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

TRS termination of:
[1] f(j(x,y),y) -> g(f(x,k(y)))
[2] f(x,h1(y,z)) -> h2(0,x,h1(y,z))
[3] g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
[4] h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
[5] i(f(x,h(y))) -> y
[6] i(h2(s(x),y,h1(x,z))) -> z
[7] k(h(x)) -> h1(0,x)
[8] k(h1(x,y)) -> h1(s(x),y)


Sub problem: 
guided: 

DP termination of:
<Marked_f(j(x,y),y) , Marked_g(f(x,k(y)))>
<Marked_f(j(x,y),y) , Marked_f(x,k(y))>
<Marked_f(j(x,y),y) , Marked_k(y)>
<Marked_f(x,h1(y,z)) , Marked_h2(0,x,h1(y,z))>
<Marked_g(h2(x,y,h1(z,u))) , Marked_h2(s(x),y,h1(z,u))>
<Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(j(x,y),y) , Marked_f(x,k(y))> 
      --> <Marked_f(j(x,y),y) , Marked_f(x,k(y))>
}

{  <Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))> 
      --> <Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  g(h2(x,y,h1(z,u))) >= h2(s(x),y,h1(z,u)) ;
  f(j(x,y),y) >= g(f(x,k(y))) ;
  f(x,h1(y,z)) >= h2(0,x,h1(y,z)) ;
  k(h1(x,y)) >= h1(s(x),y) ;
  k(h(x)) >= h1(0,x) ;
  h2(x,j(y,h1(z,u)),h1(z,u)) >= h2(s(x),y,h1(s(z),u)) ;
  i(f(x,h(y))) >= y ;
  i(h2(s(x),y,h1(x,z))) >= z ;
  Marked_f(j(x,y),y) >= Marked_f(x,k(y)) ;
 }
 + Disjunctions:{ 
{
  Marked_f(j(x,y),y) > Marked_f(x,k(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: g(h2(x,y,h1(z,u))) >= h2(s(x),y,h1(z,u))
constraint: f(j(x,y),y) >= g(f(x,k(y)))
constraint: f(x,h1(y,z)) >= h2(0,x,h1(y,z))
constraint: k(h1(x,y)) >= h1(s(x),y)
constraint: k(h(x)) >= h1(0,x)
constraint: h2(x,j(y,h1(z,u)),h1(z,u)) >= h2(s(x),y,h1(s(z),u))
constraint: i(f(x,h(y))) >= y
constraint: i(h2(s(x),y,h1(x,z))) >= z
constraint: Marked_f(j(x,y),y) >= Marked_f(x,k(y))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  g(h2(x,y,h1(z,u))) >= h2(s(x),y,h1(z,u)) ;
  f(j(x,y),y) >= g(f(x,k(y))) ;
  f(x,h1(y,z)) >= h2(0,x,h1(y,z)) ;
  k(h1(x,y)) >= h1(s(x),y) ;
  k(h(x)) >= h1(0,x) ;
  h2(x,j(y,h1(z,u)),h1(z,u)) >= h2(s(x),y,h1(s(z),u)) ;
  i(f(x,h(y))) >= y ;
  i(h2(s(x),y,h1(x,z))) >= z ;
  Marked_h2(x,j(y,h1(z,u)),h1(z,u)) >= Marked_h2(s(x),y,h1(s(z),u)) ;
 }
 + Disjunctions:{ 
{
  Marked_h2(x,j(y,h1(z,u)),h1(z,u)) > Marked_h2(s(x),y,h1(s(z),u)) ;
 }
 } 
=== 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: g(h2(x,y,h1(z,u))) >= h2(s(x),y,h1(z,u))
constraint: f(j(x,y),y) >= g(f(x,k(y)))
constraint: f(x,h1(y,z)) >= h2(0,x,h1(y,z))
constraint: k(h1(x,y)) >= h1(s(x),y)
constraint: k(h(x)) >= h1(0,x)
constraint: h2(x,j(y,h1(z,u)),h1(z,u)) >= h2(s(x),y,h1(s(z),u))
constraint: i(f(x,h(y))) >= y
constraint: i(h2(s(x),y,h1(x,z))) >= z
constraint: Marked_h2(x,j(y,h1(z,u)),h1(z,u)) >= Marked_h2(s(x),y,h1(s(z),u))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(j(x,y),y) -> g(f(x,k(y)))
[2] f(x,h1(y,z)) -> h2(0,x,h1(y,z))
[3] g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
[4] h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
[5] i(f(x,h(y))) -> y
[6] i(h2(s(x),y,h1(x,z))) -> z
[7] k(h(x)) -> h1(0,x)
[8] k(h1(x,y)) -> h1(s(x),y)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(j(x,y),y) , Marked_g(f(x,k(y)))>
<Marked_f(j(x,y),y) , Marked_f(x,k(y))>
<Marked_f(j(x,y),y) , Marked_k(y)>
<Marked_f(x,h1(y,z)) , Marked_h2(0,x,h1(y,z))>
<Marked_g(h2(x,y,h1(z,u))) , Marked_h2(s(x),y,h1(z,u))>
<Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(j(x,y),y) , Marked_f(x,k(y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ g ] (X0) = 3 + 2*X0 + 0; 
 [ i ] (X0) = 2 + 1*X0 + 0; 
 [ h2 ] (X0,X1,X2) = 3 + 1*X0 + 2*X2 + 0; 
 [ k ] (X0) = 2*X0 + 0; 
 [ h1 ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; 
 [ Marked_f ] (X0,X1) = 2*X0 + 0; 
 [ f ] (X0,X1) = 3 + 2*X0 + 2*X1 + 0; 
 [ h ] (X0) = 2 + 2*X0 + 0; 
 [ 0 ] () = 0; 
 [ j ] (X0,X1) = 3 + 3*X0 + 3*X1 + 0; 
 [ s ] (X0) = 0; 
 ]} 
{
 
DP termination of:
<Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ g ] (X0) = 2 + 3*X0 + 0; 
 [ i ] (X0) = 2 + 3*X0 + 0; 
 [ h2 ] (X0,X1,X2) = 1*X0 + 3*X2 + 0; 
 [ Marked_h2 ] (X0,X1,X2) = 2*X1 + 3*X2 + 0; 
 [ k ] (X0) = 1*X0 + 0; 
 [ h1 ] (X0,X1) = 2*X0 + 1*X1 + 0; 
 [ f ] (X0,X1) = 3*X0 + 3*X1 + 0; 
 [ h ] (X0) = 2 + 1*X0 + 0; 
 [ 0 ] () = 0; 
 [ j ] (X0,X1) = 3 + 3*X0 + 3*X1 + 0; 
 [ s ] (X0) = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.116732 seconds (real time)
Cime Exit Status: 0