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

TRS termination of:
[1] +(x,0) -> x
[2] +(x,s(y)) -> s(+(x,y))
[3] +(0,y) -> y
[4] +(s(x),y) -> s(+(x,y))
[5] +(x,+(y,z)) -> +(+(x,y),z)
[6] f(g(f(x))) -> f(h(s(0),x))
[7] f(g(h(x,y))) -> f(h(s(x),y))
[8] f(h(x,h(y,z))) -> f(h(+(x,y),z))


Sub problem: 
guided: 

DP termination of:
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_+(s(x),y) , Marked_+(x,y)>
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
<Marked_f(g(f(x))) , Marked_f(h(s(0),x))>
<Marked_f(g(h(x,y))) , Marked_f(h(s(x),y))>
<Marked_f(h(x,h(y,z))) , Marked_f(h(+(x,y),z))>
<Marked_f(h(x,h(y,z))) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(h(x,h(y,z))) , Marked_f(h(+(x,y),z))> 
      --> <Marked_f(h(x,h(y,z))) , Marked_f(h(+(x,y),z))>
}

{  <Marked_+(x,+(y,z)) , Marked_+(x,y)> 
      --> <Marked_+(x,+(y,z)) , Marked_+(x,y)>
  <Marked_+(x,+(y,z)) , Marked_+(x,y)> 
     --> <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
  <Marked_+(x,+(y,z)) , Marked_+(x,y)> --> <Marked_+(s(x),y) , Marked_+(x,y)>
  <Marked_+(x,+(y,z)) , Marked_+(x,y)> --> <Marked_+(x,s(y)) , Marked_+(x,y)>
  <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)> 
     --> <Marked_+(x,+(y,z)) , Marked_+(x,y)>
  <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)> 
     --> <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
  <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)> 
     --> <Marked_+(s(x),y) , Marked_+(x,y)>
  <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)> 
     --> <Marked_+(x,s(y)) , Marked_+(x,y)>
  <Marked_+(s(x),y) , Marked_+(x,y)> --> <Marked_+(x,+(y,z)) , Marked_+(x,y)>
  <Marked_+(s(x),y) , Marked_+(x,y)> 
     --> <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
  <Marked_+(s(x),y) , Marked_+(x,y)> --> <Marked_+(s(x),y) , Marked_+(x,y)>
  <Marked_+(s(x),y) , Marked_+(x,y)> --> <Marked_+(x,s(y)) , Marked_+(x,y)>
  <Marked_+(x,s(y)) , Marked_+(x,y)> --> <Marked_+(x,+(y,z)) , Marked_+(x,y)>
  <Marked_+(x,s(y)) , Marked_+(x,y)> 
     --> <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
  <Marked_+(x,s(y)) , Marked_+(x,y)> --> <Marked_+(s(x),y) , Marked_+(x,y)>
  <Marked_+(x,s(y)) , Marked_+(x,y)> --> <Marked_+(x,s(y)) , Marked_+(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  +(0,y) >= y ;
  +(s(x),y) >= s(+(x,y)) ;
  +(x,+(y,z)) >= +(+(x,y),z) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  f(h(x,h(y,z))) >= f(h(+(x,y),z)) ;
  f(g(f(x))) >= f(h(s(0),x)) ;
  f(g(h(x,y))) >= f(h(s(x),y)) ;
  Marked_f(h(x,h(y,z))) >= Marked_f(h(+(x,y),z)) ;
 }
 + Disjunctions:{ 
{
  Marked_f(h(x,h(y,z))) > Marked_f(h(+(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: +(0,y) >= y
constraint: +(s(x),y) >= s(+(x,y))
constraint: +(x,+(y,z)) >= +(+(x,y),z)
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: f(h(x,h(y,z))) >= f(h(+(x,y),z))
constraint: f(g(f(x))) >= f(h(s(0),x))
constraint: f(g(h(x,y))) >= f(h(s(x),y))
constraint: Marked_f(h(x,h(y,z))) >= Marked_f(h(+(x,y),z))
APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_+(s(x),y) , Marked_+(x,y)> --> <Marked_+(s(x),y) , Marked_+(x,y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] +(x,0) -> x
[2] +(x,s(y)) -> s(+(x,y))
[3] +(0,y) -> y
[4] +(s(x),y) -> s(+(x,y))
[5] +(x,+(y,z)) -> +(+(x,y),z)
[6] f(g(f(x))) -> f(h(s(0),x))
[7] f(g(h(x,y))) -> f(h(s(x),y))
[8] f(h(x,h(y,z))) -> f(h(+(x,y),z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_+(s(x),y) , Marked_+(x,y)>
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
<Marked_f(g(f(x))) , Marked_f(h(s(0),x))>
<Marked_f(g(h(x,y))) , Marked_f(h(s(x),y))>
<Marked_f(h(x,h(y,z))) , Marked_f(h(+(x,y),z))>
<Marked_f(h(x,h(y,z))) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(h(x,h(y,z))) , Marked_f(h(+(x,y),z))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ + ] (X0,X1) = 1 + 1*X0 + 2*X1 + 0; 
 [ h ] (X0,X1) = 2 + 3*X1 + 0; 
 [ s ] (X0) = 0; 
 [ Marked_f ] (X0) = 1*X0 + 0; 
 [ 0 ] () = 0; 
 [ g ] (X0) = 2 + 3*X0 + 0; 
 [ f ] (X0) = 3*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_+(s(x),y) , Marked_+(x,y)>
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_+(s(x),y) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_+(s(x),y) , Marked_+(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.067928 seconds (real time)
Cime Exit Status: 0