Problem Mixed TRS jones1

Tool Bounds

Execution Time	60.03034ms
Answer	TIMEOUT
Input	Mixed TRS jones1

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  r1(cons(x, k), a) -> r1(k, cons(x, a))
     , r1(empty(), a) -> a
     , rev(ls) -> r1(ls, empty())}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.11983681ms
Answer	YES(?,O(n^2))
Input	Mixed TRS jones1

stdout:

YES(?,O(n^2))
QUADRATIC upper bound on the derivational complexity

This TRS is terminating using the deltarestricted interpretation
cons(delta, X1, X0) =  + 1*X0 + 0*X1 + 2 + 0*X0*delta + 1*X1*delta + 0*delta
rev(delta, X0) =  + 1*X0 + 3 + 2*X0*delta + 1*delta
empty(delta) =  + 3 + 0*delta
r1(delta, X1, X0) =  + 1*X0 + 1*X1 + 0 + 0*X0*delta + 2*X1*delta + 0*delta
cons_tau_1(delta) = delta/(0 + 1 * delta)
cons_tau_2(delta) = delta/(1 + 0 * delta)
rev_tau_1(delta) = delta/(1 + 2 * delta)
r1_tau_1(delta) = delta/(1 + 2 * delta)
r1_tau_2(delta) = delta/(1 + 0 * delta)

Time: 0.079819 seconds
Statistics:
Number of monomials: 136
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.2745192ms
Answer	YES(?,O(n^2))
Input	Mixed TRS jones1

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  r1(cons(x, k), a) -> r1(k, cons(x, a))
     , r1(empty(), a) -> a
     , rev(ls) -> r1(ls, empty())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   rev(x1) = [1 2] x1 + [3]
             [0 1]      [3]
   empty() = [0]
             [1]
   r1(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                [0 1]      [0 1]      [2]
   cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 0]      [0 1]      [2]

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

Tool IDA

Execution Time	0.52249ms
Answer	YES(?,O(n^2))
Input	Mixed TRS jones1

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  r1(cons(x, k), a) -> r1(k, cons(x, a))
     , r1(empty(), a) -> a
     , rev(ls) -> r1(ls, empty())}
  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:
   rev(x1) = [1 2] x1 + [3]
             [0 1]      [3]
   empty() = [0]
             [1]
   r1(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                [0 1]      [0 1]      [2]
   cons(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 0]      [0 1]      [2]

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

Tool TRI

Execution Time	0.13653994ms
Answer	YES(?,O(n^2))
Input	Mixed TRS jones1

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  r1(cons(x, k), a) -> r1(k, cons(x, a))
     , r1(empty(), a) -> a
     , rev(ls) -> r1(ls, empty())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   rev(x1) = [1 3] x1 + [3]
             [0 1]      [3]
   empty() = [0]
             [0]
   r1(x1, x2) = [1 2] x1 + [1 0] x2 + [1]
                [0 1]      [0 1]      [2]
   cons(x1, x2) = [1 1] x1 + [1 0] x2 + [3]
                  [0 0]      [0 1]      [2]

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

Tool TRI2

Execution Time	0.113845825ms
Answer	YES(?,O(n^2))
Input	Mixed TRS jones1

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  r1(cons(x, k), a) -> r1(k, cons(x, a))
     , r1(empty(), a) -> a
     , rev(ls) -> r1(ls, empty())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   rev(x1) = [1 3] x1 + [3]
             [0 1]      [3]
   empty() = [0]
             [0]
   r1(x1, x2) = [1 2] x1 + [1 0] x2 + [1]
                [0 1]      [0 1]      [2]
   cons(x1, x2) = [1 1] x1 + [1 0] x2 + [3]
                  [0 0]      [0 1]      [2]

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