Problem Transformed CSR 04 Ex4 7 77 Bor03 GM

Tool Bounds

Execution Time	60.032635ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex4 7 77 Bor03 GM

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  a__tail(X) -> tail(X)
     , a__zeros() -> zeros()
     , mark(0()) -> 0()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(zeros()) -> a__zeros()
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__zeros() -> cons(0(), zeros())}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.3782301ms
Answer	MAYBE
Input	Transformed CSR 04 Ex4 7 77 Bor03 GM

stdout:

MAYBE

Statistics:
Number of monomials: 246
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.4456811ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 77 Bor03 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__tail(X) -> tail(X)
     , a__zeros() -> zeros()
     , mark(0()) -> 0()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(zeros()) -> a__zeros()
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__zeros() -> cons(0(), zeros())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   a__zeros() = [3]
                [3]
   0() = [0]
         [0]
   zeros() = [1]
             [1]
   cons(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
                  [0 1]      [0 1]      [2]
   a__tail(x1) = [1 1] x1 + [2]
                 [0 1]      [3]
   mark(x1) = [1 2] x1 + [1]
              [0 1]      [3]
   tail(x1) = [1 1] x1 + [0]
              [0 1]      [3]

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

Tool IDA

Execution Time	0.62275696ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 77 Bor03 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__tail(X) -> tail(X)
     , a__zeros() -> zeros()
     , mark(0()) -> 0()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(zeros()) -> a__zeros()
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__zeros() -> cons(0(), zeros())}
  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:
   a__zeros() = [3]
                [3]
   0() = [0]
         [1]
   zeros() = [0]
             [1]
   cons(x1, x2) = [1 0] x1 + [1 1] x2 + [1]
                  [0 1]      [0 1]      [1]
   a__tail(x1) = [1 0] x1 + [3]
                 [0 1]      [3]
   mark(x1) = [1 1] x1 + [3]
              [0 1]      [3]
   tail(x1) = [1 0] x1 + [2]
              [0 1]      [3]

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

Tool TRI

Execution Time	0.18443394ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 77 Bor03 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__tail(X) -> tail(X)
     , a__zeros() -> zeros()
     , mark(0()) -> 0()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(zeros()) -> a__zeros()
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__zeros() -> cons(0(), zeros())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a__zeros() = [1]
                [2]
   0() = [0]
         [0]
   zeros() = [0]
             [1]
   cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [1]
   a__tail(x1) = [1 1] x1 + [3]
                 [0 1]      [3]
   mark(x1) = [1 1] x1 + [1]
              [0 1]      [1]
   tail(x1) = [1 1] x1 + [2]
              [0 1]      [3]

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

Tool TRI2

Execution Time	0.12798381ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex4 7 77 Bor03 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__tail(X) -> tail(X)
     , a__zeros() -> zeros()
     , mark(0()) -> 0()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(zeros()) -> a__zeros()
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__zeros() -> cons(0(), zeros())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a__zeros() = [3]
                [2]
   0() = [0]
         [0]
   zeros() = [1]
             [1]
   cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [1]
   a__tail(x1) = [1 3] x1 + [2]
                 [0 1]      [2]
   mark(x1) = [1 3] x1 + [1]
              [0 1]      [1]
   tail(x1) = [1 3] x1 + [0]
              [0 1]      [2]

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