Initial Problem

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

Preprocessing

Found invariant 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_l1___1

Problem after Preprocessing

Start: n_l0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_l0, n_l1___1, n_l1___2
Transitions:
0:n_l0(Arg_0,Arg_1) -> n_l1___2(Arg_0,Arg_1)
1:n_l1___1(Arg_0,Arg_1) -> n_l1___1(2*Arg_0,Arg_1+1):|:1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && Arg_0<=2*Arg_1 && 1<=Arg_0 && Arg_0<=1+Arg_1
2:n_l1___2(Arg_0,Arg_1) -> n_l1___1(2*Arg_0,Arg_1+1):|:1<=Arg_0 && Arg_0<=1+Arg_1

MPRF for transition 1:n_l1___1(Arg_0,Arg_1) -> n_l1___1(2*Arg_0,Arg_1+1):|:1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && Arg_0<=2*Arg_1 && 1<=Arg_0 && Arg_0<=1+Arg_1 of depth 1:

new bound:

2*Arg_0+Arg_1+3 {O(n)}

MPRF:

n_l1___1 [Arg_1+2-Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0+Arg_1+5 {O(n)}
0: n_l0->n_l1___2: 1 {O(1)}
1: n_l1___1->n_l1___1: 2*Arg_0+Arg_1+3 {O(n)}
2: n_l1___2->n_l1___1: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0+Arg_1+5 {O(n)}
0: n_l0->n_l1___2: 1 {O(1)}
1: n_l1___1->n_l1___1: 2*Arg_0+Arg_1+3 {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)}
1: n_l1___1->n_l1___1, Arg_0: 2*2^(2*Arg_0+Arg_1+3)*Arg_0 {O(EXP)}
1: n_l1___1->n_l1___1, Arg_1: 2*Arg_0+2*Arg_1+4 {O(n)}
2: n_l1___2->n_l1___1, Arg_0: 2*Arg_0 {O(n)}
2: n_l1___2->n_l1___1, Arg_1: Arg_1+1 {O(n)}