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

TRS termination of:
[1] f(0) -> 0
[2] f(s(0)) -> s(0)
[3] f(s(s(x))) -> p(h(g(x)))
[4] g(0) -> pair(s(0),s(0))
[5] g(s(x)) -> h(g(x))
[6] h(x) -> pair(+(p(x),q(x)),p(x))
[7] p(pair(x,y)) -> x
[8] q(pair(x,y)) -> y
[9] +(x,0) -> x
[10] +(x,s(y)) -> s(+(x,y))
[11] f(s(s(x))) -> +(p(g(x)),q(g(x)))
[12] g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x)))


Sub problem: 
guided: 

DP termination of:
<Marked_f(s(s(x))) , Marked_p(h(g(x)))>
<Marked_f(s(s(x))) , Marked_h(g(x))>
<Marked_f(s(s(x))) , Marked_g(x)>
<Marked_g(s(x)) , Marked_h(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_h(x) , Marked_+(p(x),q(x))>
<Marked_h(x) , Marked_p(x)>
<Marked_h(x) , Marked_q(x)>
<Marked_h(x) , Marked_p(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_f(s(s(x))) , Marked_+(p(g(x)),q(g(x)))>
<Marked_f(s(s(x))) , Marked_p(g(x))>
<Marked_f(s(s(x))) , Marked_g(x)>
<Marked_f(s(s(x))) , Marked_q(g(x))>
<Marked_f(s(s(x))) , Marked_g(x)>
<Marked_g(s(x)) , Marked_+(p(g(x)),q(g(x)))>
<Marked_g(s(x)) , Marked_p(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_g(s(x)) , Marked_q(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_g(s(x)) , Marked_p(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
}

{  <Marked_+(x,s(y)) , Marked_+(x,y)> --> <Marked_+(x,s(y)) , Marked_+(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(0) >= 0 ;
  f(s(0)) >= s(0) ;
  f(s(s(x))) >= p(h(g(x))) ;
  f(s(s(x))) >= +(p(g(x)),q(g(x))) ;
  p(pair(x,y)) >= x ;
  h(x) >= pair(+(p(x),q(x)),p(x)) ;
  g(0) >= pair(s(0),s(0)) ;
  g(s(x)) >= h(g(x)) ;
  g(s(x)) >= pair(+(p(g(x)),q(g(x))),p(g(x))) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  q(pair(x,y)) >= y ;
  Marked_g(s(x)) >= Marked_g(x) ;
 }
 + Disjunctions:{ 
{
  Marked_g(s(x)) > Marked_g(x) ;
 }
 } 
=== 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== STOPING TIMER virtual ===
constraint: f(0) >= 0
constraint: f(s(0)) >= s(0)
constraint: f(s(s(x))) >= p(h(g(x)))
constraint: f(s(s(x))) >= +(p(g(x)),q(g(x)))
constraint: p(pair(x,y)) >= x
constraint: h(x) >= pair(+(p(x),q(x)),p(x))
constraint: g(0) >= pair(s(0),s(0))
constraint: g(s(x)) >= h(g(x))
constraint: g(s(x)) >= pair(+(p(g(x)),q(g(x))),p(g(x)))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: q(pair(x,y)) >= y
constraint: Marked_g(s(x)) >= Marked_g(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(0) >= 0 ;
  f(s(0)) >= s(0) ;
  f(s(s(x))) >= p(h(g(x))) ;
  f(s(s(x))) >= +(p(g(x)),q(g(x))) ;
  p(pair(x,y)) >= x ;
  h(x) >= pair(+(p(x),q(x)),p(x)) ;
  g(0) >= pair(s(0),s(0)) ;
  g(s(x)) >= h(g(x)) ;
  g(s(x)) >= pair(+(p(g(x)),q(g(x))),p(g(x))) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  q(pair(x,y)) >= y ;
  Marked_+(x,s(y)) >= Marked_+(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_+(x,s(y)) > Marked_+(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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== STOPING TIMER virtual ===
constraint: f(0) >= 0
constraint: f(s(0)) >= s(0)
constraint: f(s(s(x))) >= p(h(g(x)))
constraint: f(s(s(x))) >= +(p(g(x)),q(g(x)))
constraint: p(pair(x,y)) >= x
constraint: h(x) >= pair(+(p(x),q(x)),p(x))
constraint: g(0) >= pair(s(0),s(0))
constraint: g(s(x)) >= h(g(x))
constraint: g(s(x)) >= pair(+(p(g(x)),q(g(x))),p(g(x)))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: q(pair(x,y)) >= y
constraint: Marked_+(x,s(y)) >= Marked_+(x,y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(0) -> 0
[2] f(s(0)) -> s(0)
[3] f(s(s(x))) -> p(h(g(x)))
[4] g(0) -> pair(s(0),s(0))
[5] g(s(x)) -> h(g(x))
[6] h(x) -> pair(+(p(x),q(x)),p(x))
[7] p(pair(x,y)) -> x
[8] q(pair(x,y)) -> y
[9] +(x,0) -> x
[10] +(x,s(y)) -> s(+(x,y))
[11] f(s(s(x))) -> +(p(g(x)),q(g(x)))
[12] g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(s(x))) , Marked_p(h(g(x)))>
<Marked_f(s(s(x))) , Marked_h(g(x))>
<Marked_f(s(s(x))) , Marked_g(x)>
<Marked_g(s(x)) , Marked_h(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_h(x) , Marked_+(p(x),q(x))>
<Marked_h(x) , Marked_p(x)>
<Marked_h(x) , Marked_q(x)>
<Marked_h(x) , Marked_p(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_f(s(s(x))) , Marked_+(p(g(x)),q(g(x)))>
<Marked_f(s(s(x))) , Marked_p(g(x))>
<Marked_f(s(s(x))) , Marked_g(x)>
<Marked_f(s(s(x))) , Marked_q(g(x))>
<Marked_f(s(s(x))) , Marked_g(x)>
<Marked_g(s(x)) , Marked_+(p(g(x)),q(g(x)))>
<Marked_g(s(x)) , Marked_p(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_g(s(x)) , Marked_q(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_g(s(x)) , Marked_p(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_g(s(x)) , Marked_g(x)>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_g(s(x)) , Marked_g(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { f  >  s ; f  >  p ; f  >  h ; f  >  g ;
                                   f  >  pair ; f  >  + ; f  >  q ; s  <  f ;
                                   s  <  h ; s  <  g ; s  <  + ; p  <  f ;
                                   p  <  h ; p  <  g ; h  <  f ; h  >  s ;
                                   h  >  p ; h  <  g ; h  >  pair ; h  >  + ;
                                   h  >  q ; g  <  f ; g  >  s ; g  >  p ;
                                   g  >  h ; g  >  pair ; g  >  + ; g  >  q ;
                                   pair  <  f ; pair  <  h ; pair  <  g ;
                                   +  <  f ; +  >  s ; +  <  h ; +  <  g ;
                                   q  <  f ; q  <  h ; q  <  g ; }

 ]} 
{
 
DP termination of:
<Marked_+(x,s(y)) , Marked_+(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { f  >  s ; f  >  p ; f  >  h ; f  >  g ;
                                   f  >  pair ; f  >  + ; f  >  q ; s  <  f ;
                                   s  <  h ; s  <  g ; s  <  + ; p  <  f ;
                                   p  <  h ; p  <  g ; h  <  f ; h  >  s ;
                                   h  >  p ; h  <  g ; h  >  pair ; h  >  + ;
                                   h  >  q ; g  <  f ; g  >  s ; g  >  p ;
                                   g  >  h ; g  >  pair ; g  >  + ; g  >  q ;
                                   pair  <  f ; pair  <  h ; pair  <  g ;
                                   +  <  f ; +  >  s ; +  <  h ; +  <  g ;
                                   q  <  f ; q  <  h ; q  <  g ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.192247 seconds (real time)
Cime Exit Status: 0