Initial Problem

Start: n_l0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_l0, n_l1___1, n_l1___2
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2) -> n_l1___2(Arg_0,Arg_1,Arg_2)
1:n_l1___1(Arg_0,Arg_1,Arg_2) -> n_l1___1(Arg_0+Arg_1+Arg_2,-Arg_2-1,Arg_2):|:1+Arg_1+Arg_2<=0 && 0<=1+Arg_1+Arg_2 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
2:n_l1___2(Arg_0,Arg_1,Arg_2) -> n_l1___1(Arg_0+Arg_1+Arg_2,-Arg_2-1,Arg_2):|:0<=Arg_0+Arg_1 && 0<=Arg_0

Preprocessing

Found invariant 1+Arg_1+Arg_2<=0 && 0<=1+Arg_1+Arg_2 for location n_l1___1

Problem after Preprocessing

Start: n_l0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_l0, n_l1___1, n_l1___2
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2) -> n_l1___2(Arg_0,Arg_1,Arg_2)
1:n_l1___1(Arg_0,Arg_1,Arg_2) -> n_l1___1(Arg_0+Arg_1+Arg_2,-Arg_2-1,Arg_2):|:1+Arg_1+Arg_2<=0 && 0<=1+Arg_1+Arg_2 && 1+Arg_1+Arg_2<=0 && 0<=1+Arg_1+Arg_2 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
2:n_l1___2(Arg_0,Arg_1,Arg_2) -> n_l1___1(Arg_0+Arg_1+Arg_2,-Arg_2-1,Arg_2):|:0<=Arg_0+Arg_1 && 0<=Arg_0

MPRF for transition 1:n_l1___1(Arg_0,Arg_1,Arg_2) -> n_l1___1(Arg_0+Arg_1+Arg_2,-Arg_2-1,Arg_2):|:1+Arg_1+Arg_2<=0 && 0<=1+Arg_1+Arg_2 && 1+Arg_1+Arg_2<=0 && 0<=1+Arg_1+Arg_2 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1+Arg_2+1 {O(n)}

MPRF:

n_l1___1 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+Arg_1+Arg_2+3 {O(n)}
0: n_l0->n_l1___2: 1 {O(1)}
1: n_l1___1->n_l1___1: Arg_0+Arg_1+Arg_2+1 {O(n)}
2: n_l1___2->n_l1___1: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+Arg_1+Arg_2+3 {O(n)}
0: n_l0->n_l1___2: 1 {O(1)}
1: n_l1___1->n_l1___1: Arg_0+Arg_1+Arg_2+1 {O(n)}
2: n_l1___2->n_l1___1: 1 {O(1)}

Sizebounds

0: n_l0->n_l1___2, Arg_0: Arg_0 {O(n)}
0: n_l0->n_l1___2, Arg_1: Arg_1 {O(n)}
0: n_l0->n_l1___2, Arg_2: Arg_2 {O(n)}
1: n_l1___1->n_l1___1, Arg_0: Arg_0+Arg_1+Arg_2+1 {O(n)}
1: n_l1___1->n_l1___1, Arg_1: Arg_2+1 {O(n)}
1: n_l1___1->n_l1___1, Arg_2: Arg_2 {O(n)}
2: n_l1___2->n_l1___1, Arg_0: Arg_0+Arg_1+Arg_2 {O(n)}
2: n_l1___2->n_l1___1, Arg_1: Arg_2+1 {O(n)}
2: n_l1___2->n_l1___1, Arg_2: Arg_2 {O(n)}