Initial Problem

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_div___4, n_div___5, n_end___1, n_end___2, n_end___3, n_start
Transitions:
0:n_div___4(Arg_0,Arg_1) -> n_div___4(Arg_0,Arg_1-Arg_0):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1
1:n_div___4(Arg_0,Arg_1) -> n_end___1(Arg_0,Arg_1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && Arg_1<=Arg_0
2:n_div___5(Arg_0,Arg_1) -> n_div___4(Arg_0,Arg_1-Arg_0):|:1<=Arg_0 && 1+Arg_0<=Arg_1
3:n_div___5(Arg_0,Arg_1) -> n_end___2(Arg_0,Arg_1):|:Arg_1<=Arg_0
4:n_div___5(Arg_0,Arg_1) -> n_end___3(Arg_0,Arg_1):|:Arg_0<=0
5:n_start(Arg_0,Arg_1) -> n_div___5(Arg_0,Arg_1)

Preprocessing

Found invariant 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_div___4

Found invariant Arg_0<=0 for location n_end___3

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_end___1

Found invariant Arg_1<=Arg_0 for location n_end___2

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_div___4, n_div___5, n_end___1, n_end___2, n_end___3, n_start
Transitions:
0:n_div___4(Arg_0,Arg_1) -> n_div___4(Arg_0,Arg_1-Arg_0):|:2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1
1:n_div___4(Arg_0,Arg_1) -> n_end___1(Arg_0,Arg_1):|:2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && Arg_1<=Arg_0
2:n_div___5(Arg_0,Arg_1) -> n_div___4(Arg_0,Arg_1-Arg_0):|:1<=Arg_0 && 1+Arg_0<=Arg_1
3:n_div___5(Arg_0,Arg_1) -> n_end___2(Arg_0,Arg_1):|:Arg_1<=Arg_0
4:n_div___5(Arg_0,Arg_1) -> n_end___3(Arg_0,Arg_1):|:Arg_0<=0
5:n_start(Arg_0,Arg_1) -> n_div___5(Arg_0,Arg_1)

MPRF for transition 0:n_div___4(Arg_0,Arg_1) -> n_div___4(Arg_0,Arg_1-Arg_0):|:2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

n_div___4 [Arg_1 ]

All Bounds

Timebounds

Overall timebound:Arg_1+5 {O(n)}
0: n_div___4->n_div___4: Arg_1 {O(n)}
1: n_div___4->n_end___1: 1 {O(1)}
2: n_div___5->n_div___4: 1 {O(1)}
3: n_div___5->n_end___2: 1 {O(1)}
4: n_div___5->n_end___3: 1 {O(1)}
5: n_start->n_div___5: 1 {O(1)}

Costbounds

Overall costbound: Arg_1+5 {O(n)}
0: n_div___4->n_div___4: Arg_1 {O(n)}
1: n_div___4->n_end___1: 1 {O(1)}
2: n_div___5->n_div___4: 1 {O(1)}
3: n_div___5->n_end___2: 1 {O(1)}
4: n_div___5->n_end___3: 1 {O(1)}
5: n_start->n_div___5: 1 {O(1)}

Sizebounds

0: n_div___4->n_div___4, Arg_0: Arg_0 {O(n)}
0: n_div___4->n_div___4, Arg_1: Arg_1 {O(n)}
1: n_div___4->n_end___1, Arg_0: 2*Arg_0 {O(n)}
1: n_div___4->n_end___1, Arg_1: 2*Arg_1 {O(n)}
2: n_div___5->n_div___4, Arg_0: Arg_0 {O(n)}
2: n_div___5->n_div___4, Arg_1: Arg_1 {O(n)}
3: n_div___5->n_end___2, Arg_0: Arg_0 {O(n)}
3: n_div___5->n_end___2, Arg_1: Arg_1 {O(n)}
4: n_div___5->n_end___3, Arg_0: Arg_0 {O(n)}
4: n_div___5->n_end___3, Arg_1: Arg_1 {O(n)}
5: n_start->n_div___5, Arg_0: Arg_0 {O(n)}
5: n_start->n_div___5, Arg_1: Arg_1 {O(n)}