Initial Problem
Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars: NoDet0
Locations: n_ack___1, n_ack___2, n_ack___3, n_start
Transitions:
0:n_ack___1(Arg_0,Arg_1) -> n_ack___1(Arg_0,Arg_1-1):|:1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
1:n_ack___1(Arg_0,Arg_1) -> n_ack___2(Arg_0-1,NoDet0):|:1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && 1<=Arg_0
2:n_ack___2(Arg_0,Arg_1) -> n_ack___1(Arg_0,Arg_1-1):|:0<=Arg_0 && 1<=Arg_0 && 1<=Arg_1
3:n_ack___2(Arg_0,Arg_1) -> n_ack___2(Arg_0-1,NoDet0):|:0<=Arg_0 && 1<=Arg_1 && 1<=Arg_0
4:n_ack___3(Arg_0,Arg_1) -> n_ack___1(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1
5:n_ack___3(Arg_0,Arg_1) -> n_ack___2(Arg_0-1,NoDet0):|:1<=Arg_1 && 1<=Arg_0
6:n_start(Arg_0,Arg_1) -> n_ack___3(Arg_0,Arg_1)
Preprocessing
Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_ack___1
Found invariant 0<=Arg_0 for location n_ack___2
Problem after Preprocessing
Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars: NoDet0
Locations: n_ack___1, n_ack___2, n_ack___3, n_start
Transitions:
0:n_ack___1(Arg_0,Arg_1) -> n_ack___1(Arg_0,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
1:n_ack___1(Arg_0,Arg_1) -> n_ack___2(Arg_0-1,NoDet0):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && 1<=Arg_0
2:n_ack___2(Arg_0,Arg_1) -> n_ack___1(Arg_0,Arg_1-1):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 1<=Arg_1
3:n_ack___2(Arg_0,Arg_1) -> n_ack___2(Arg_0-1,NoDet0):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 1<=Arg_0
4:n_ack___3(Arg_0,Arg_1) -> n_ack___1(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1
5:n_ack___3(Arg_0,Arg_1) -> n_ack___2(Arg_0-1,NoDet0):|:1<=Arg_1 && 1<=Arg_0
6:n_start(Arg_0,Arg_1) -> n_ack___3(Arg_0,Arg_1)
MPRF for transition 1:n_ack___1(Arg_0,Arg_1) -> n_ack___2(Arg_0-1,NoDet0):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && 1<=Arg_0 of depth 1:
new bound:
2*Arg_0+2 {O(n)}
MPRF:
n_ack___1 [Arg_0+1 ]
n_ack___2 [Arg_0+1 ]
MPRF for transition 2:n_ack___2(Arg_0,Arg_1) -> n_ack___1(Arg_0,Arg_1-1):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
2*Arg_0+1 {O(n)}
MPRF:
n_ack___1 [Arg_0 ]
n_ack___2 [Arg_0+1 ]
MPRF for transition 3:n_ack___2(Arg_0,Arg_1) -> n_ack___2(Arg_0-1,NoDet0):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 of depth 1:
new bound:
2*Arg_0+1 {O(n)}
MPRF:
n_ack___1 [Arg_0 ]
n_ack___2 [Arg_0+1 ]
All Bounds
Timebounds
Overall timebound:inf {Infinity}
0: n_ack___1->n_ack___1: inf {Infinity}
1: n_ack___1->n_ack___2: 2*Arg_0+2 {O(n)}
2: n_ack___2->n_ack___1: 2*Arg_0+1 {O(n)}
3: n_ack___2->n_ack___2: 2*Arg_0+1 {O(n)}
4: n_ack___3->n_ack___1: 1 {O(1)}
5: n_ack___3->n_ack___2: 1 {O(1)}
6: n_start->n_ack___3: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
0: n_ack___1->n_ack___1: inf {Infinity}
1: n_ack___1->n_ack___2: 2*Arg_0+2 {O(n)}
2: n_ack___2->n_ack___1: 2*Arg_0+1 {O(n)}
3: n_ack___2->n_ack___2: 2*Arg_0+1 {O(n)}
4: n_ack___3->n_ack___1: 1 {O(1)}
5: n_ack___3->n_ack___2: 1 {O(1)}
6: n_start->n_ack___3: 1 {O(1)}
Sizebounds
0: n_ack___1->n_ack___1, Arg_0: 4*Arg_0 {O(n)}
1: n_ack___1->n_ack___2, Arg_0: 4*Arg_0 {O(n)}
2: n_ack___2->n_ack___1, Arg_0: 4*Arg_0 {O(n)}
3: n_ack___2->n_ack___2, Arg_0: 4*Arg_0 {O(n)}
4: n_ack___3->n_ack___1, Arg_0: Arg_0 {O(n)}
4: n_ack___3->n_ack___1, Arg_1: Arg_1 {O(n)}
5: n_ack___3->n_ack___2, Arg_0: Arg_0 {O(n)}
6: n_start->n_ack___3, Arg_0: Arg_0 {O(n)}
6: n_start->n_ack___3, Arg_1: Arg_1 {O(n)}