) = [1 1 0] x1 + [1 0 0] x2 + [3]
               [0 0 0]      [0 0 0]      [0]
               [0 0 0]      [0 0 0]      [0]
   c(x1) = [1 0 0] x1 + [0]
           [0 0 0]      [0]
           [0 0 0]      [0]
   0() = [0]
         [2]
         [1]
   a(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
               [0 1 3]      [0 0 0]      [0]
               [0 0 1]      [0 0 0]      [0]

Hurray, we answered YES(?,O(n^3))

Tool TRI

Execution Time	1.490865ms
Answer	YES(?,O(n^3))
Input	Secret 06 TRS 6

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  a(y, c(b(a(0(), x), 0()))) -> b(a(c(b(0(), y)), x), 0())
     , a(y, x) -> y
     , b(x, y) -> c(a(c(y), a(0(), x)))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^3))

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

Hurray, we answered YES(?,O(n^3))

Tool TRI2

Execution Time	0.336967ms
Answer	MAYBE
Input	Secret 06 TRS 6

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a(y, c(b(a(0(), x), 0()))) -> b(a(c(b(0(), y)), x), 0())
     , a(y, x) -> y
     , b(x, y) -> c(a(c(y), a(0(), x)))}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..