Problem Maude 06 PALINDROME nosorts-noand

Tool Bounds

Execution Time	60.033398ms
Answer	TIMEOUT
Input	Maude 06 PALINDROME nosorts-noand

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  isNePal(__(I, __(P, I))) -> U11(tt())
     , U12(tt()) -> tt()
     , U11(tt()) -> U12(tt())
     , __(nil(), X) -> X
     , __(X, nil()) -> X
     , __(__(X, Y), Z) -> __(X, __(Y, Z))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.75470686ms
Answer	MAYBE
Input	Maude 06 PALINDROME nosorts-noand

stdout:

MAYBE

Statistics:
Number of monomials: 362
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.3502419ms
Answer	YES(?,O(n^2))
Input	Maude 06 PALINDROME nosorts-noand

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  isNePal(__(I, __(P, I))) -> U11(tt())
     , U12(tt()) -> tt()
     , U11(tt()) -> U12(tt())
     , __(nil(), X) -> X
     , __(X, nil()) -> X
     , __(__(X, Y), Z) -> __(X, __(Y, Z))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   __(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                [0 1]      [0 1]      [2]
   nil() = [1]
           [0]
   U11(x1) = [1 0] x1 + [2]
             [0 0]      [0]
   tt() = [0]
          [0]
   U12(x1) = [1 0] x1 + [1]
             [0 0]      [0]
   isNePal(x1) = [1 0] x1 + [3]
                 [0 0]      [3]

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

Tool IDA

Execution Time	0.54777384ms
Answer	YES(?,O(n^2))
Input	Maude 06 PALINDROME nosorts-noand

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  isNePal(__(I, __(P, I))) -> U11(tt())
     , U12(tt()) -> tt()
     , U11(tt()) -> U12(tt())
     , __(nil(), X) -> X
     , __(X, nil()) -> X
     , __(__(X, Y), Z) -> __(X, __(Y, Z))}
  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:
   __(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                [0 1]      [0 1]      [2]
   nil() = [1]
           [0]
   U11(x1) = [1 0] x1 + [2]
             [0 0]      [0]
   tt() = [0]
          [0]
   U12(x1) = [1 0] x1 + [1]
             [0 0]      [0]
   isNePal(x1) = [1 0] x1 + [3]
                 [0 0]      [3]

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

Tool TRI

Execution Time	0.16134906ms
Answer	YES(?,O(n^2))
Input	Maude 06 PALINDROME nosorts-noand

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  isNePal(__(I, __(P, I))) -> U11(tt())
     , U12(tt()) -> tt()
     , U11(tt()) -> U12(tt())
     , __(nil(), X) -> X
     , __(X, nil()) -> X
     , __(__(X, Y), Z) -> __(X, __(Y, Z))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   __(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                [0 1]      [0 1]      [2]
   nil() = [1]
           [0]
   U11(x1) = [1 1] x1 + [3]
             [0 1]      [3]
   tt() = [0]
          [1]
   U12(x1) = [1 0] x1 + [1]
             [0 1]      [3]
   isNePal(x1) = [1 2] x1 + [3]
                 [0 1]      [3]

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

Tool TRI2

Execution Time	0.115991116ms
Answer	YES(?,O(n^2))
Input	Maude 06 PALINDROME nosorts-noand

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  isNePal(__(I, __(P, I))) -> U11(tt())
     , U12(tt()) -> tt()
     , U11(tt()) -> U12(tt())
     , __(nil(), X) -> X
     , __(X, nil()) -> X
     , __(__(X, Y), Z) -> __(X, __(Y, Z))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   __(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                [0 1]      [0 1]      [2]
   nil() = [1]
           [0]
   U11(x1) = [1 3] x1 + [2]
             [0 1]      [3]
   tt() = [0]
          [0]
   U12(x1) = [1 3] x1 + [1]
             [0 1]      [3]
   isNePal(x1) = [1 0] x1 + [3]
                 [0 1]      [3]

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