Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f0, n_f2___5, n_f4___3, n_f4___4, n_f5___1, n_f5___2
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f2___5(Arg_0,Arg_1,1):|:1<=Arg_0
1:n_f0(Arg_0,Arg_1,Arg_2) -> n_f4___4(Arg_0,Arg_1,0):|:Arg_0<=0
2:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && 1<=Arg_1
3:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f5___1(Arg_0,Arg_1,1):|:0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && Arg_1<=0 && Arg_0<=0
4:n_f4___4(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && 1<=Arg_1
5:n_f4___4(Arg_0,Arg_1,Arg_2) -> n_f5___2(Arg_0,Arg_1,1):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && Arg_1<=0 && Arg_0<=0

Preprocessing

Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 for location n_f4___3

Found invariant Arg_2<=1 && Arg_1+Arg_2<=1 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 1+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=0 && Arg_0+Arg_1<=0 && Arg_0<=0 for location n_f5___2

Found invariant Arg_2<=1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_0 for location n_f2___5

Found invariant Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=0 for location n_f4___4

Found invariant Arg_2<=1 && Arg_2<=1+Arg_1 && Arg_1+Arg_2<=1 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 for location n_f5___1

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f0, n_f2___5, n_f4___3, n_f4___4, n_f5___1, n_f5___2
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f2___5(Arg_0,Arg_1,1):|:1<=Arg_0
1:n_f0(Arg_0,Arg_1,Arg_2) -> n_f4___4(Arg_0,Arg_1,0):|:Arg_0<=0
2:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && 1<=Arg_1
3:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f5___1(Arg_0,Arg_1,1):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && Arg_1<=0 && Arg_0<=0
4:n_f4___4(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=0 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && 1<=Arg_1
5:n_f4___4(Arg_0,Arg_1,Arg_2) -> n_f5___2(Arg_0,Arg_1,1):|:Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=0 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && Arg_1<=0 && Arg_0<=0

MPRF for transition 2:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f4___3 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:Arg_1+6 {O(n)}
0: n_f0->n_f2___5: 1 {O(1)}
1: n_f0->n_f4___4: 1 {O(1)}
2: n_f4___3->n_f4___3: Arg_1+1 {O(n)}
3: n_f4___3->n_f5___1: 1 {O(1)}
4: n_f4___4->n_f4___3: 1 {O(1)}
5: n_f4___4->n_f5___2: 1 {O(1)}

Costbounds

Overall costbound: Arg_1+6 {O(n)}
0: n_f0->n_f2___5: 1 {O(1)}
1: n_f0->n_f4___4: 1 {O(1)}
2: n_f4___3->n_f4___3: Arg_1+1 {O(n)}
3: n_f4___3->n_f5___1: 1 {O(1)}
4: n_f4___4->n_f4___3: 1 {O(1)}
5: n_f4___4->n_f5___2: 1 {O(1)}

Sizebounds

0: n_f0->n_f2___5, Arg_0: Arg_0 {O(n)}
0: n_f0->n_f2___5, Arg_1: Arg_1 {O(n)}
0: n_f0->n_f2___5, Arg_2: 1 {O(1)}
1: n_f0->n_f4___4, Arg_0: Arg_0 {O(n)}
1: n_f0->n_f4___4, Arg_1: Arg_1 {O(n)}
1: n_f0->n_f4___4, Arg_2: 0 {O(1)}
2: n_f4___3->n_f4___3, Arg_0: Arg_0 {O(n)}
2: n_f4___3->n_f4___3, Arg_1: Arg_1 {O(n)}
2: n_f4___3->n_f4___3, Arg_2: 0 {O(1)}
3: n_f4___3->n_f5___1, Arg_0: 2*Arg_0 {O(n)}
3: n_f4___3->n_f5___1, Arg_1: 0 {O(1)}
3: n_f4___3->n_f5___1, Arg_2: 1 {O(1)}
4: n_f4___4->n_f4___3, Arg_0: Arg_0 {O(n)}
4: n_f4___4->n_f4___3, Arg_1: Arg_1 {O(n)}
4: n_f4___4->n_f4___3, Arg_2: 0 {O(1)}
5: n_f4___4->n_f5___2, Arg_0: Arg_0 {O(n)}
5: n_f4___4->n_f5___2, Arg_1: Arg_1 {O(n)}
5: n_f4___4->n_f5___2, Arg_2: 1 {O(1)}