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

TRS termination of:
[1] .(1,x) -> x
[2] .(x,1) -> x
[3] .(i(x),x) -> 1
[4] .(x,i(x)) -> 1
[5] i(1) -> 1
[6] i(i(x)) -> x
[7] .(i(y),.(y,z)) -> z
[8] .(y,.(i(y),z)) -> z
[9] .(.(x,y),z) -> .(x,.(y,z))
[10] i(.(x,y)) -> .(i(y),i(x))


Sub problem: 
guided: 

DP termination of:
<Marked_.(.(x,y),z) , Marked_.(x,.(y,z))>
<Marked_.(.(x,y),z) , Marked_.(y,z)>
<Marked_i(.(x,y)) , Marked_.(i(y),i(x))>
<Marked_i(.(x,y)) , Marked_i(y)>
<Marked_i(.(x,y)) , Marked_i(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_i(.(x,y)) , Marked_i(x)> --> <Marked_i(.(x,y)) , Marked_i(x)>
  <Marked_i(.(x,y)) , Marked_i(x)> --> <Marked_i(.(x,y)) , Marked_i(y)>
  <Marked_i(.(x,y)) , Marked_i(y)> --> <Marked_i(.(x,y)) , Marked_i(x)>
  <Marked_i(.(x,y)) , Marked_i(y)> --> <Marked_i(.(x,y)) , Marked_i(y)>
}

{  <Marked_.(.(x,y),z) , Marked_.(y,z)> 
      --> <Marked_.(.(x,y),z) , Marked_.(y,z)>
  <Marked_.(.(x,y),z) , Marked_.(y,z)> 
     --> <Marked_.(.(x,y),z) , Marked_.(x,.(y,z))>
  <Marked_.(.(x,y),z) , Marked_.(x,.(y,z))> 
     --> <Marked_.(.(x,y),z) , Marked_.(y,z)>
  <Marked_.(.(x,y),z) , Marked_.(x,.(y,z))> 
     --> <Marked_.(.(x,y),z) , Marked_.(x,.(y,z))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  .(.(x,y),z) >= .(x,.(y,z)) ;
  .(1,x) >= x ;
  .(i(x),x) >= 1 ;
  .(i(y),.(y,z)) >= z ;
  .(x,1) >= x ;
  .(x,i(x)) >= 1 ;
  .(y,.(i(y),z)) >= z ;
  i(.(x,y)) >= .(i(y),i(x)) ;
  i(1) >= 1 ;
  i(i(x)) >= x ;
  Marked_i(.(x,y)) >= Marked_i(x) ;
  Marked_i(.(x,y)) >= Marked_i(y) ;
 }
 + Disjunctions:{ 
{
  Marked_i(.(x,y)) > Marked_i(x) ;
 }
{
  Marked_i(.(x,y)) > Marked_i(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: .(.(x,y),z) >= .(x,.(y,z))
constraint: .(1,x) >= x
constraint: .(i(x),x) >= 1
constraint: .(i(y),.(y,z)) >= z
constraint: .(x,1) >= x
constraint: .(x,i(x)) >= 1
constraint: .(y,.(i(y),z)) >= z
constraint: i(.(x,y)) >= .(i(y),i(x))
constraint: i(1) >= 1
constraint: i(i(x)) >= x
constraint: Marked_i(.(x,y)) >= Marked_i(x)
constraint: Marked_i(.(x,y)) >= Marked_i(y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  .(.(x,y),z) >= .(x,.(y,z)) ;
  .(1,x) >= x ;
  .(i(x),x) >= 1 ;
  .(i(y),.(y,z)) >= z ;
  .(x,1) >= x ;
  .(x,i(x)) >= 1 ;
  .(y,.(i(y),z)) >= z ;
  i(.(x,y)) >= .(i(y),i(x)) ;
  i(1) >= 1 ;
  i(i(x)) >= x ;
  Marked_.(.(x,y),z) >= Marked_.(x,.(y,z)) ;
  Marked_.(.(x,y),z) >= Marked_.(y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_.(.(x,y),z) > Marked_.(x,.(y,z)) ;
 }
{
  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: .(.(x,y),z) >= .(x,.(y,z))
constraint: .(1,x) >= x
constraint: .(i(x),x) >= 1
constraint: .(i(y),.(y,z)) >= z
constraint: .(x,1) >= x
constraint: .(x,i(x)) >= 1
constraint: .(y,.(i(y),z)) >= z
constraint: i(.(x,y)) >= .(i(y),i(x))
constraint: i(1) >= 1
constraint: i(i(x)) >= x
constraint: Marked_.(.(x,y),z) >= Marked_.(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] .(1,x) -> x
[2] .(x,1) -> x
[3] .(i(x),x) -> 1
[4] .(x,i(x)) -> 1
[5] i(1) -> 1
[6] i(i(x)) -> x
[7] .(i(y),.(y,z)) -> z
[8] .(y,.(i(y),z)) -> z
[9] .(.(x,y),z) -> .(x,.(y,z))
[10] i(.(x,y)) -> .(i(y),i(x))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_.(.(x,y),z) , Marked_.(x,.(y,z))>
<Marked_.(.(x,y),z) , Marked_.(y,z)>
<Marked_i(.(x,y)) , Marked_.(i(y),i(x))>
<Marked_i(.(x,y)) , Marked_i(y)>
<Marked_i(.(x,y)) , Marked_i(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_i(.(x,y)) , Marked_i(y)>
<Marked_i(.(x,y)) , Marked_i(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ . ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; 
 [ i ] (X0) = 2*X0 + 0; 
 [ 1 ] () = 0; 
 [ Marked_i ] (X0) = 3*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_.(.(x,y),z) , Marked_.(x,.(y,z))>
<Marked_.(.(x,y),z) , Marked_.(y,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ . ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; 
 [ Marked_. ] (X0,X1) = 3*X0 + 0; 
 [ i ] (X0) = 2*X0 + 0; 
 [ 1 ] () = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.052814 seconds (real time)
Cime Exit Status: 0