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Welcome to CiME version 2.02 - Built on 14/04/2004 13:29:51

- : unit = ()
- : unit = ()
X : variable_set = <variable set>

F : signature = <signature>
R : HTRS = { zeros -> cons(0,zeros),
             and(tt,X) -> X,
             length(nil) -> 0,
             length(cons(N,L)) -> s(length(L)),
             take(0,IL) -> nil,
             take(s(M),cons(N,IL)) -> cons(N,take(M,IL)) } (6 rules)
Termination now uses minimal decomposition
- : unit = ()
Entering the termination expert for modules. Verbose level = 0
Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ take(0,V_0) -> nil,
  take(s(V_2),cons(V_3,V_0)) -> cons(V_3,take(V_2,V_0)) } (2 rules)

The dependency graph is
(1 nodes)
Checking each of the 1 strongly connected components :
Checking component 1
Trying simple graph criterion.
Trying to solve the following constraints:
(3 termination constraints)
Search parameters: linear polynomials, coefficient bound is 2.
Solution found for these constraints:
[0] = 0; 
[cons](X0,X1) = 0; 
[nil] = 0; 
[s](X0) = X0 + 1; 
[take](X0,X1) = 0; 
['take`](X0,X1) = X0; 


Checking module:
{ length(cons(V_3,V_1)) -> s(length(V_1)),
  length(nil) -> 0 } (2 rules)

The dependency graph is
(1 nodes)
Checking each of the 1 strongly connected components :
Checking component 1
Trying simple graph criterion.
Trying to solve the following constraints:
(3 termination constraints)
Search parameters: linear polynomials, coefficient bound is 2.
Solution found for these constraints:
[0] = 0; 
[cons](X0,X1) = X1 + 1; 
[nil] = 0; 
[s](X0) = 0; 
[length](X0) = 0; 
['length`](X0) = X0; 


Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ and(tt,V_4) -> V_4 } (1 rules)

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ zeros -> cons(0,zeros) } (1 rules)

The dependency graph is
(1 nodes)
Checking each of the 1 strongly connected components :
Checking component 1
Trying simple graph criterion.
Trying to solve the following constraints:
(2 termination constraints)
Search parameters: linear polynomials, coefficient bound is 2.
No solution found for these parameters.
Search parameters: simple polynomials, coefficient bound is 3.
No solution found for these parameters.
No solution found for these constraints.
Trying strongly connected part criterion.
Trying to solve the following constraints:
(2 termination constraints)
Search parameters: linear polynomials, coefficient bound is 2.
No solution found for these parameters.
Search parameters: simple polynomials, coefficient bound is 3.
No solution found for these parameters.
No solution found for these constraints.
No modular termination proof found.
- : unit = ()
The last proof attempt failed.
- : unit = ()

Quitting.
Standard error: