Problem Zantema 06 while2

Tool Bounds

Execution Time60.036106ms
Answer
TIMEOUT
InputZantema 06 while2

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time60.04687ms
Answer
TIMEOUT
InputZantema 06 while2

stdout:

TIMEOUT

Statistics:
Number of monomials: 1830
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time60.03793ms
Answer
TIMEOUT
InputZantema 06 while2

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool IDA

Execution Time60.053368ms
Answer
TIMEOUT
InputZantema 06 while2

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool TRI

Execution Time2.776066ms
Answer
YES(?,O(n^3))
InputZantema 06 while2

stdout:

YES(?,O(n^3))

We consider the following Problem:

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

Certificate: YES(?,O(n^3))

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

Hurray, we answered YES(?,O(n^3))

Tool TRI2

Execution Time0.19306993ms
Answer
MAYBE
InputZantema 06 while2

stdout:

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..