Start: n_sqrt
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_end___1, n_end___3, n_f___2, n_f___4, n_sqrt
Transitions:
0:n_f___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_end___1(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_1 && 2<=Arg_1 && Arg_2<=Arg_1+Arg_3 && 1+Arg_3<=Arg_2
1:n_f___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f___2(Arg_0+1,Arg_1+2,Arg_1+Arg_2+2,Arg_3):|:0<=Arg_1 && 2<=Arg_1 && Arg_2<=Arg_1+Arg_3 && 0<=Arg_1 && Arg_2<=Arg_3
2:n_f___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_end___3(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_1 && Arg_2<=1 && 1<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=1 && 1<=Arg_1 && 1+Arg_3<=Arg_2
3:n_f___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f___2(Arg_0+1,Arg_1+2,Arg_1+Arg_2+2,Arg_3):|:0<=Arg_1 && Arg_2<=1 && 1<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_1 && Arg_2<=Arg_3
4:n_sqrt(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f___4(0,1,1,Arg_3)
Found invariant Arg_3<=0 && 1+Arg_3<=Arg_2 && Arg_2+Arg_3<=1 && 1+Arg_3<=Arg_1 && Arg_1+Arg_3<=1 && Arg_3<=Arg_0 && Arg_0+Arg_3<=0 && Arg_2<=1 && Arg_2<=Arg_1 && Arg_1+Arg_2<=2 && Arg_2<=1+Arg_0 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_end___3
Found invariant 1+Arg_3<=Arg_2 && 1<=Arg_3 && 5<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 4<=Arg_2 && 7<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && 3+Arg_0<=Arg_2 && 3<=Arg_1 && 4<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 1<=Arg_0 for location n_end___1
Found invariant Arg_2<=1 && Arg_2<=Arg_1 && Arg_1+Arg_2<=2 && Arg_2<=1+Arg_0 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f___4
Found invariant 1<=Arg_3 && 5<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 4<=Arg_2 && 7<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && 3+Arg_0<=Arg_2 && 3<=Arg_1 && 4<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 1<=Arg_0 for location n_f___2
Start: n_sqrt
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_end___1, n_end___3, n_f___2, n_f___4, n_sqrt
Transitions:
0:n_f___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_end___1(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 5<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 4<=Arg_2 && 7<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && 3+Arg_0<=Arg_2 && 3<=Arg_1 && 4<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 2<=Arg_1 && Arg_2<=Arg_1+Arg_3 && 1+Arg_3<=Arg_2
1:n_f___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f___2(Arg_0+1,Arg_1+2,Arg_1+Arg_2+2,Arg_3):|:1<=Arg_3 && 5<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 4<=Arg_2 && 7<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && 3+Arg_0<=Arg_2 && 3<=Arg_1 && 4<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 2<=Arg_1 && Arg_2<=Arg_1+Arg_3 && 0<=Arg_1 && Arg_2<=Arg_3
2:n_f___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_end___3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=1 && Arg_2<=Arg_1 && Arg_1+Arg_2<=2 && Arg_2<=1+Arg_0 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && Arg_2<=1 && 1<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=1 && 1<=Arg_1 && 1+Arg_3<=Arg_2
3:n_f___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f___2(Arg_0+1,Arg_1+2,Arg_1+Arg_2+2,Arg_3):|:Arg_2<=1 && Arg_2<=Arg_1 && Arg_1+Arg_2<=2 && Arg_2<=1+Arg_0 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && Arg_2<=1 && 1<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_1 && Arg_2<=Arg_3
4:n_sqrt(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f___4(0,1,1,Arg_3)
new bound:
2*Arg_3+1 {O(n)}
MPRF:
n_f___2 [2*Arg_3-Arg_0 ]
Overall timebound:2*Arg_3+5 {O(n)}
0: n_f___2->n_end___1: 1 {O(1)}
1: n_f___2->n_f___2: 2*Arg_3+1 {O(n)}
2: n_f___4->n_end___3: 1 {O(1)}
3: n_f___4->n_f___2: 1 {O(1)}
4: n_sqrt->n_f___4: 1 {O(1)}
Overall costbound: 2*Arg_3+5 {O(n)}
0: n_f___2->n_end___1: 1 {O(1)}
1: n_f___2->n_f___2: 2*Arg_3+1 {O(n)}
2: n_f___4->n_end___3: 1 {O(1)}
3: n_f___4->n_f___2: 1 {O(1)}
4: n_sqrt->n_f___4: 1 {O(1)}
0: n_f___2->n_end___1, Arg_0: 2*Arg_3+3 {O(n)}
0: n_f___2->n_end___1, Arg_1: 4*Arg_3+8 {O(n)}
0: n_f___2->n_end___1, Arg_2: 2*2^(2*Arg_3+1)*Arg_3+2^(2*Arg_3+1)*5+4 {O(EXP)}
0: n_f___2->n_end___1, Arg_3: 2*Arg_3 {O(n)}
1: n_f___2->n_f___2, Arg_0: 2*Arg_3+2 {O(n)}
1: n_f___2->n_f___2, Arg_1: 4*Arg_3+5 {O(n)}
1: n_f___2->n_f___2, Arg_2: 2*2^(2*Arg_3+1)*Arg_3+2^(2*Arg_3+1)*5 {O(EXP)}
1: n_f___2->n_f___2, Arg_3: Arg_3 {O(n)}
2: n_f___4->n_end___3, Arg_0: 0 {O(1)}
2: n_f___4->n_end___3, Arg_1: 1 {O(1)}
2: n_f___4->n_end___3, Arg_2: 1 {O(1)}
2: n_f___4->n_end___3, Arg_3: Arg_3 {O(n)}
3: n_f___4->n_f___2, Arg_0: 1 {O(1)}
3: n_f___4->n_f___2, Arg_1: 3 {O(1)}
3: n_f___4->n_f___2, Arg_2: 4 {O(1)}
3: n_f___4->n_f___2, Arg_3: Arg_3 {O(n)}
4: n_sqrt->n_f___4, Arg_0: 0 {O(1)}
4: n_sqrt->n_f___4, Arg_1: 1 {O(1)}
4: n_sqrt->n_f___4, Arg_2: 1 {O(1)}
4: n_sqrt->n_f___4, Arg_3: Arg_3 {O(n)}