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

TRS termination of:
[1] s(a) -> a
[2] s(s(x)) -> x
[3] s(f(x,y)) -> f(s(y),s(x))
[4] s(g(x,y)) -> g(s(x),s(y))
[5] f(x,a) -> x
[6] f(a,y) -> y
[7] f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
[8] g(a,a) -> a


Sub problem: 
guided: 

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

{  <Marked_s(g(x,y)) , Marked_s(y)> --> <Marked_s(g(x,y)) , Marked_s(y)>
  <Marked_s(g(x,y)) , Marked_s(y)> --> <Marked_s(g(x,y)) , Marked_s(x)>
  <Marked_s(g(x,y)) , Marked_s(y)> --> <Marked_s(f(x,y)) , Marked_s(x)>
  <Marked_s(g(x,y)) , Marked_s(y)> --> <Marked_s(f(x,y)) , Marked_s(y)>
  <Marked_s(g(x,y)) , Marked_s(x)> --> <Marked_s(g(x,y)) , Marked_s(y)>
  <Marked_s(g(x,y)) , Marked_s(x)> --> <Marked_s(g(x,y)) , Marked_s(x)>
  <Marked_s(g(x,y)) , Marked_s(x)> --> <Marked_s(f(x,y)) , Marked_s(x)>
  <Marked_s(g(x,y)) , Marked_s(x)> --> <Marked_s(f(x,y)) , Marked_s(y)>
  <Marked_s(f(x,y)) , Marked_s(x)> --> <Marked_s(g(x,y)) , Marked_s(y)>
  <Marked_s(f(x,y)) , Marked_s(x)> --> <Marked_s(g(x,y)) , Marked_s(x)>
  <Marked_s(f(x,y)) , Marked_s(x)> --> <Marked_s(f(x,y)) , Marked_s(x)>
  <Marked_s(f(x,y)) , Marked_s(x)> --> <Marked_s(f(x,y)) , Marked_s(y)>
  <Marked_s(f(x,y)) , Marked_s(y)> --> <Marked_s(g(x,y)) , Marked_s(y)>
  <Marked_s(f(x,y)) , Marked_s(y)> --> <Marked_s(g(x,y)) , Marked_s(x)>
  <Marked_s(f(x,y)) , Marked_s(y)> --> <Marked_s(f(x,y)) , Marked_s(x)>
  <Marked_s(f(x,y)) , Marked_s(y)> --> <Marked_s(f(x,y)) , Marked_s(y)>
}

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

Cime worked for 0.056005 seconds (real time)
Cime Exit Status: 0