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

TRS termination of:
[1] max(L(x)) -> x
[2] max(N(L(0),L(y))) -> y
[3] max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
[4] max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))


Sub problem: 
guided: 

DP termination of:
<Marked_max(N(L(s(x)),L(s(y)))) , Marked_max(N(L(x),L(y)))>
<Marked_max(N(L(x),N(y,z))) , Marked_max(N(L(x),L(max(N(y,z)))))>
<Marked_max(N(L(x),N(y,z))) , Marked_max(N(y,z))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_max(N(L(x),N(y,z))) , Marked_max(N(y,z))> 
      --> <Marked_max(N(L(x),N(y,z))) , Marked_max(N(y,z))>
}

{  <Marked_max(N(L(s(x)),L(s(y)))) , Marked_max(N(L(x),L(y)))> 
      --> <Marked_max(N(L(s(x)),L(s(y)))) , Marked_max(N(L(x),L(y)))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  max(L(x)) >= x ;
  max(N(L(0),L(y))) >= y ;
  max(N(L(s(x)),L(s(y)))) >= s(max(N(L(x),L(y)))) ;
  max(N(L(x),N(y,z))) >= max(N(L(x),L(max(N(y,z))))) ;
  Marked_max(N(L(x),N(y,z))) >= Marked_max(N(y,z)) ;
 }
 + Disjunctions:{ 
{
  Marked_max(N(L(x),N(y,z))) > Marked_max(N(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: max(L(x)) >= x
constraint: max(N(L(0),L(y))) >= y
constraint: max(N(L(s(x)),L(s(y)))) >= s(max(N(L(x),L(y))))
constraint: max(N(L(x),N(y,z))) >= max(N(L(x),L(max(N(y,z)))))
constraint: Marked_max(N(L(x),N(y,z))) >= Marked_max(N(y,z))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  max(L(x)) >= x ;
  max(N(L(0),L(y))) >= y ;
  max(N(L(s(x)),L(s(y)))) >= s(max(N(L(x),L(y)))) ;
  max(N(L(x),N(y,z))) >= max(N(L(x),L(max(N(y,z))))) ;
  Marked_max(N(L(s(x)),L(s(y)))) >= Marked_max(N(L(x),L(y))) ;
 }
 + Disjunctions:{ 
{
  Marked_max(N(L(s(x)),L(s(y)))) > Marked_max(N(L(x),L(y))) ;
 }
 } 
=== 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: max(L(x)) >= x
constraint: max(N(L(0),L(y))) >= y
constraint: max(N(L(s(x)),L(s(y)))) >= s(max(N(L(x),L(y))))
constraint: max(N(L(x),N(y,z))) >= max(N(L(x),L(max(N(y,z)))))
constraint: Marked_max(N(L(s(x)),L(s(y)))) >= Marked_max(N(L(x),L(y)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] max(L(x)) -> x
[2] max(N(L(0),L(y))) -> y
[3] max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
[4] max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_max(N(L(s(x)),L(s(y)))) , Marked_max(N(L(x),L(y)))>
<Marked_max(N(L(x),N(y,z))) , Marked_max(N(L(x),L(max(N(y,z)))))>
<Marked_max(N(L(x),N(y,z))) , Marked_max(N(y,z))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_max(N(L(x),N(y,z))) , Marked_max(N(y,z))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ max ] (X0) = 1*X0 + 0; 
 [ s ] (X0) = 0; 
 [ N ] (X0,X1) = 1 + 1*X1 + 0; 
 [ L ] (X0) = 1*X0 + 0; 
 [ Marked_max ] (X0) = 2*X0 + 0; 
 [ 0 ] () = 2 + 0; 
 ]} 
{
 
DP termination of:
<Marked_max(N(L(s(x)),L(s(y)))) , Marked_max(N(L(x),L(y)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ max ] (X0) = 1*X0 + 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ N ] (X0,X1) = 1*X1 + 0; 
 [ L ] (X0) = 1*X0 + 0; 
 [ Marked_max ] (X0) = 2*X0 + 0; 
 [ 0 ] () = 3 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.176211 seconds (real time)
Cime Exit Status: 0