Initial Problem

Start: eval0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval0, eval1
Transitions:
0:eval0(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_2):|:1<=Arg_0
1:eval1(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1+Arg_0,Arg_2):|:Arg_1+1<=Arg_0 && Arg_0+1<=Arg_2 && 1<=Arg_0
2:eval1(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_1-Arg_0):|:Arg_1+1<=Arg_0 && Arg_0+1<=Arg_2 && 1<=Arg_0

Preprocessing

Found invariant 1<=Arg_0 for location eval1

Problem after Preprocessing

Start: eval0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval0, eval1
Transitions:
0:eval0(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_2):|:1<=Arg_0
1:eval1(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1+Arg_0,Arg_2):|:1<=Arg_0 && Arg_1+1<=Arg_0 && Arg_0+1<=Arg_2 && 1<=Arg_0
2:eval1(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_1-Arg_0):|:1<=Arg_0 && Arg_1+1<=Arg_0 && Arg_0+1<=Arg_2 && 1<=Arg_0

MPRF for transition 1:eval1(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1+Arg_0,Arg_2):|:1<=Arg_0 && Arg_1+1<=Arg_0 && Arg_0+1<=Arg_2 && 1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

eval1 [Arg_0-Arg_1 ]

MPRF for transition 2:eval1(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_1-Arg_0):|:1<=Arg_0 && Arg_1+1<=Arg_0 && Arg_0+1<=Arg_2 && 1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_2 {O(n)}

MPRF:

eval1 [Arg_2-Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0+Arg_1+Arg_2+1 {O(n)}
0: eval0->eval1: 1 {O(1)}
1: eval1->eval1: Arg_0+Arg_1 {O(n)}
2: eval1->eval1: Arg_0+Arg_2 {O(n)}

Costbounds

Overall costbound: 2*Arg_0+Arg_1+Arg_2+1 {O(n)}
0: eval0->eval1: 1 {O(1)}
1: eval1->eval1: Arg_0+Arg_1 {O(n)}
2: eval1->eval1: Arg_0+Arg_2 {O(n)}

Sizebounds

0: eval0->eval1, Arg_0: Arg_0 {O(n)}
0: eval0->eval1, Arg_1: Arg_1 {O(n)}
0: eval0->eval1, Arg_2: Arg_2 {O(n)}
1: eval1->eval1, Arg_0: Arg_0 {O(n)}
1: eval1->eval1, Arg_1: 2*Arg_0*Arg_0+2*Arg_0*Arg_1+2*Arg_0+Arg_1 {O(n^2)}
1: eval1->eval1, Arg_2: Arg_2 {O(n)}
2: eval1->eval1, Arg_0: 2*Arg_0 {O(n)}
2: eval1->eval1, Arg_1: 2*Arg_0*Arg_0+2*Arg_0*Arg_1+2*Arg_0+2*Arg_1 {O(n^2)}
2: eval1->eval1, Arg_2: 2*Arg_0*Arg_0+2*Arg_0*Arg_1+2*Arg_1+4*Arg_0 {O(n^2)}