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

TRS termination of:
[1] f(0) -> true
[2] f(1) -> false
[3] f(s(x)) -> f(x)
[4] if(true,s(x),s(y)) -> s(x)
[5] if(false,s(x),s(y)) -> s(y)
[6] g(x,c(y)) -> c(g(x,y))
[7] g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))


Sub problem: 
guided: 

DP termination of:
<Marked_f(s(x)) , Marked_f(x)>
<Marked_g(x,c(y)) , Marked_g(x,y)>
<Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))>
<Marked_g(x,c(y)) , Marked_if(f(x),c(g(s(x),y)),c(y))>
<Marked_g(x,c(y)) , Marked_f(x)>
<Marked_g(x,c(y)) , Marked_g(s(x),y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_g(x,c(y)) , Marked_g(s(x),y)> 
      --> <Marked_g(x,c(y)) , Marked_g(s(x),y)>
  <Marked_g(x,c(y)) , Marked_g(s(x),y)> 
     --> <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))>
  <Marked_g(x,c(y)) , Marked_g(s(x),y)> --> <Marked_g(x,c(y)) , Marked_g(x,y)>
  <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))> 
     --> <Marked_g(x,c(y)) , Marked_g(s(x),y)>
  <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))> 
     --> <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))>
  <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))> 
     --> <Marked_g(x,c(y)) , Marked_g(x,y)>
  <Marked_g(x,c(y)) , Marked_g(x,y)> --> <Marked_g(x,c(y)) , Marked_g(s(x),y)>
  <Marked_g(x,c(y)) , Marked_g(x,y)> 
     --> <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))>
  <Marked_g(x,c(y)) , Marked_g(x,y)> --> <Marked_g(x,c(y)) , Marked_g(x,y)>
}

{  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(0) >= true ;
  f(1) >= false ;
  f(s(x)) >= f(x) ;
  if(true,s(x),s(y)) >= s(x) ;
  if(false,s(x),s(y)) >= s(y) ;
  g(x,c(y)) >= c(g(x,y)) ;
  g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y))) ;
  Marked_g(x,c(y)) >= Marked_g(s(x),y) ;
  Marked_g(x,c(y)) >= Marked_g(x,if(f(x),c(g(s(x),y)),c(y))) ;
  Marked_g(x,c(y)) >= Marked_g(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_g(x,c(y)) > Marked_g(s(x),y) ;
 }
{
  Marked_g(x,c(y)) > Marked_g(x,if(f(x),c(g(s(x),y)),c(y))) ;
 }
{
  Marked_g(x,c(y)) > Marked_g(x,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: f(0) >= true
constraint: f(1) >= false
constraint: f(s(x)) >= f(x)
constraint: if(true,s(x),s(y)) >= s(x)
constraint: if(false,s(x),s(y)) >= s(y)
constraint: g(x,c(y)) >= c(g(x,y))
constraint: g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y)))
constraint: Marked_g(x,c(y)) >= Marked_g(s(x),y)
constraint: Marked_g(x,c(y)) >= Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))
constraint: Marked_g(x,c(y)) >= Marked_g(x,y)
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))> 
      --> <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(0) >= true ;
  f(1) >= false ;
  f(s(x)) >= f(x) ;
  if(true,s(x),s(y)) >= s(x) ;
  if(false,s(x),s(y)) >= s(y) ;
  g(x,c(y)) >= c(g(x,y)) ;
  g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y))) ;
  Marked_g(x,c(y)) >= Marked_g(x,if(f(x),c(g(s(x),y)),c(y))) ;
 }
 + Disjunctions:{ 
{
  Marked_g(x,c(y)) > Marked_g(x,if(f(x),c(g(s(x),y)),c(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: f(0) >= true
constraint: f(1) >= false
constraint: f(s(x)) >= f(x)
constraint: if(true,s(x),s(y)) >= s(x)
constraint: if(false,s(x),s(y)) >= s(y)
constraint: g(x,c(y)) >= c(g(x,y))
constraint: g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y)))
constraint: Marked_g(x,c(y)) >= Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(0) -> true
[2] f(1) -> false
[3] f(s(x)) -> f(x)
[4] if(true,s(x),s(y)) -> s(x)
[5] if(false,s(x),s(y)) -> s(y)
[6] g(x,c(y)) -> c(g(x,y))
[7] g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(x)) , Marked_f(x)>
<Marked_g(x,c(y)) , Marked_g(x,y)>
<Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))>
<Marked_g(x,c(y)) , Marked_if(f(x),c(g(s(x),y)),c(y))>
<Marked_g(x,c(y)) , Marked_f(x)>
<Marked_g(x,c(y)) , Marked_g(s(x),y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_g(x,c(y)) , Marked_g(x,y)>
<Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))>
<Marked_g(x,c(y)) , Marked_g(s(x),y)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ true ] () = 0; 
 [ g ] (X0,X1) = 1*X1; 
 [ 1 ] () = 0; 
 [ 0 ] () = 0; 
 [ if ] (X0,X1,X2) = 2; 
 [ f ] (X0) = 0; 
 [ Marked_g ] (X0,X1) = 2*X1 + 1*X0; 
 [ s ] (X0) = 2; 
 [ false ] () = 0; 
 [ c ] (X0) = 2*X0 + 2; 
 removing <Marked_g(x,c(y)),Marked_g(x,y)><Marked_g(x,c(y)),Marked_g(s(x),y)>
 [ {
      
     DP termination of:
     <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_g(x,c(y)) , Marked_g(x,if(f(x),c(g(s(x),y)),c(y)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ true ] () = 0; 
 [ g ] (X0,X1) = 2 + 2*X1 + 0; 
 [ 1 ] () = 0; 
 [ 0 ] () = 0; 
 [ if ] (X0,X1,X2) = 1*X0 + 0; 
 [ f ] (X0) = 1 + 0; 
 [ Marked_g ] (X0,X1) = 1*X1 + 0; 
 [ s ] (X0) = 0; 
 [ false ] () = 0; 
 [ c ] (X0) = 2 + 1*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_f(s(x)) , Marked_f(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.284717 seconds (real time)
Cime Exit Status: 0