Initial Problem

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval1___1, n_eval1___4, n_eval2___2, n_eval2___3, n_start
Transitions:
0:n_eval1___1(Arg_0,Arg_1) -> n_eval2___3(Arg_0,0):|:0<=Arg_0 && 1+Arg_0<=Arg_1 && 1<=Arg_0
1:n_eval1___4(Arg_0,Arg_1) -> n_eval2___3(Arg_0,0):|:1<=Arg_0
2:n_eval2___2(Arg_0,Arg_1) -> n_eval1___1(Arg_0-1,Arg_1):|:1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && Arg_0<=Arg_1
3:n_eval2___2(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1+1):|:1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1
4:n_eval2___3(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1+1):|:1<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1
5:n_start(Arg_0,Arg_1) -> n_eval1___4(Arg_0,Arg_1)

Preprocessing

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval2___2

Found invariant Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location n_eval1___1

Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval2___3

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval1___1, n_eval1___4, n_eval2___2, n_eval2___3, n_start
Transitions:
0:n_eval1___1(Arg_0,Arg_1) -> n_eval2___3(Arg_0,0):|:Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_0<=Arg_1 && 1<=Arg_0
1:n_eval1___4(Arg_0,Arg_1) -> n_eval2___3(Arg_0,0):|:1<=Arg_0
2:n_eval2___2(Arg_0,Arg_1) -> n_eval1___1(Arg_0-1,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && Arg_0<=Arg_1
3:n_eval2___2(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1+1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1
4:n_eval2___3(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1+1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1
5:n_start(Arg_0,Arg_1) -> n_eval1___4(Arg_0,Arg_1)

MPRF for transition 0:n_eval1___1(Arg_0,Arg_1) -> n_eval2___3(Arg_0,0):|:Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_eval1___1 [Arg_1 ]
n_eval2___3 [Arg_0 ]
n_eval2___2 [Arg_0 ]

MPRF for transition 2:n_eval2___2(Arg_0,Arg_1) -> n_eval1___1(Arg_0-1,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_eval1___1 [Arg_1-1 ]
n_eval2___3 [Arg_0 ]
n_eval2___2 [Arg_0 ]

MPRF for transition 4:n_eval2___3(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1+1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_eval1___1 [Arg_0 ]
n_eval2___3 [Arg_0 ]
n_eval2___2 [Arg_0-1 ]

MPRF for transition 3:n_eval2___2(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1+1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

3*Arg_0*Arg_0+Arg_0 {O(n^2)}

MPRF:

n_eval2___3 [2*Arg_0-1 ]
n_eval1___1 [3*Arg_0-Arg_1 ]
n_eval2___2 [3*Arg_0-Arg_1 ]

All Bounds

Timebounds

Overall timebound:3*Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}
0: n_eval1___1->n_eval2___3: Arg_0 {O(n)}
1: n_eval1___4->n_eval2___3: 1 {O(1)}
2: n_eval2___2->n_eval1___1: Arg_0 {O(n)}
3: n_eval2___2->n_eval2___2: 3*Arg_0*Arg_0+Arg_0 {O(n^2)}
4: n_eval2___3->n_eval2___2: Arg_0 {O(n)}
5: n_start->n_eval1___4: 1 {O(1)}

Costbounds

Overall costbound: 3*Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}
0: n_eval1___1->n_eval2___3: Arg_0 {O(n)}
1: n_eval1___4->n_eval2___3: 1 {O(1)}
2: n_eval2___2->n_eval1___1: Arg_0 {O(n)}
3: n_eval2___2->n_eval2___2: 3*Arg_0*Arg_0+Arg_0 {O(n^2)}
4: n_eval2___3->n_eval2___2: Arg_0 {O(n)}
5: n_start->n_eval1___4: 1 {O(1)}

Sizebounds

0: n_eval1___1->n_eval2___3, Arg_0: Arg_0 {O(n)}
0: n_eval1___1->n_eval2___3, Arg_1: 0 {O(1)}
1: n_eval1___4->n_eval2___3, Arg_0: Arg_0 {O(n)}
1: n_eval1___4->n_eval2___3, Arg_1: 0 {O(1)}
2: n_eval2___2->n_eval1___1, Arg_0: Arg_0 {O(n)}
2: n_eval2___2->n_eval1___1, Arg_1: 3*Arg_0*Arg_0+Arg_0+2 {O(n^2)}
3: n_eval2___2->n_eval2___2, Arg_0: Arg_0 {O(n)}
3: n_eval2___2->n_eval2___2, Arg_1: 3*Arg_0*Arg_0+Arg_0+1 {O(n^2)}
4: n_eval2___3->n_eval2___2, Arg_0: Arg_0 {O(n)}
4: n_eval2___3->n_eval2___2, Arg_1: 1 {O(1)}
5: n_start->n_eval1___4, Arg_0: Arg_0 {O(n)}
5: n_start->n_eval1___4, Arg_1: Arg_1 {O(n)}