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

TRS termination of:
[1] U11(tt,M,N) -> U12(tt,activate(M),activate(N))
[2] U12(tt,M,N) -> s(plus(activate(N),activate(M)))
[3] U21(tt,M,N) -> U22(tt,activate(M),activate(N))
[4] U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N))
[5] plus(N,0) -> N
[6] plus(N,s(M)) -> U11(tt,M,N)
[7] x(N,0) -> 0
[8] x(N,s(M)) -> U21(tt,M,N)
[9] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_U11(tt,M,N) , Marked_U12(tt,activate(M),activate(N))>
<Marked_U11(tt,M,N) , Marked_activate(M)>
<Marked_U11(tt,M,N) , Marked_activate(N)>
<Marked_U12(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U12(tt,M,N) , Marked_activate(N)>
<Marked_U12(tt,M,N) , Marked_activate(M)>
<Marked_U21(tt,M,N) , Marked_U22(tt,activate(M),activate(N))>
<Marked_U21(tt,M,N) , Marked_activate(M)>
<Marked_U21(tt,M,N) , Marked_activate(N)>
<Marked_U22(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))>
<Marked_U22(tt,M,N) , Marked_x(activate(N),activate(M))>
<Marked_U22(tt,M,N) , Marked_activate(N)>
<Marked_U22(tt,M,N) , Marked_activate(M)>
<Marked_U22(tt,M,N) , Marked_activate(N)>
<Marked_plus(N,s(M)) , Marked_U11(tt,M,N)>
<Marked_x(N,s(M)) , Marked_U21(tt,M,N)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_x(N,s(M)) , Marked_U21(tt,M,N)> 
      --> <Marked_U21(tt,M,N) , Marked_U22(tt,activate(M),activate(N))>
  <Marked_U22(tt,M,N) , Marked_x(activate(N),activate(M))> 
     --> <Marked_x(N,s(M)) , Marked_U21(tt,M,N)>
  <Marked_U21(tt,M,N) , Marked_U22(tt,activate(M),activate(N))> 
     --> <Marked_U22(tt,M,N) , Marked_x(activate(N),activate(M))>
}

{  <Marked_plus(N,s(M)) , Marked_U11(tt,M,N)> 
      --> <Marked_U11(tt,M,N) , Marked_U12(tt,activate(M),activate(N))>
  <Marked_U12(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_U11(tt,M,N)>
  <Marked_U11(tt,M,N) , Marked_U12(tt,activate(M),activate(N))> 
     --> <Marked_U12(tt,M,N) , Marked_plus(activate(N),activate(M))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  U12(tt,M,N) >= s(plus(activate(N),activate(M))) ;
  activate(X) >= X ;
  U11(tt,M,N) >= U12(tt,activate(M),activate(N)) ;
  plus(N,s(M)) >= U11(tt,M,N) ;
  plus(N,0) >= N ;
  U22(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ;
  U21(tt,M,N) >= U22(tt,activate(M),activate(N)) ;
  x(N,s(M)) >= U21(tt,M,N) ;
  x(N,0) >= 0 ;
  Marked_x(N,s(M)) >= Marked_U21(tt,M,N) ;
  Marked_U21(tt,M,N) >= Marked_U22(tt,activate(M),activate(N)) ;
  Marked_U22(tt,M,N) >= Marked_x(activate(N),activate(M)) ;
 }
 + Disjunctions:{ 
{
  Marked_x(N,s(M)) > Marked_U21(tt,M,N) ;
 }
{
  Marked_U21(tt,M,N) > Marked_U22(tt,activate(M),activate(N)) ;
 }
{
  Marked_U22(tt,M,N) > Marked_x(activate(N),activate(M)) ;
 }
 } 
=== 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 ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: U12(tt,M,N) >= s(plus(activate(N),activate(M)))
constraint: activate(X) >= X
constraint: U11(tt,M,N) >= U12(tt,activate(M),activate(N))
constraint: plus(N,s(M)) >= U11(tt,M,N)
constraint: plus(N,0) >= N
constraint: U22(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N))
constraint: U21(tt,M,N) >= U22(tt,activate(M),activate(N))
constraint: x(N,s(M)) >= U21(tt,M,N)
constraint: x(N,0) >= 0
constraint: Marked_x(N,s(M)) >= Marked_U21(tt,M,N)
constraint: Marked_U21(tt,M,N) >= Marked_U22(tt,activate(M),activate(N))
constraint: Marked_U22(tt,M,N) >= Marked_x(activate(N),activate(M))
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  U12(tt,M,N) >= s(plus(activate(N),activate(M))) ;
  activate(X) >= X ;
  U11(tt,M,N) >= U12(tt,activate(M),activate(N)) ;
  plus(N,s(M)) >= U11(tt,M,N) ;
  plus(N,0) >= N ;
  U22(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ;
  U21(tt,M,N) >= U22(tt,activate(M),activate(N)) ;
  x(N,s(M)) >= U21(tt,M,N) ;
  x(N,0) >= 0 ;
  Marked_plus(N,s(M)) >= Marked_U11(tt,M,N) ;
  Marked_U11(tt,M,N) >= Marked_U12(tt,activate(M),activate(N)) ;
  Marked_U12(tt,M,N) >= Marked_plus(activate(N),activate(M)) ;
 }
 + Disjunctions:{ 
{
  Marked_plus(N,s(M)) > Marked_U11(tt,M,N) ;
 }
{
  Marked_U11(tt,M,N) > Marked_U12(tt,activate(M),activate(N)) ;
 }
{
  Marked_U12(tt,M,N) > Marked_plus(activate(N),activate(M)) ;
 }
 } 
=== 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 ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: U12(tt,M,N) >= s(plus(activate(N),activate(M)))
constraint: activate(X) >= X
constraint: U11(tt,M,N) >= U12(tt,activate(M),activate(N))
constraint: plus(N,s(M)) >= U11(tt,M,N)
constraint: plus(N,0) >= N
constraint: U22(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N))
constraint: U21(tt,M,N) >= U22(tt,activate(M),activate(N))
constraint: x(N,s(M)) >= U21(tt,M,N)
constraint: x(N,0) >= 0
constraint: Marked_plus(N,s(M)) >= Marked_U11(tt,M,N)
constraint: Marked_U11(tt,M,N) >= Marked_U12(tt,activate(M),activate(N))
constraint: Marked_U12(tt,M,N) >= Marked_plus(activate(N),activate(M))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] U11(tt,M,N) -> U12(tt,activate(M),activate(N))
[2] U12(tt,M,N) -> s(plus(activate(N),activate(M)))
[3] U21(tt,M,N) -> U22(tt,activate(M),activate(N))
[4] U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N))
[5] plus(N,0) -> N
[6] plus(N,s(M)) -> U11(tt,M,N)
[7] x(N,0) -> 0
[8] x(N,s(M)) -> U21(tt,M,N)
[9] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_U11(tt,M,N) , Marked_U12(tt,activate(M),activate(N))>
<Marked_U11(tt,M,N) , Marked_activate(M)>
<Marked_U11(tt,M,N) , Marked_activate(N)>
<Marked_U12(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U12(tt,M,N) , Marked_activate(N)>
<Marked_U12(tt,M,N) , Marked_activate(M)>
<Marked_U21(tt,M,N) , Marked_U22(tt,activate(M),activate(N))>
<Marked_U21(tt,M,N) , Marked_activate(M)>
<Marked_U21(tt,M,N) , Marked_activate(N)>
<Marked_U22(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))>
<Marked_U22(tt,M,N) , Marked_x(activate(N),activate(M))>
<Marked_U22(tt,M,N) , Marked_activate(N)>
<Marked_U22(tt,M,N) , Marked_activate(M)>
<Marked_U22(tt,M,N) , Marked_activate(N)>
<Marked_plus(N,s(M)) , Marked_U11(tt,M,N)>
<Marked_x(N,s(M)) , Marked_U21(tt,M,N)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_U21(tt,M,N) , Marked_U22(tt,activate(M),activate(N))>
<Marked_U22(tt,M,N) , Marked_x(activate(N),activate(M))>
<Marked_x(N,s(M)) , Marked_U21(tt,M,N)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ U12 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0 + 1; 
 [ x ] (X0,X1) = 2*X1*X0; 
 [ s ] (X0) = 1*X0 + 1; 
 [ Marked_U21 ] (X0,X1,X2) = 2*X2*X0 + 1*X1; 
 [ activate ] (X0) = 1*X0; 
 [ U22 ] (X0,X1,X2) = 2*X2*X1 + 1*X2; 
 [ tt ] () = 0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1*X1 + 1*X0; 
 [ U11 ] (X0,X1,X2) = 2*X2*X1*X0 + 2*X2*X0 + 1*X2 + 2*X1*X0 + 1*X1 + 2*X0 + 1; 
 [ Marked_x ] (X0,X1) = 1*X1; 
 [ U21 ] (X0,X1,X2) = 2*X2*X1 + 2*X2*X0 + 1*X2; 
 [ Marked_U22 ] (X0,X1,X2) = 1*X1; 
 removing <Marked_x(N,s(M)),Marked_U21(tt,M,N)>
 [ {
      
     DP termination of:
     <Marked_U21(tt,M,N) , Marked_U22(tt,activate(M),activate(N))>
<Marked_U22(tt,M,N) , Marked_x(activate(N),activate(M))>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
{
 
DP termination of:
<Marked_U11(tt,M,N) , Marked_U12(tt,activate(M),activate(N))>
<Marked_U12(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_plus(N,s(M)) , Marked_U11(tt,M,N)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ U12 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0 + 2; 
 [ Marked_U12 ] (X0,X1,X2) = 1*X1 + 2*X0; 
 [ x ] (X0,X1) = 1*X1*X0; 
 [ s ] (X0) = 1*X0 + 2; 
 [ activate ] (X0) = 1*X0; 
 [ U22 ] (X0,X1,X2) = 1*X2*X1 + 2*X2; 
 [ Marked_U11 ] (X0,X1,X2) = 1*X1 + 2*X0; 
 [ tt ] () = 0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1*X1 + 1*X0; 
 [ Marked_plus ] (X0,X1) = 1*X1; 
 [ U11 ] (X0,X1,X2) = 1*X2 + 2*X1*X0 + 1*X1 + 2; 
 [ U21 ] (X0,X1,X2) = 2*X2*X1*X0 + 1*X2*X1 + 2*X2 + 2*X1*X0 + 2*X0; 
 removing <Marked_plus(N,s(M)),Marked_U11(tt,M,N)>
 [ {
      
     DP termination of:
     <Marked_U11(tt,M,N) , Marked_U12(tt,activate(M),activate(N))>
<Marked_U12(tt,M,N) , Marked_plus(activate(N),activate(M))>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 42.047211 seconds (real time)
Cime Exit Status: 0