Initial Problem

Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: end, start, sumto
Transitions:
2:start(Arg_0,Arg_1) -> sumto(Arg_0,Arg_1)
0:sumto(Arg_0,Arg_1) -> end(Arg_0,Arg_1):|:Arg_1+1<=Arg_0
1:sumto(Arg_0,Arg_1) -> sumto(Arg_0+1,Arg_1):|:Arg_0<=Arg_1

Preprocessing

Found invariant 1+Arg_1<=Arg_0 for location end

Problem after Preprocessing

Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: end, start, sumto
Transitions:
2:start(Arg_0,Arg_1) -> sumto(Arg_0,Arg_1)
0:sumto(Arg_0,Arg_1) -> end(Arg_0,Arg_1):|:Arg_1+1<=Arg_0
1:sumto(Arg_0,Arg_1) -> sumto(Arg_0+1,Arg_1):|:Arg_0<=Arg_1

MPRF for transition 1:sumto(Arg_0,Arg_1) -> sumto(Arg_0+1,Arg_1):|:Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1+1 {O(n)}

MPRF:

sumto [Arg_1+1-Arg_0 ]

All Bounds

Timebounds

Overall timebound:Arg_0+Arg_1+3 {O(n)}
2: start->sumto: 1 {O(1)}
0: sumto->end: 1 {O(1)}
1: sumto->sumto: Arg_0+Arg_1+1 {O(n)}

Costbounds

Overall costbound: Arg_0+Arg_1+3 {O(n)}
2: start->sumto: 1 {O(1)}
0: sumto->end: 1 {O(1)}
1: sumto->sumto: Arg_0+Arg_1+1 {O(n)}

Sizebounds

2: start->sumto, Arg_0: Arg_0 {O(n)}
2: start->sumto, Arg_1: Arg_1 {O(n)}
0: sumto->end, Arg_0: 3*Arg_0+Arg_1+1 {O(n)}
0: sumto->end, Arg_1: 2*Arg_1 {O(n)}
1: sumto->sumto, Arg_0: 2*Arg_0+Arg_1+1 {O(n)}
1: sumto->sumto, Arg_1: Arg_1 {O(n)}