Initial Problem
Start: n_start
Program_Vars: Arg_0
Temp_Vars: A_P
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_start
Transitions:
0:n_eval___1(Arg_0) -> n_eval___1(A_P):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 1+Arg_0<=3*A_P && 2*A_P<=Arg_0
1:n_eval___1(Arg_0) -> n_eval___2(A_P):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
2:n_eval___1(Arg_0) -> n_eval___3(0):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0
3:n_eval___2(Arg_0) -> n_eval___1(A_P):|:0<=Arg_0 && 1+Arg_0<=3*A_P && 2*A_P<=Arg_0
4:n_eval___2(Arg_0) -> n_eval___2(A_P):|:0<=Arg_0 && 0<=A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
5:n_eval___2(Arg_0) -> n_eval___3(0):|:0<=Arg_0 && Arg_0<=1 && 1<=Arg_0
6:n_eval___4(Arg_0) -> n_eval___1(A_P):|:1+Arg_0<=3*A_P && 2*A_P<=Arg_0
7:n_eval___4(Arg_0) -> n_eval___2(A_P):|:0<=A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
8:n_eval___4(Arg_0) -> n_eval___3(0):|:Arg_0<=1 && 1<=Arg_0
9:n_start(Arg_0) -> n_eval___4(Arg_0)
Preprocessing
Found invariant 0<=Arg_0 for location n_eval___2
Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval___3
Problem after Preprocessing
Start: n_start
Program_Vars: Arg_0
Temp_Vars: A_P
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_start
Transitions:
0:n_eval___1(Arg_0) -> n_eval___1(A_P):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 1+Arg_0<=3*A_P && 2*A_P<=Arg_0
1:n_eval___1(Arg_0) -> n_eval___2(A_P):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
2:n_eval___1(Arg_0) -> n_eval___3(0):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0
3:n_eval___2(Arg_0) -> n_eval___1(A_P):|:0<=Arg_0 && 0<=Arg_0 && 1+Arg_0<=3*A_P && 2*A_P<=Arg_0
4:n_eval___2(Arg_0) -> n_eval___2(A_P):|:0<=Arg_0 && 0<=Arg_0 && 0<=A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
5:n_eval___2(Arg_0) -> n_eval___3(0):|:0<=Arg_0 && 0<=Arg_0 && Arg_0<=1 && 1<=Arg_0
6:n_eval___4(Arg_0) -> n_eval___1(A_P):|:1+Arg_0<=3*A_P && 2*A_P<=Arg_0
7:n_eval___4(Arg_0) -> n_eval___2(A_P):|:0<=A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
8:n_eval___4(Arg_0) -> n_eval___3(0):|:Arg_0<=1 && 1<=Arg_0
9:n_start(Arg_0) -> n_eval___4(Arg_0)
MPRF for transition 0:n_eval___1(Arg_0) -> n_eval___1(A_P):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 1+Arg_0<=3*A_P && 2*A_P<=Arg_0 of depth 1:
new bound:
3*Arg_0+2 {O(n)}
MPRF:
n_eval___1 [2*Arg_0+1 ]
n_eval___2 [Arg_0+1 ]
MPRF for transition 1:n_eval___1(Arg_0) -> n_eval___2(A_P):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0 of depth 1:
new bound:
4*Arg_0+2 {O(n)}
MPRF:
n_eval___1 [2*Arg_0+1 ]
n_eval___2 [2*Arg_0+1 ]
MPRF for transition 3:n_eval___2(Arg_0) -> n_eval___1(A_P):|:0<=Arg_0 && 0<=Arg_0 && 1+Arg_0<=3*A_P && 2*A_P<=Arg_0 of depth 1:
new bound:
3*Arg_0+1 {O(n)}
MPRF:
n_eval___1 [2*Arg_0 ]
n_eval___2 [Arg_0+1 ]
MPRF for transition 4:n_eval___2(Arg_0) -> n_eval___2(A_P):|:0<=Arg_0 && 0<=Arg_0 && 0<=A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0 of depth 1:
new bound:
4*Arg_0+1 {O(n)}
MPRF:
n_eval___1 [2*Arg_0 ]
n_eval___2 [2*Arg_0+1 ]
All Bounds
Timebounds
Overall timebound:14*Arg_0+12 {O(n)}
0: n_eval___1->n_eval___1: 3*Arg_0+2 {O(n)}
1: n_eval___1->n_eval___2: 4*Arg_0+2 {O(n)}
2: n_eval___1->n_eval___3: 1 {O(1)}
3: n_eval___2->n_eval___1: 3*Arg_0+1 {O(n)}
4: n_eval___2->n_eval___2: 4*Arg_0+1 {O(n)}
5: n_eval___2->n_eval___3: 1 {O(1)}
6: n_eval___4->n_eval___1: 1 {O(1)}
7: n_eval___4->n_eval___2: 1 {O(1)}
8: n_eval___4->n_eval___3: 1 {O(1)}
9: n_start->n_eval___4: 1 {O(1)}
Costbounds
Overall costbound: 14*Arg_0+12 {O(n)}
0: n_eval___1->n_eval___1: 3*Arg_0+2 {O(n)}
1: n_eval___1->n_eval___2: 4*Arg_0+2 {O(n)}
2: n_eval___1->n_eval___3: 1 {O(1)}
3: n_eval___2->n_eval___1: 3*Arg_0+1 {O(n)}
4: n_eval___2->n_eval___2: 4*Arg_0+1 {O(n)}
5: n_eval___2->n_eval___3: 1 {O(1)}
6: n_eval___4->n_eval___1: 1 {O(1)}
7: n_eval___4->n_eval___2: 1 {O(1)}
8: n_eval___4->n_eval___3: 1 {O(1)}
9: n_start->n_eval___4: 1 {O(1)}
Sizebounds
0: n_eval___1->n_eval___1, Arg_0: 4*Arg_0 {O(n)}
1: n_eval___1->n_eval___2, Arg_0: 4*Arg_0 {O(n)}
2: n_eval___1->n_eval___3, Arg_0: 0 {O(1)}
3: n_eval___2->n_eval___1, Arg_0: 4*Arg_0 {O(n)}
4: n_eval___2->n_eval___2, Arg_0: 4*Arg_0 {O(n)}
5: n_eval___2->n_eval___3, Arg_0: 0 {O(1)}
6: n_eval___4->n_eval___1, Arg_0: Arg_0 {O(n)}
7: n_eval___4->n_eval___2, Arg_0: Arg_0 {O(n)}
8: n_eval___4->n_eval___3, Arg_0: 0 {O(1)}
9: n_start->n_eval___4, Arg_0: Arg_0 {O(n)}