Problem Zantema 04 z093

Tool Bounds

Execution Time8.546184ms
Answer
MAYBE
InputZantema 04 z093

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a(a(a(a(x1)))) -> b(c(x1))
     , c(b(x1)) -> a(a(a(x1)))
     , b(c(x1)) -> c(b(x1))}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  None of the processors succeeded.
  

Arrrr..

Tool CDI

Execution Time4.8115897ms
Answer
MAYBE
InputZantema 04 z093

stdout:

MAYBE

Statistics:
Number of monomials: 534
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time0.5053339ms
Answer
YES(?,O(n^2))
InputZantema 04 z093

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a(a(a(a(x1)))) -> b(c(x1))
     , c(b(x1)) -> a(a(a(x1)))
     , b(c(x1)) -> c(b(x1))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

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

Hurray, we answered YES(?,O(n^2))

Tool IDA

Execution Time0.6509881ms
Answer
YES(?,O(n^2))
InputZantema 04 z093

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a(a(a(a(x1)))) -> b(c(x1))
     , c(b(x1)) -> a(a(a(x1)))
     , b(c(x1)) -> c(b(x1))}
  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:
   c(x1) = [1 3] x1 + [2]
           [0 1]      [2]
   b(x1) = [1 3] x1 + [2]
           [0 1]      [1]
   a(x1) = [1 2] x1 + [0]
           [0 1]      [1]

Hurray, we answered YES(?,O(n^2))

Tool TRI

Execution Time0.179492ms
Answer
YES(?,O(n^2))
InputZantema 04 z093

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a(a(a(a(x1)))) -> b(c(x1))
     , c(b(x1)) -> a(a(a(x1)))
     , b(c(x1)) -> c(b(x1))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

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

Hurray, we answered YES(?,O(n^2))

Tool TRI2

Execution Time0.1363461ms
Answer
YES(?,O(n^2))
InputZantema 04 z093

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a(a(a(a(x1)))) -> b(c(x1))
     , c(b(x1)) -> a(a(a(x1)))
     , b(c(x1)) -> c(b(x1))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

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

Hurray, we answered YES(?,O(n^2))