Problem CSR 04 Ex23 Luc06

Tool Bounds

Execution Time	2.6288033e-2ms
Answer	YES(?,O(n^1))
Input	CSR 04 Ex23 Luc06

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {f(f(a())) -> c(f(g(f(a()))))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^1))

Proof:
  The problem is match-bounded by 1.
  The enriched problem is compatible with the following automaton:
  {  f_0(1) -> 1
   , f_0(2) -> 1
   , f_0(3) -> 1
   , f_0(4) -> 1
   , f_1(6) -> 5
   , f_1(8) -> 7
   , a_0() -> 2
   , a_1() -> 8
   , c_0(1) -> 3
   , c_0(2) -> 3
   , c_0(3) -> 3
   , c_0(4) -> 3
   , c_1(5) -> 1
   , g_0(1) -> 4
   , g_0(2) -> 4
   , g_0(3) -> 4
   , g_0(4) -> 4
   , g_1(7) -> 6}

Hurray, we answered YES(?,O(n^1))

Tool CDI

Execution Time	60.040184ms
Answer	TIMEOUT
Input	CSR 04 Ex23 Luc06

stdout:

TIMEOUT

Statistics:
Number of monomials: 2478
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.67759585ms
Answer	YES(?,O(n^2))
Input	CSR 04 Ex23 Luc06

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {f(f(a())) -> c(f(g(f(a()))))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1) = [1 2] x1 + [0]
           [0 1]      [0]
   a() = [0]
         [1]
   c(x1) = [1 0] x1 + [1]
           [0 0]      [1]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool IDA

Execution Time	0.81231785ms
Answer	YES(?,O(n^2))
Input	CSR 04 Ex23 Luc06

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {f(f(a())) -> c(f(g(f(a()))))}
  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:
   f(x1) = [1 2] x1 + [0]
           [0 1]      [0]
   a() = [0]
         [1]
   c(x1) = [1 0] x1 + [1]
           [0 0]      [1]
   g(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool TRI

Execution Time	0.19386888ms
Answer	YES(?,O(n^1))
Input	CSR 04 Ex23 Luc06

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {f(f(a())) -> c(f(g(f(a()))))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^1))

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

Hurray, we answered YES(?,O(n^1))

Tool TRI2

Execution Time	0.15316701ms
Answer	YES(?,O(n^2))
Input	CSR 04 Ex23 Luc06

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {f(f(a())) -> c(f(g(f(a()))))}
  StartTerms: all
  Strategy: none

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

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

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