Initial Problem

Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars: C
Locations: ack, start
Transitions:
0:ack(Arg_0,Arg_1) -> ack(Arg_0-1,C):|:1<=Arg_0 && 1<=Arg_1
1:ack(Arg_0,Arg_1) -> ack(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1
2:start(Arg_0,Arg_1) -> ack(Arg_0,Arg_1)

Preprocessing

Problem after Preprocessing

Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars: C
Locations: ack, start
Transitions:
0:ack(Arg_0,Arg_1) -> ack(Arg_0-1,C):|:1<=Arg_0 && 1<=Arg_1
1:ack(Arg_0,Arg_1) -> ack(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1
2:start(Arg_0,Arg_1) -> ack(Arg_0,Arg_1)

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

new bound:

Arg_0 {O(n)}

MPRF:

ack [Arg_0 ]

Analysing control-flow refined program

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

MPRF for transition 30: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 31: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 32: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 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: ack->ack: Arg_0 {O(n)}
1: ack->ack: inf {Infinity}
2: start->ack: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: ack->ack: Arg_0 {O(n)}
1: ack->ack: inf {Infinity}
2: start->ack: 1 {O(1)}

Sizebounds

0: ack->ack, Arg_0: 2*Arg_0 {O(n)}
1: ack->ack, Arg_0: 2*Arg_0 {O(n)}
2: start->ack, Arg_0: Arg_0 {O(n)}
2: start->ack, Arg_1: Arg_1 {O(n)}