Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
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,Arg_6) -> eval_foo_bb1_in(Arg_4,Arg_5,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_1,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_0<=Arg_6
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<Arg_2
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_2<=Arg_6
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2-1,Arg_3,Arg_4,Arg_5,Arg_6)
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
8:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)

Preprocessing

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

Found invariant Arg_0<=Arg_6 && Arg_1<=Arg_5 && Arg_0<=Arg_4 for location eval_foo_bb5_in

Found invariant Arg_0<=Arg_6 && Arg_1<=Arg_5 && Arg_0<=Arg_4 for location eval_foo_stop

Found invariant 1+Arg_6<=Arg_5 && 1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_2 && 1+Arg_6<=Arg_1 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_2<=Arg_1 for location eval_foo_bb3_in

Found invariant 1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_2<=Arg_1 for location eval_foo_bb2_in

Found invariant Arg_1<=Arg_5 && Arg_0<=Arg_4 for location eval_foo_bb1_in

Found invariant 1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_6 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_2<=Arg_4 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_4, Arg_5, Arg_6
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_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_4,Arg_5,Arg_2,Arg_4,Arg_5,Arg_6)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_1,Arg_4,Arg_5,Arg_6):|:Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_6<Arg_0
20:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6):|:Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_0<=Arg_6
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6):|:1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && Arg_6<Arg_2
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6):|:1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && Arg_2<=Arg_6
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2-1,Arg_4,Arg_5,Arg_6):|:1+Arg_6<=Arg_5 && 1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_2 && 1+Arg_6<=Arg_1 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_2<=Arg_1
24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_2,Arg_4,Arg_5,Arg_6):|:1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_6 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_2<=Arg_4 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0
25:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6):|:Arg_0<=Arg_6 && Arg_1<=Arg_5 && Arg_0<=Arg_4
26:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6)

MPRF for transition 19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_1,Arg_4,Arg_5,Arg_6):|:Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_6<Arg_0 of depth 1:

new bound:

Arg_4+Arg_6 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_0-Arg_6-1 ]
eval_foo_bb2_in [Arg_0-Arg_6-1 ]
eval_foo_bb4_in [Arg_0-Arg_6-1 ]
eval_foo_bb1_in [Arg_0-Arg_6 ]

MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6):|:1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && Arg_6<Arg_2 of depth 1:

new bound:

Arg_5+Arg_6 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_2-Arg_6-1 ]
eval_foo_bb2_in [Arg_2-Arg_6 ]
eval_foo_bb4_in [Arg_2-Arg_6 ]
eval_foo_bb1_in [Arg_1-Arg_6 ]

MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6):|:1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && Arg_2<=Arg_6 of depth 1:

new bound:

Arg_4+Arg_6+1 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_0+1-Arg_6 ]
eval_foo_bb2_in [Arg_0+1-Arg_6 ]
eval_foo_bb4_in [Arg_0-Arg_6 ]
eval_foo_bb1_in [Arg_0+1-Arg_6 ]

MPRF for transition 23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2-1,Arg_4,Arg_5,Arg_6):|:1+Arg_6<=Arg_5 && 1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_2 && 1+Arg_6<=Arg_1 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_0<=Arg_4 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_5+Arg_6 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_2-Arg_6 ]
eval_foo_bb2_in [Arg_2-Arg_6 ]
eval_foo_bb4_in [Arg_2-Arg_6 ]
eval_foo_bb1_in [Arg_1-Arg_6 ]

MPRF for transition 24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_2,Arg_4,Arg_5,Arg_6):|:1+Arg_6<=Arg_4 && 1+Arg_6<=Arg_0 && Arg_2<=Arg_6 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_2<=Arg_4 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 of depth 1:

new bound:

Arg_4+Arg_6 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_0-Arg_6 ]
eval_foo_bb2_in [Arg_0-Arg_6 ]
eval_foo_bb4_in [Arg_0-Arg_6 ]
eval_foo_bb1_in [Arg_0-Arg_6 ]

All Bounds

Timebounds

Overall timebound:2*Arg_5+3*Arg_4+5*Arg_6+5 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+Arg_6 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_5+Arg_6 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_4+Arg_6+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_5+Arg_6 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_4+Arg_6 {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: 2*Arg_5+3*Arg_4+5*Arg_6+5 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+Arg_6 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_5+Arg_6 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_4+Arg_6+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_5+Arg_6 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_4+Arg_6 {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_5 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_4+Arg_6 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 3*Arg_5+Arg_6 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_5+Arg_6 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_5: Arg_5 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_6: Arg_6 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 3*Arg_4+Arg_6 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: 3*Arg_5+Arg_6 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_2: 2*Arg_5+Arg_2+Arg_6 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_4: 2*Arg_4 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_5: 2*Arg_5 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_6: 2*Arg_6 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: 2*Arg_4+Arg_6 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 3*Arg_5+Arg_6 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: 2*Arg_5+Arg_6 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_5: Arg_5 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_6: Arg_6 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: 2*Arg_4+Arg_6 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 2*Arg_6+6*Arg_5 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_2: 2*Arg_5+Arg_6 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_4: Arg_4 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_5: Arg_5 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_6: Arg_6 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: 2*Arg_4+Arg_6 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_1: 3*Arg_5+Arg_6 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_2: 2*Arg_5+Arg_6 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_5: Arg_5 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_6: Arg_6 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: 2*Arg_4+Arg_6 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: 2*Arg_5+Arg_6 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_2: 2*Arg_5+Arg_6 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: 3*Arg_4+Arg_6 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: 3*Arg_5+Arg_6 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_2: 2*Arg_5+Arg_2+Arg_6 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_4: 2*Arg_4 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_5: 2*Arg_5 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_6: 2*Arg_6 {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_2: Arg_2 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_5: Arg_5 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_6: Arg_6 {O(n)}