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

TRS termination of:
[1] merge(nil,y) -> y
[2] merge(x,nil) -> x
[3] merge(.(x,y),.(u,v)) ->
 if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
[4] ++(nil,y) -> y
[5] ++(.(x,y),z) -> .(x,++(y,z))
[6] if(true,x,y) -> x
[7] if(false,x,y) -> x


Sub problem: 
guided: 

DP termination of:
<Marked_merge(.(x,y),.(u,v)) , Marked_if(<(x,u),.(x,merge(y,.(u,v))),
                                .(u,merge(.(x,y),v)))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
<Marked_++(.(x,y),z) , Marked_++(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)> 
      --> <Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
  <Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)> 
     --> <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
  <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))> 
     --> <Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
  <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))> 
     --> <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
}

{  <Marked_++(.(x,y),z) , Marked_++(y,z)> 
      --> <Marked_++(.(x,y),z) , Marked_++(y,z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  merge(nil,y) >= y ;
  merge(.(x,y),.(u,v)) >= if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v))) ;
  merge(x,nil) >= x ;
  if(true,x,y) >= x ;
  if(false,x,y) >= x ;
  ++(nil,y) >= y ;
  ++(.(x,y),z) >= .(x,++(y,z)) ;
  Marked_merge(.(x,y),.(u,v)) >= Marked_merge(.(x,y),v) ;
  Marked_merge(.(x,y),.(u,v)) >= Marked_merge(y,.(u,v)) ;
 }
 + Disjunctions:{ 
{
  Marked_merge(.(x,y),.(u,v)) > Marked_merge(.(x,y),v) ;
 }
{
  Marked_merge(.(x,y),.(u,v)) > Marked_merge(y,.(u,v)) ;
 }
 } 
=== 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: merge(nil,y) >= y
constraint: merge(.(x,y),.(u,v)) >= if(<(x,u),.(x,merge(y,.(u,v))),
                                     .(u,merge(.(x,y),v)))
constraint: merge(x,nil) >= x
constraint: if(true,x,y) >= x
constraint: if(false,x,y) >= x
constraint: ++(nil,y) >= y
constraint: ++(.(x,y),z) >= .(x,++(y,z))
constraint: Marked_merge(.(x,y),.(u,v)) >= Marked_merge(.(x,y),v)
constraint: Marked_merge(.(x,y),.(u,v)) >= Marked_merge(y,.(u,v))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  merge(nil,y) >= y ;
  merge(.(x,y),.(u,v)) >= if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v))) ;
  merge(x,nil) >= x ;
  if(true,x,y) >= x ;
  if(false,x,y) >= x ;
  ++(nil,y) >= y ;
  ++(.(x,y),z) >= .(x,++(y,z)) ;
  Marked_++(.(x,y),z) >= Marked_++(y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_++(.(x,y),z) > Marked_++(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: merge(nil,y) >= y
constraint: merge(.(x,y),.(u,v)) >= if(<(x,u),.(x,merge(y,.(u,v))),
                                     .(u,merge(.(x,y),v)))
constraint: merge(x,nil) >= x
constraint: if(true,x,y) >= x
constraint: if(false,x,y) >= x
constraint: ++(nil,y) >= y
constraint: ++(.(x,y),z) >= .(x,++(y,z))
constraint: Marked_++(.(x,y),z) >= Marked_++(y,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] merge(nil,y) -> y
[2] merge(x,nil) -> x
[3] merge(.(x,y),.(u,v)) ->
 if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
[4] ++(nil,y) -> y
[5] ++(.(x,y),z) -> .(x,++(y,z))
[6] if(true,x,y) -> x
[7] if(false,x,y) -> x
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_merge(.(x,y),.(u,v)) , Marked_if(<(x,u),.(x,merge(y,.(u,v))),
                                     .(u,merge(.(x,y),v)))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
<Marked_++(.(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ merge ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ . ] (X0,X1) = 1 + 1*X1 + 0; 
 [ if ] (X0,X1,X2) = 1*X1 + 0; 
 [ Marked_merge ] (X0,X1) = 3*X0 + 3*X1 + 0; 
 [ true ] () = 3 + 0; 
 [ nil ] () = 3 + 0; 
 [ ++ ] (X0,X1) = 2*X0 + 3*X1 + 0; 
 [ < ] (X0,X1) = 0; 
 [ false ] () = 2 + 0; 
 ]} 
{
 
DP termination of:
<Marked_++(.(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ merge ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ . ] (X0,X1) = 1 + 1*X1 + 0; 
 [ if ] (X0,X1,X2) = 1*X1 + 0; 
 [ true ] () = 2 + 0; 
 [ nil ] () = 3 + 0; 
 [ Marked_++ ] (X0,X1) = 3*X0 + 0; 
 [ ++ ] (X0,X1) = 2*X0 + 3*X1 + 0; 
 [ < ] (X0,X1) = 0; 
 [ false ] () = 2 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.107806 seconds (real time)
Cime Exit Status: 0