Problem Transformed CSR 04 Ex6 GM04 GM

Tool Bounds

Execution Time	4.8305035e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 GM04 GM

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , a__c() -> c()
     , mark(g(X)) -> g(X)
     , mark(f(X)) -> a__f(X)
     , mark(c()) -> a__c()
     , a__f(g(X)) -> g(X)
     , a__c() -> a__f(g(c()))}
  StartTerms: all
  Strategy: none

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

Proof:
  The problem is match-bounded by 3.
  The enriched problem is compatible with the following automaton:
  {  a__c_0() -> 1
   , a__c_1() -> 5
   , c_0() -> 2
   , c_1() -> 1
   , c_2() -> 5
   , c_2() -> 8
   , g_0(1) -> 3
   , g_0(2) -> 3
   , g_0(3) -> 3
   , g_0(4) -> 3
   , g_0(5) -> 3
   , g_0(6) -> 3
   , g_1(1) -> 4
   , g_1(1) -> 5
   , g_1(2) -> 4
   , g_1(2) -> 5
   , g_1(3) -> 4
   , g_1(3) -> 5
   , g_1(4) -> 4
   , g_1(4) -> 5
   , g_1(5) -> 4
   , g_1(5) -> 5
   , g_1(6) -> 4
   , g_1(6) -> 5
   , g_1(8) -> 4
   , g_1(8) -> 5
   , g_2(1) -> 1
   , g_2(1) -> 5
   , g_2(2) -> 1
   , g_2(2) -> 5
   , g_2(3) -> 1
   , g_2(3) -> 5
   , g_2(4) -> 1
   , g_2(4) -> 5
   , g_2(5) -> 1
   , g_2(5) -> 5
   , g_2(6) -> 1
   , g_2(6) -> 5
   , g_2(8) -> 1
   , g_2(8) -> 5
   , g_2(8) -> 7
   , g_3(8) -> 5
   , a__f_0(1) -> 4
   , a__f_0(2) -> 4
   , a__f_0(3) -> 4
   , a__f_0(4) -> 4
   , a__f_0(5) -> 4
   , a__f_0(6) -> 4
   , a__f_1(1) -> 5
   , a__f_1(2) -> 5
   , a__f_1(3) -> 5
   , a__f_1(4) -> 5
   , a__f_1(5) -> 1
   , a__f_1(5) -> 5
   , a__f_1(6) -> 5
   , a__f_1(7) -> 5
   , a__f_2(7) -> 5
   , mark_0(1) -> 5
   , mark_0(2) -> 5
   , mark_0(3) -> 5
   , mark_0(4) -> 5
   , mark_0(5) -> 5
   , mark_0(6) -> 5
   , f_0(1) -> 6
   , f_0(2) -> 6
   , f_0(3) -> 6
   , f_0(4) -> 6
   , f_0(5) -> 6
   , f_0(6) -> 6
   , f_1(1) -> 4
   , f_1(2) -> 4
   , f_1(3) -> 4
   , f_1(4) -> 4
   , f_1(5) -> 4
   , f_1(6) -> 4
   , f_2(1) -> 5
   , f_2(2) -> 5
   , f_2(3) -> 5
   , f_2(4) -> 5
   , f_2(5) -> 1
   , f_2(5) -> 5
   , f_2(6) -> 5
   , f_2(7) -> 5
   , f_3(7) -> 5}

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

Tool CDI

Execution Time	0.21845698ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex6 GM04 GM

stdout:

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

This TRS is terminating using the deltarestricted interpretation
f(delta, X0) =  + 1*X0 + 1 + 0*X0*delta + 0*delta
mark(delta, X0) =  + 1*X0 + 3 + 0*X0*delta + 3*delta
a__c(delta) =  + 2 + 2*delta
c(delta) =  + 0 + 0*delta
g(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 0*delta
a__f(delta, X0) =  + 1*X0 + 1 + 0*X0*delta + 1*delta
f_tau_1(delta) = delta/(1 + 0 * delta)
mark_tau_1(delta) = delta/(1 + 0 * delta)
g_tau_1(delta) = delta/(1 + 0 * delta)
a__f_tau_1(delta) = delta/(1 + 0 * delta)

Time: 0.177175 seconds
Statistics:
Number of monomials: 163
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.12909484ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 GM04 GM

stdout:

Tool IDA

Execution Time	0.19217896ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 GM04 GM

stdout:

Tool TRI

Execution Time	8.455706e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 GM04 GM

stdout:

Tool TRI2

Execution Time	0.10259199ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex6 GM04 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__f(X) -> f(X)
     , a__c() -> c()
     , mark(g(X)) -> g(X)
     , mark(f(X)) -> a__f(X)
     , mark(c()) -> a__c()
     , a__f(g(X)) -> g(X)
     , a__c() -> a__f(g(c()))}
  StartTerms: all
  Strategy: none

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

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

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