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

TRS termination of:
[1] g(s(x),s(y)) ->
 if(and(f(s(x)),f(s(y))),
  t(g(k(minus(m(x,y),n(x,y)),s(s(0))),k(n(s(x),s(y)),s(s(0))))),
  g(minus(m(x,y),n(x,y)),n(s(x),s(y))))
[2] n(0,y) -> 0
[3] n(x,0) -> 0
[4] n(s(x),s(y)) -> s(n(x,y))
[5] m(0,y) -> y
[6] m(x,0) -> x
[7] m(s(x),s(y)) -> s(m(x,y))
[8] k(0,s(y)) -> 0
[9] k(s(x),s(y)) -> s(k(minus(x,y),s(y)))
[10] t(x) -> p(x,x)
[11] p(s(x),s(y)) -> s(s(p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
[12] p(s(x),x) -> p(if(gt(x,x),id(x),id(x)),s(x))
[13] p(0,y) -> y
[14] p(id(x),s(y)) -> s(p(x,if(gt(s(y),y),y,s(y))))
[15] minus(x,0) -> x
[16] minus(s(x),s(y)) -> minus(x,y)
[17] id(x) -> x
[18] if(true,x,y) -> x
[19] if(false,x,y) -> y
[20] not(x) -> if(x,false,true)
[21] and(x,false) -> false
[22] and(true,true) -> true
[23] f(0) -> true
[24] f(s(x)) -> h(x)
[25] h(0) -> false
[26] h(s(x)) -> f(x)
[27] gt(s(x),0) -> true
[28] gt(0,y) -> false
[29] gt(s(x),s(y)) -> gt(x,y)


Sub problem: 
guided: 

DP termination of:
<Marked_g(s(x),s(y)) , Marked_if(and(f(s(x)),f(s(y))),
                        t(g(k(minus(m(x,y),n(x,y)),s(s(0))),
                           k(n(s(x),s(y)),s(s(0))))),
                        g(minus(m(x,y),n(x,y)),n(s(x),s(y))))>
<Marked_g(s(x),s(y)) , Marked_and(f(s(x)),f(s(y)))>
<Marked_g(s(x),s(y)) , Marked_f(s(x))>
<Marked_g(s(x),s(y)) , Marked_f(s(y))>
<Marked_g(s(x),s(y)) , Marked_t(g(k(minus(m(x,y),n(x,y)),s(s(0))),
                                 k(n(s(x),s(y)),s(s(0)))))>
<Marked_g(s(x),s(y)) , Marked_g(k(minus(m(x,y),n(x,y)),s(s(0))),
                        k(n(s(x),s(y)),s(s(0))))>
<Marked_g(s(x),s(y)) , Marked_k(minus(m(x,y),n(x,y)),s(s(0)))>
<Marked_g(s(x),s(y)) , Marked_minus(m(x,y),n(x,y))>
<Marked_g(s(x),s(y)) , Marked_m(x,y)>
<Marked_g(s(x),s(y)) , Marked_n(x,y)>
<Marked_g(s(x),s(y)) , Marked_k(n(s(x),s(y)),s(s(0)))>
<Marked_g(s(x),s(y)) , Marked_n(s(x),s(y))>
<Marked_g(s(x),s(y)) , Marked_g(minus(m(x,y),n(x,y)),n(s(x),s(y)))>
<Marked_g(s(x),s(y)) , Marked_minus(m(x,y),n(x,y))>
<Marked_g(s(x),s(y)) , Marked_m(x,y)>
<Marked_g(s(x),s(y)) , Marked_n(x,y)>
<Marked_g(s(x),s(y)) , Marked_n(s(x),s(y))>
<Marked_n(s(x),s(y)) , Marked_n(x,y)>
<Marked_m(s(x),s(y)) , Marked_m(x,y)>
<Marked_k(s(x),s(y)) , Marked_k(minus(x,y),s(y))>
<Marked_k(s(x),s(y)) , Marked_minus(x,y)>
<Marked_t(x) , Marked_p(x,x)>
<Marked_p(s(x),s(y)) , Marked_p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))>
<Marked_p(s(x),s(y)) , Marked_if(gt(x,y),x,y)>
<Marked_p(s(x),s(y)) , Marked_gt(x,y)>
<Marked_p(s(x),s(y)) , Marked_if(not(gt(x,y)),id(x),id(y))>
<Marked_p(s(x),s(y)) , Marked_not(gt(x,y))>
<Marked_p(s(x),s(y)) , Marked_gt(x,y)>
<Marked_p(s(x),s(y)) , Marked_id(x)>
<Marked_p(s(x),s(y)) , Marked_id(y)>
<Marked_p(s(x),x) , Marked_p(if(gt(x,x),id(x),id(x)),s(x))>
<Marked_p(s(x),x) , Marked_if(gt(x,x),id(x),id(x))>
<Marked_p(s(x),x) , Marked_gt(x,x)>
<Marked_p(s(x),x) , Marked_id(x)>
<Marked_p(s(x),x) , Marked_id(x)>
<Marked_p(id(x),s(y)) , Marked_p(x,if(gt(s(y),y),y,s(y)))>
<Marked_p(id(x),s(y)) , Marked_if(gt(s(y),y),y,s(y))>
<Marked_p(id(x),s(y)) , Marked_gt(s(y),y)>
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_not(x) , Marked_if(x,false,true)>
<Marked_f(s(x)) , Marked_h(x)>
<Marked_h(s(x)) , Marked_f(x)>
<Marked_gt(s(x),s(y)) , Marked_gt(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 8 components:

{  <Marked_g(s(x),s(y)) , Marked_g(minus(m(x,y),n(x,y)),n(s(x),s(y)))> 
      --> <Marked_g(s(x),s(y)) , Marked_g(minus(m(x,y),n(x,y)),n(s(x),s(y)))>
  <Marked_g(s(x),s(y)) , Marked_g(minus(m(x,y),n(x,y)),n(s(x),s(y)))> 
     --> <Marked_g(s(x),s(y)) , Marked_g(k(minus(m(x,y),n(x,y)),s(s(0))),
                                 k(n(s(x),s(y)),s(s(0))))>
  <Marked_g(s(x),s(y)) , Marked_g(k(minus(m(x,y),n(x,y)),s(s(0))),
                          k(n(s(x),s(y)),s(s(0))))> 
     --> <Marked_g(s(x),s(y)) , Marked_g(minus(m(x,y),n(x,y)),n(s(x),s(y)))>
  <Marked_g(s(x),s(y)) , Marked_g(k(minus(m(x,y),n(x,y)),s(s(0))),
                          k(n(s(x),s(y)),s(s(0))))> 
     --> <Marked_g(s(x),s(y)) , Marked_g(k(minus(m(x,y),n(x,y)),s(s(0))),
                                 k(n(s(x),s(y)),s(s(0))))>
}

{  <Marked_n(s(x),s(y)) , Marked_n(x,y)> 
      --> <Marked_n(s(x),s(y)) , Marked_n(x,y)>
}

{  <Marked_m(s(x),s(y)) , Marked_m(x,y)> 
      --> <Marked_m(s(x),s(y)) , Marked_m(x,y)>
}

{  <Marked_k(s(x),s(y)) , Marked_k(minus(x,y),s(y))> 
      --> <Marked_k(s(x),s(y)) , Marked_k(minus(x,y),s(y))>
}

{  <Marked_p(id(x),s(y)) , Marked_p(x,if(gt(s(y),y),y,s(y)))> 
      --> <Marked_p(id(x),s(y)) , Marked_p(x,if(gt(s(y),y),y,s(y)))>
  <Marked_p(id(x),s(y)) , Marked_p(x,if(gt(s(y),y),y,s(y)))> 
     --> <Marked_p(s(x),x) , Marked_p(if(gt(x,x),id(x),id(x)),s(x))>
  <Marked_p(id(x),s(y)) , Marked_p(x,if(gt(s(y),y),y,s(y)))> 
     --> <Marked_p(s(x),s(y)) , Marked_p(if(gt(x,y),x,y),
                                 if(not(gt(x,y)),id(x),id(y)))>
  <Marked_p(s(x),x) , Marked_p(if(gt(x,x),id(x),id(x)),s(x))> 
     --> <Marked_p(id(x),s(y)) , Marked_p(x,if(gt(s(y),y),y,s(y)))>
  <Marked_p(s(x),x) , Marked_p(if(gt(x,x),id(x),id(x)),s(x))> 
     --> <Marked_p(s(x),x) , Marked_p(if(gt(x,x),id(x),id(x)),s(x))>
  <Marked_p(s(x),x) , Marked_p(if(gt(x,x),id(x),id(x)),s(x))> 
     --> <Marked_p(s(x),s(y)) , Marked_p(if(gt(x,y),x,y),
                                 if(not(gt(x,y)),id(x),id(y)))>
  <Marked_p(s(x),s(y)) , Marked_p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))> 
     --> <Marked_p(id(x),s(y)) , Marked_p(x,if(gt(s(y),y),y,s(y)))>
  <Marked_p(s(x),s(y)) , Marked_p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))> 
     --> <Marked_p(s(x),x) , Marked_p(if(gt(x,x),id(x),id(x)),s(x))>
  <Marked_p(s(x),s(y)) , Marked_p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))> 
     --> <Marked_p(s(x),s(y)) , Marked_p(if(gt(x,y),x,y),
                                 if(not(gt(x,y)),id(x),id(y)))>
}

{  <Marked_minus(s(x),s(y)) , Marked_minus(x,y)> 
      --> <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
}

{  <Marked_h(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_h(x)>
  <Marked_f(s(x)) , Marked_h(x)> --> <Marked_h(s(x)) , Marked_f(x)>
}

{  <Marked_gt(s(x),s(y)) , Marked_gt(x,y)> 
      --> <Marked_gt(s(x),s(y)) , Marked_gt(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  if(true,x,y) >= x ;
  if(false,x,y) >= y ;
  and(true,true) >= true ;
  and(x,false) >= false ;
  f(s(x)) >= h(x) ;
  f(0) >= true ;
  t(x) >= p(x,x) ;
  g(s(x),s(y)) >= if(and(f(s(x)),f(s(y))),
                   t(g(k(minus(m(x,y),n(x,y)),s(s(0))),k(n(s(x),s(y)),s(s(0))))),
                   g(minus(m(x,y),n(x,y)),n(s(x),s(y)))) ;
  k(s(x),s(y)) >= s(k(minus(x,y),s(y))) ;
  k(0,s(y)) >= 0 ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  m(s(x),s(y)) >= s(m(x,y)) ;
  m(0,y) >= y ;
  m(x,0) >= x ;
  n(s(x),s(y)) >= s(n(x,y)) ;
  n(0,y) >= 0 ;
  n(x,0) >= 0 ;
  p(s(x),s(y)) >= s(s(p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) ;
  p(s(x),x) >= p(if(gt(x,x),id(x),id(x)),s(x)) ;
  p(0,y) >= y ;
  p(id(x),s(y)) >= s(p(x,if(gt(s(y),y),y,s(y)))) ;
  gt(s(x),s(y)) >= gt(x,y) ;
  gt(s(x),0) >= true ;
  gt(0,y) >= false ;
  not(x) >= if(x,false,true) ;
  id(x) >= x ;
  h(s(x)) >= f(x) ;
  h(0) >= false ;
  Marked_g(s(x),s(y)) >= Marked_g(k(minus(m(x,y),n(x,y)),s(s(0))),
                          k(n(s(x),s(y)),s(s(0)))) ;
  Marked_g(s(x),s(y)) >= Marked_g(minus(m(x,y),n(x,y)),n(s(x),s(y))) ;
 }
 + Disjunctions:{ 
{
  Marked_g(s(x),s(y)) > Marked_g(k(minus(m(x,y),n(x,y)),s(s(0))),
                         k(n(s(x),s(y)),s(s(0)))) ;
 }
{
  Marked_g(s(x),s(y)) > Marked_g(minus(m(x,y),n(x,y)),n(s(x),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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  if(true,x,y) >= x ;
  if(false,x,y) >= y ;
  and(true,true) >= true ;
  and(x,false) >= false ;
  f(s(x)) >= h(x) ;
  f(0) >= true ;
  t(x) >= p(x,x) ;
  g(s(x),s(y)) >= if(and(f(s(x)),f(s(y))),
                   t(g(k(minus(m(x,y),n(x,y)),s(s(0))),k(n(s(x),s(y)),s(s(0))))),
                   g(minus(m(x,y),n(x,y)),n(s(x),s(y)))) ;
  k(s(x),s(y)) >= s(k(minus(x,y),s(y))) ;
  k(0,s(y)) >= 0 ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  m(s(x),s(y)) >= s(m(x,y)) ;
  m(0,y) >= y ;
  m(x,0) >= x ;
  n(s(x),s(y)) >= s(n(x,y)) ;
  n(0,y) >= 0 ;
  n(x,0) >= 0 ;
  p(s(x),s(y)) >= s(s(p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) ;
  p(s(x),x) >= p(if(gt(x,x),id(x),id(x)),s(x)) ;
  p(0,y) >= y ;
  p(id(x),s(y)) >= s(p(x,if(gt(s(y),y),y,s(y)))) ;
  gt(s(x),s(y)) >= gt(x,y) ;
  gt(s(x),0) >= true ;
  gt(0,y) >= false ;
  not(x) >= if(x,false,true) ;
  id(x) >= x ;
  h(s(x)) >= f(x) ;
  h(0) >= false ;
  Marked_g(s(x),s(y)) > Marked_g(k(minus(m(x,y),n(x,y)),s(s(0))),
                         k(n(s(x),s(y)),s(s(0)))) ;
  Marked_g(s(x),s(y)) > Marked_g(minus(m(x,y),n(x,y)),n(s(x),s(y))) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  if(true,x,y) >= x ;
  if(false,x,y) >= y ;
  and(true,true) >= true ;
  and(x,false) >= false ;
  f(s(x)) >= h(x) ;
  f(0) >= true ;
  t(x) >= p(x,x) ;
  g(s(x),s(y)) >= if(and(f(s(x)),f(s(y))),
                   t(g(k(minus(m(x,y),n(x,y)),s(s(0))),k(n(s(x),s(y)),s(s(0))))),
                   g(minus(m(x,y),n(x,y)),n(s(x),s(y)))) ;
  k(s(x),s(y)) >= s(k(minus(x,y),s(y))) ;
  k(0,s(y)) >= 0 ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  m(s(x),s(y)) >= s(m(x,y)) ;
  m(0,y) >= y ;
  m(x,0) >= x ;
  n(s(x),s(y)) >= s(n(x,y)) ;
  n(0,y) >= 0 ;
  n(x,0) >= 0 ;
  p(s(x),s(y)) >= s(s(p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) ;
  p(s(x),x) >= p(if(gt(x,x),id(x),id(x)),s(x)) ;
  p(0,y) >= y ;
  p(id(x),s(y)) >= s(p(x,if(gt(s(y),y),y,s(y)))) ;
  gt(s(x),s(y)) >= gt(x,y) ;
  gt(s(x),0) >= true ;
  gt(0,y) >= false ;
  not(x) >= if(x,false,true) ;
  id(x) >= x ;
  h(s(x)) >= f(x) ;
  h(0) >= false ;
  Marked_g(s(x),s(y)) > Marked_g(k(minus(m(x,y),n(x,y)),s(s(0))),
                         k(n(s(x),s(y)),s(s(0)))) ;
  Marked_g(s(x),s(y)) > Marked_g(minus(m(x,y),n(x,y)),n(s(x),s(y))) ;
 }
 + Disjunctions:{ 
 } 
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 215.347432 seconds (real time)
Cime Exit Status: 0