Problem Transformed CSR 04 Ex1 Zan97 GM

Tool Bounds

Execution Time	3.9724827e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex1 Zan97 GM

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a__c() -> c()
     , a__h(X) -> h(X)
     , a__g(X) -> g(X)
     , mark(d()) -> d()
     , mark(c()) -> a__c()
     , mark(h(X)) -> a__h(X)
     , mark(g(X)) -> a__g(X)
     , a__h(d()) -> a__g(c())
     , a__c() -> d()
     , a__g(X) -> a__h(X)}
  StartTerms: all
  Strategy: none

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

Proof:
  The problem is match-bounded by 5.
  The enriched problem is compatible with the following automaton:
  {  a__g_0(1) -> 1
   , a__g_1(1) -> 1
   , a__g_1(2) -> 1
   , a__g_1(3) -> 1
   , a__g_2(2) -> 1
   , a__g_3(3) -> 1
   , a__h_0(1) -> 1
   , a__h_1(1) -> 1
   , a__h_1(2) -> 1
   , a__h_1(3) -> 1
   , a__h_2(1) -> 1
   , a__h_2(2) -> 1
   , a__h_2(3) -> 1
   , a__h_3(2) -> 1
   , a__h_4(3) -> 1
   , a__c_0() -> 1
   , a__c_1() -> 1
   , d_0() -> 1
   , d_1() -> 1
   , d_2() -> 1
   , c_0() -> 1
   , c_1() -> 1
   , c_2() -> 1
   , c_2() -> 2
   , c_3() -> 3
   , g_0(1) -> 1
   , g_1(1) -> 1
   , g_2(1) -> 1
   , g_2(2) -> 1
   , g_2(3) -> 1
   , g_3(2) -> 1
   , g_4(3) -> 1
   , mark_0(1) -> 1
   , h_0(1) -> 1
   , h_1(1) -> 1
   , h_2(1) -> 1
   , h_2(2) -> 1
   , h_2(3) -> 1
   , h_3(1) -> 1
   , h_3(2) -> 1
   , h_3(3) -> 1
   , h_4(2) -> 1
   , h_5(3) -> 1}

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

Tool CDI

Execution Time	0.15255189ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex1 Zan97 GM

stdout:

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

This TRS is terminating using the deltarestricted interpretation
h(delta, X0) =  + 0*X0 + 0 + 1*X0*delta + 0*delta
g(delta, X0) =  + 0*X0 + 0 + 1*X0*delta + 2*delta
mark(delta, X0) =  + 1*X0 + 3 + 1*X0*delta + 3*delta
c(delta) =  + 1 + 0*delta
a__c(delta) =  + 3 + 1*delta
d(delta) =  + 3 + 0*delta
a__g(delta, X0) =  + 0*X0 + 0 + 1*X0*delta + 3*delta
a__h(delta, X0) =  + 0*X0 + 0 + 1*X0*delta + 2*delta
h_tau_1(delta) = delta/(0 + 1 * delta)
g_tau_1(delta) = delta/(0 + 1 * delta)
mark_tau_1(delta) = delta/(1 + 1 * delta)
a__g_tau_1(delta) = delta/(0 + 1 * delta)
a__h_tau_1(delta) = delta/(0 + 1 * delta)

Time: 0.111393 seconds
Statistics:
Number of monomials: 188
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.2555492ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex1 Zan97 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__c() -> c()
     , a__h(X) -> h(X)
     , a__g(X) -> g(X)
     , mark(d()) -> d()
     , mark(c()) -> a__c()
     , mark(h(X)) -> a__h(X)
     , mark(g(X)) -> a__g(X)
     , a__h(d()) -> a__g(c())
     , a__c() -> d()
     , a__g(X) -> a__h(X)}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   a__g(x1) = [1 3] x1 + [3]
              [0 0]      [0]
   a__h(x1) = [1 3] x1 + [2]
              [0 0]      [0]
   a__c() = [3]
            [2]
   d() = [2]
         [2]
   c() = [1]
         [0]
   g(x1) = [1 3] x1 + [2]
           [0 0]      [0]
   mark(x1) = [1 2] x1 + [3]
              [0 0]      [2]
   h(x1) = [1 3] x1 + [0]
           [0 0]      [0]

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

Tool IDA

Execution Time	0.525373ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex1 Zan97 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__c() -> c()
     , a__h(X) -> h(X)
     , a__g(X) -> g(X)
     , mark(d()) -> d()
     , mark(c()) -> a__c()
     , mark(h(X)) -> a__h(X)
     , mark(g(X)) -> a__g(X)
     , a__h(d()) -> a__g(c())
     , a__c() -> d()
     , a__g(X) -> a__h(X)}
  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__g(x1) = [1 3] x1 + [3]
              [0 0]      [1]
   a__h(x1) = [1 3] x1 + [2]
              [0 0]      [1]
   a__c() = [1]
            [3]
   d() = [0]
         [3]
   c() = [0]
         [2]
   g(x1) = [1 3] x1 + [1]
           [0 0]      [1]
   mark(x1) = [1 2] x1 + [1]
              [0 0]      [3]
   h(x1) = [1 3] x1 + [0]
           [0 0]      [1]

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

Tool TRI

Execution Time	0.138057ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex1 Zan97 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__c() -> c()
     , a__h(X) -> h(X)
     , a__g(X) -> g(X)
     , mark(d()) -> d()
     , mark(c()) -> a__c()
     , mark(h(X)) -> a__h(X)
     , mark(g(X)) -> a__g(X)
     , a__h(d()) -> a__g(c())
     , a__c() -> d()
     , a__g(X) -> a__h(X)}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.10061407ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex1 Zan97 GM

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a__c() -> c()
     , a__h(X) -> h(X)
     , a__g(X) -> g(X)
     , mark(d()) -> d()
     , mark(c()) -> a__c()
     , mark(h(X)) -> a__h(X)
     , mark(g(X)) -> a__g(X)
     , a__h(d()) -> a__g(c())
     , a__c() -> d()
     , a__g(X) -> a__h(X)}
  StartTerms: all
  Strategy: none

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

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

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