- : unit = ()
h : heuristic =
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)
TRS termination of:
[1] .(1,x) -> x
[2] .(x,1) -> x
[3] .(i(x),x) -> 1
[4] .(x,i(x)) -> 1
[5] i(1) -> 1
[6] i(i(x)) -> x
[7] .(i(y),.(y,z)) -> z
[8] .(y,.(i(y),z)) -> z
[9] .(.(x,y),z) -> .(x,.(y,z))
[10] i(.(x,y)) -> .(i(y),i(x))
Sub problem:
guided:
DP termination of:
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:
{ -->
-->
-->
-->
}
{
-->
-->
-->
-->
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
.(.(x,y),z) >= .(x,.(y,z)) ;
.(1,x) >= x ;
.(i(x),x) >= 1 ;
.(i(y),.(y,z)) >= z ;
.(x,1) >= x ;
.(x,i(x)) >= 1 ;
.(y,.(i(y),z)) >= z ;
i(.(x,y)) >= .(i(y),i(x)) ;
i(1) >= 1 ;
i(i(x)) >= x ;
Marked_i(.(x,y)) >= Marked_i(x) ;
Marked_i(.(x,y)) >= Marked_i(y) ;
}
+ Disjunctions:{
{
Marked_i(.(x,y)) > Marked_i(x) ;
}
{
Marked_i(.(x,y)) > Marked_i(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: .(.(x,y),z) >= .(x,.(y,z))
constraint: .(1,x) >= x
constraint: .(i(x),x) >= 1
constraint: .(i(y),.(y,z)) >= z
constraint: .(x,1) >= x
constraint: .(x,i(x)) >= 1
constraint: .(y,.(i(y),z)) >= z
constraint: i(.(x,y)) >= .(i(y),i(x))
constraint: i(1) >= 1
constraint: i(i(x)) >= x
constraint: Marked_i(.(x,y)) >= Marked_i(x)
constraint: Marked_i(.(x,y)) >= Marked_i(y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
.(.(x,y),z) >= .(x,.(y,z)) ;
.(1,x) >= x ;
.(i(x),x) >= 1 ;
.(i(y),.(y,z)) >= z ;
.(x,1) >= x ;
.(x,i(x)) >= 1 ;
.(y,.(i(y),z)) >= z ;
i(.(x,y)) >= .(i(y),i(x)) ;
i(1) >= 1 ;
i(i(x)) >= x ;
Marked_.(.(x,y),z) >= Marked_.(x,.(y,z)) ;
Marked_.(.(x,y),z) >= Marked_.(y,z) ;
}
+ Disjunctions:{
{
Marked_.(.(x,y),z) > Marked_.(x,.(y,z)) ;
}
{
Marked_.(.(x,y),z) > Marked_.(y,z) ;
}
}
=== 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: .(.(x,y),z) >= .(x,.(y,z))
constraint: .(1,x) >= x
constraint: .(i(x),x) >= 1
constraint: .(i(y),.(y,z)) >= z
constraint: .(x,1) >= x
constraint: .(x,i(x)) >= 1
constraint: .(y,.(i(y),z)) >= z
constraint: i(.(x,y)) >= .(i(y),i(x))
constraint: i(1) >= 1
constraint: i(i(x)) >= x
constraint: Marked_.(.(x,y),z) >= Marked_.(x,.(y,z))
constraint: Marked_.(.(x,y),z) >= Marked_.(y,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
TRS termination of:
[1] .(1,x) -> x
[2] .(x,1) -> x
[3] .(i(x),x) -> 1
[4] .(x,i(x)) -> 1
[5] i(1) -> 1
[6] i(i(x)) -> x
[7] .(i(y),.(y,z)) -> z
[8] .(y,.(i(y),z)) -> z
[9] .(.(x,y),z) -> .(x,.(y,z))
[10] i(.(x,y)) -> .(i(y),i(x))
,
CRITERION: MDP
[ {
DP termination of:
,
CRITERION: SG
[ {
DP termination of:
,
CRITERION: ORD
[
Solution found:
polynomial interpretation =
[ . ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0;
[ i ] (X0) = 2*X0 + 0;
[ 1 ] () = 0;
[ Marked_i ] (X0) = 3*X0 + 0;
]}
{
DP termination of:
,
CRITERION: ORD
[
Solution found:
polynomial interpretation =
[ . ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0;
[ Marked_. ] (X0,X1) = 3*X0 + 0;
[ i ] (X0) = 2*X0 + 0;
[ 1 ] () = 0;
]}
]}
]}
Cime worked for 0.052814 seconds (real time)
Cime Exit Status: 0