Initial Problem

Start: n_l0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_l0, n_l1___3, n_l1___4, n_l2___1, n_l2___2
Transitions:
0:n_l0(Arg_0,Arg_1) -> n_l1___4(0,Arg_1)
1:n_l1___3(Arg_0,Arg_1) -> n_l1___3(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_1
2:n_l1___3(Arg_0,Arg_1) -> n_l2___1(Arg_0,Arg_1):|:0<=Arg_1 && Arg_1<=0
3:n_l1___4(Arg_0,Arg_1) -> n_l1___3(Arg_0+1,Arg_1-1):|:Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1
4:n_l1___4(Arg_0,Arg_1) -> n_l2___2(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=0

Preprocessing

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_l1___4

Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_l1___3

Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_l2___1

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 for location n_l2___2

Problem after Preprocessing

Start: n_l0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_l0, n_l1___3, n_l1___4, n_l2___1, n_l2___2
Transitions:
0:n_l0(Arg_0,Arg_1) -> n_l1___4(0,Arg_1)
1:n_l1___3(Arg_0,Arg_1) -> n_l1___3(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1
2:n_l1___3(Arg_0,Arg_1) -> n_l2___1(Arg_0,Arg_1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_1 && Arg_1<=0
3:n_l1___4(Arg_0,Arg_1) -> n_l1___3(Arg_0+1,Arg_1-1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1
4:n_l1___4(Arg_0,Arg_1) -> n_l2___2(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0

MPRF for transition 1:n_l1___3(Arg_0,Arg_1) -> n_l1___3(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_l1___3 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:Arg_1+5 {O(n)}
0: n_l0->n_l1___4: 1 {O(1)}
1: n_l1___3->n_l1___3: Arg_1+1 {O(n)}
2: n_l1___3->n_l2___1: 1 {O(1)}
3: n_l1___4->n_l1___3: 1 {O(1)}
4: n_l1___4->n_l2___2: 1 {O(1)}

Costbounds

Overall costbound: Arg_1+5 {O(n)}
0: n_l0->n_l1___4: 1 {O(1)}
1: n_l1___3->n_l1___3: Arg_1+1 {O(n)}
2: n_l1___3->n_l2___1: 1 {O(1)}
3: n_l1___4->n_l1___3: 1 {O(1)}
4: n_l1___4->n_l2___2: 1 {O(1)}

Sizebounds

0: n_l0->n_l1___4, Arg_0: 0 {O(1)}
0: n_l0->n_l1___4, Arg_1: Arg_1 {O(n)}
1: n_l1___3->n_l1___3, Arg_0: Arg_1+2 {O(n)}
1: n_l1___3->n_l1___3, Arg_1: Arg_1 {O(n)}
2: n_l1___3->n_l2___1, Arg_0: Arg_1+3 {O(n)}
2: n_l1___3->n_l2___1, Arg_1: 0 {O(1)}
3: n_l1___4->n_l1___3, Arg_0: 1 {O(1)}
3: n_l1___4->n_l1___3, Arg_1: Arg_1 {O(n)}
4: n_l1___4->n_l2___2, Arg_0: 0 {O(1)}
4: n_l1___4->n_l2___2, Arg_1: Arg_1 {O(n)}