Tool Bounds
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
stdout:
MAYBE
Statistics:
Number of monomials: 534
Last formula building started for bound 3
Last SAT solving started for bound 3Tool EDA
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
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
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
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))