Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_4,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_0,Arg_2,Arg_3,Arg_4,Arg_5):|:1<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=1
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<=1
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1-2,Arg_2,Arg_3,Arg_4,Arg_5)
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
8:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Eliminate variables {Arg_2,Arg_3,Arg_5} that do not contribute to the problem

Found invariant Arg_0<=Arg_4 && Arg_0<=1 for location eval_foo_bb5_in

Found invariant Arg_0<=Arg_4 && Arg_0<=1 for location eval_foo_stop

Found invariant 2<=Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb3_in

Found invariant 2<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_4 for location eval_foo_bb1_in

Found invariant 2<=Arg_4 && 2<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=1 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_4
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
18:eval_foo_bb0_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb1_in(Arg_4,Arg_1,Arg_4)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_0,Arg_4):|:Arg_0<=Arg_4 && 1<Arg_0
20:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_4):|:Arg_0<=Arg_4 && Arg_0<=1
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<Arg_1
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=1
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1-2,Arg_4):|:2<=Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0
24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb1_in(Arg_1,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=1 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0
25:eval_foo_bb5_in(Arg_0,Arg_1,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_4):|:Arg_0<=Arg_4 && Arg_0<=1
26:eval_foo_start(Arg_0,Arg_1,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_4)

knowledge_propagation leads to new time bound 1 {O(1)} for transition 19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_0,Arg_4):|:Arg_0<=Arg_4 && 1<Arg_0

MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<Arg_1 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_1-1 ]
eval_foo_bb2_in [Arg_1+1 ]
eval_foo_bb4_in [Arg_1+1 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=1 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_0+1 ]
eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1-2,Arg_4):|:2<=Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_1-1 ]
eval_foo_bb2_in [Arg_1-1 ]
eval_foo_bb4_in [Arg_1-1 ]
eval_foo_bb1_in [Arg_0-1 ]

MPRF for transition 24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb1_in(Arg_1,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=1 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb3_in [1 ]
eval_foo_bb2_in [1 ]
eval_foo_bb4_in [1 ]
eval_foo_bb1_in [Arg_0-1 ]

All Bounds

Timebounds

Overall timebound:4*Arg_4+9 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: 1 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_4+1 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_4+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_4+1 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_4+1 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
26: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_4+9 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: 1 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_4+1 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_4+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_4+1 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_4+1 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
26: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_4 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_4 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_4 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: Arg_4+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: Arg_1+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_4: 2*Arg_4 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_4 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: Arg_4 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: Arg_4 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 1 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_4: Arg_4 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: Arg_4 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_1: Arg_4 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: 1 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: 1 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: Arg_4+1 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: Arg_1+1 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_4: 2*Arg_4 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}