- : unit = ()
- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] f(nil) -> nil
[2] f(.(nil,y)) -> .(nil,f(y))
[3] f(.(.(x,y),z)) -> f(.(x,.(y,z)))
[4] g(nil) -> nil
[5] g(.(x,nil)) -> .(g(x),nil)
[6] g(.(x,.(y,z))) -> g(.(.(x,y),z))


Sub problem: 
guided: 

DP termination of:
<Marked_f(.(nil,y)) , Marked_f(y)>
<Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))>
<Marked_g(.(x,nil)) , Marked_g(x)>
<Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))> 
      --> <Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))>
  <Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))> 
     --> <Marked_f(.(nil,y)) , Marked_f(y)>
  <Marked_f(.(nil,y)) , Marked_f(y)> 
     --> <Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))>
  <Marked_f(.(nil,y)) , Marked_f(y)> --> <Marked_f(.(nil,y)) , Marked_f(y)>
}

{  <Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))> 
      --> <Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))>
  <Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))> 
     --> <Marked_g(.(x,nil)) , Marked_g(x)>
  <Marked_g(.(x,nil)) , Marked_g(x)> 
     --> <Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))>
  <Marked_g(.(x,nil)) , Marked_g(x)> --> <Marked_g(.(x,nil)) , Marked_g(x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(nil) >= nil ;
  f(.(nil,y)) >= .(nil,f(y)) ;
  f(.(.(x,y),z)) >= f(.(x,.(y,z))) ;
  g(nil) >= nil ;
  g(.(x,nil)) >= .(g(x),nil) ;
  g(.(x,.(y,z))) >= g(.(.(x,y),z)) ;
  Marked_f(.(nil,y)) >= Marked_f(y) ;
  Marked_f(.(.(x,y),z)) >= Marked_f(.(x,.(y,z))) ;
 }
 + Disjunctions:{ 
{
  Marked_f(.(nil,y)) > Marked_f(y) ;
 }
{
  Marked_f(.(.(x,y),z)) > Marked_f(.(x,.(y,z))) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(nil) >= nil
constraint: f(.(nil,y)) >= .(nil,f(y))
constraint: f(.(.(x,y),z)) >= f(.(x,.(y,z)))
constraint: g(nil) >= nil
constraint: g(.(x,nil)) >= .(g(x),nil)
constraint: g(.(x,.(y,z))) >= g(.(.(x,y),z))
constraint: Marked_f(.(nil,y)) >= Marked_f(y)
constraint: Marked_f(.(.(x,y),z)) >= Marked_f(.(x,.(y,z)))
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(nil) >= nil ;
  f(.(nil,y)) >= .(nil,f(y)) ;
  f(.(.(x,y),z)) >= f(.(x,.(y,z))) ;
  g(nil) >= nil ;
  g(.(x,nil)) >= .(g(x),nil) ;
  g(.(x,.(y,z))) >= g(.(.(x,y),z)) ;
  Marked_g(.(x,nil)) >= Marked_g(x) ;
  Marked_g(.(x,.(y,z))) >= Marked_g(.(.(x,y),z)) ;
 }
 + Disjunctions:{ 
{
  Marked_g(.(x,nil)) > Marked_g(x) ;
 }
{
  Marked_g(.(x,.(y,z))) > Marked_g(.(.(x,y),z)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(nil) >= nil
constraint: f(.(nil,y)) >= .(nil,f(y))
constraint: f(.(.(x,y),z)) >= f(.(x,.(y,z)))
constraint: g(nil) >= nil
constraint: g(.(x,nil)) >= .(g(x),nil)
constraint: g(.(x,.(y,z))) >= g(.(.(x,y),z))
constraint: Marked_g(.(x,nil)) >= Marked_g(x)
constraint: Marked_g(.(x,.(y,z))) >= Marked_g(.(.(x,y),z))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))> 
      --> <Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(nil) >= nil ;
  f(.(nil,y)) >= .(nil,f(y)) ;
  f(.(.(x,y),z)) >= f(.(x,.(y,z))) ;
  g(nil) >= nil ;
  g(.(x,nil)) >= .(g(x),nil) ;
  g(.(x,.(y,z))) >= g(.(.(x,y),z)) ;
  Marked_f(.(.(x,y),z)) >= Marked_f(.(x,.(y,z))) ;
 }
 + Disjunctions:{ 
{
  Marked_f(.(.(x,y),z)) > Marked_f(.(x,.(y,z))) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(nil) >= nil
constraint: f(.(nil,y)) >= .(nil,f(y))
constraint: f(.(.(x,y),z)) >= f(.(x,.(y,z)))
constraint: g(nil) >= nil
constraint: g(.(x,nil)) >= .(g(x),nil)
constraint: g(.(x,.(y,z))) >= g(.(.(x,y),z))
constraint: Marked_f(.(.(x,y),z)) >= Marked_f(.(x,.(y,z)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))> 
      --> <Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(nil) >= nil ;
  f(.(nil,y)) >= .(nil,f(y)) ;
  f(.(.(x,y),z)) >= f(.(x,.(y,z))) ;
  g(nil) >= nil ;
  g(.(x,nil)) >= .(g(x),nil) ;
  g(.(x,.(y,z))) >= g(.(.(x,y),z)) ;
  Marked_g(.(x,.(y,z))) >= Marked_g(.(.(x,y),z)) ;
 }
 + Disjunctions:{ 
{
  Marked_g(.(x,.(y,z))) > Marked_g(.(.(x,y),z)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(nil) >= nil
constraint: f(.(nil,y)) >= .(nil,f(y))
constraint: f(.(.(x,y),z)) >= f(.(x,.(y,z)))
constraint: g(nil) >= nil
constraint: g(.(x,nil)) >= .(g(x),nil)
constraint: g(.(x,.(y,z))) >= g(.(.(x,y),z))
constraint: Marked_g(.(x,.(y,z))) >= Marked_g(.(.(x,y),z))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(nil) -> nil
[2] f(.(nil,y)) -> .(nil,f(y))
[3] f(.(.(x,y),z)) -> f(.(x,.(y,z)))
[4] g(nil) -> nil
[5] g(.(x,nil)) -> .(g(x),nil)
[6] g(.(x,.(y,z))) -> g(.(.(x,y),z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(.(nil,y)) , Marked_f(y)>
<Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))>
<Marked_g(.(x,nil)) , Marked_g(x)>
<Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(.(nil,y)) , Marked_f(y)>
<Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ nil ] () = 2; 
 [ . ] (X0,X1) = 1*X1 + 1*X0; 
 [ f ] (X0) = 2*X0; 
 [ Marked_f ] (X0) = 1*X0; 
 [ g ] (X0) = 1*X0; 
 removing <Marked_f(.(nil,y)),Marked_f(y)>
 [ {
      
     DP termination of:
     <Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(.(.(x,y),z)) , Marked_f(.(x,.(y,z)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
      [ nil ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ . ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ f ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_f ] (X0) = [ [ 1 , 0 , 0 ] [ 1 , 0 , 1 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ g ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_g(.(x,nil)) , Marked_g(x)>
<Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ nil ] () = 1; 
 [ Marked_g ] (X0) = 1*X0; 
 [ . ] (X0,X1) = 1*X1 + 1*X0; 
 [ f ] (X0) = 2*X0; 
 [ g ] (X0) = 1*X0; 
 removing <Marked_g(.(x,nil)),Marked_g(x)>
 [ {
      
     DP termination of:
     <Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_g(.(x,.(y,z))) , Marked_g(.(.(x,y),z))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
      [ nil ] () = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_g ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ . ] (X0,X1) = [ [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + 
[ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ f ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 1 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ g ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 1.706938 seconds (real time)
Cime Exit Status: 0