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

TRS termination of:
[1] h(x,c(y,z)) -> h(c(s(y),x),z)
[2] h(c(s(x),c(s(0),y)),z) -> h(y,c(s(0),c(x,z)))


Sub problem: 
guided: 

DP termination of:
<Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)>
<Marked_h(c(s(x),c(s(0),y)),z) , Marked_h(y,c(s(0),c(x,z)))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_h(c(s(x),c(s(0),y)),z) , Marked_h(y,c(s(0),c(x,z)))> 
      --> <Marked_h(c(s(x),c(s(0),y)),z) , Marked_h(y,c(s(0),c(x,z)))>
  <Marked_h(c(s(x),c(s(0),y)),z) , Marked_h(y,c(s(0),c(x,z)))> 
     --> <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)>
  <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)> 
     --> <Marked_h(c(s(x),c(s(0),y)),z) , Marked_h(y,c(s(0),c(x,z)))>
  <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)> 
     --> <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  h(c(s(x),c(s(0),y)),z) >= h(y,c(s(0),c(x,z))) ;
  h(x,c(y,z)) >= h(c(s(y),x),z) ;
  Marked_h(c(s(x),c(s(0),y)),z) >= Marked_h(y,c(s(0),c(x,z))) ;
  Marked_h(x,c(y,z)) >= Marked_h(c(s(y),x),z) ;
 }
 + Disjunctions:{ 
{
  Marked_h(c(s(x),c(s(0),y)),z) > Marked_h(y,c(s(0),c(x,z))) ;
 }
{
  Marked_h(x,c(y,z)) > Marked_h(c(s(y),x),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 : 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: h(c(s(x),c(s(0),y)),z) >= h(y,c(s(0),c(x,z)))
constraint: h(x,c(y,z)) >= h(c(s(y),x),z)
constraint: Marked_h(c(s(x),c(s(0),y)),z) >= Marked_h(y,c(s(0),c(x,z)))
constraint: Marked_h(x,c(y,z)) >= Marked_h(c(s(y),x),z)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)> 
      --> <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_h -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] h(x,c(y,z)) -> h(c(s(y),x),z)
[2] h(c(s(x),c(s(0),y)),z) -> h(y,c(s(0),c(x,z)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)>
<Marked_h(c(s(x),c(s(0),y)),z) , Marked_h(y,c(s(0),c(x,z)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)>
<Marked_h(c(s(x),c(s(0),y)),z) , Marked_h(y,c(s(0),c(x,z)))>
 ,
 CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
 [ h ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_h ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + 
[ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ s ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ c ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 1 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ 0 ] () = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 removing <Marked_h(c(s(x),c(s(0),y)),z),Marked_h(y,c(s(0),c(x,z)))>
 [ {
      
     DP termination of:
     <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_h(x,c(y,z)) , Marked_h(c(s(y),x),z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 4.096346 seconds (real time)
Cime Exit Status: 0