Initial Problem
Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
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) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_0,Arg_2,Arg_3):|:Arg_0<10
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:10<=Arg_0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=0
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2,Arg_3)
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3)
8:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)
Preprocessing
Eliminate variables {Arg_3} that do not contribute to the problem
Found invariant Arg_2<=Arg_0 && 10<=Arg_0 for location eval_foo_bb5_in
Found invariant Arg_2<=Arg_0 && 10<=Arg_0 for location eval_foo_stop
Found invariant Arg_2<=9 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && 1<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=9 for location eval_foo_bb3_in
Found invariant Arg_2<=9 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && Arg_0<=Arg_1 && Arg_0<=9 for location eval_foo_bb2_in
Found invariant Arg_2<=Arg_0 for location eval_foo_bb1_in
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_1<=0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0 for location eval_foo_bb4_in
Problem after Preprocessing
Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
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) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_0,Arg_2):|:Arg_2<=Arg_0 && Arg_0<10
20:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 10<=Arg_0
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=9 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && Arg_0<=Arg_1 && Arg_0<=9 && 0<Arg_1
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=9 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && Arg_0<=Arg_1 && Arg_0<=9 && Arg_1<=0
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=9 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && 1<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=9
24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_1<=0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0
25:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 10<=Arg_0
26:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)
MPRF for transition 19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_0,Arg_2):|:Arg_2<=Arg_0 && Arg_0<10 of depth 1:
new bound:
Arg_2+10 {O(n)}
MPRF:
eval_foo_bb3_in [9-Arg_0 ]
eval_foo_bb2_in [9-Arg_0 ]
eval_foo_bb4_in [9-Arg_0 ]
eval_foo_bb1_in [10-Arg_0 ]
MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=9 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && Arg_0<=Arg_1 && Arg_0<=9 && Arg_1<=0 of depth 1:
new bound:
Arg_2+10 {O(n)}
MPRF:
eval_foo_bb3_in [10-Arg_0 ]
eval_foo_bb2_in [10-Arg_0 ]
eval_foo_bb4_in [9-Arg_0 ]
eval_foo_bb1_in [10-Arg_0 ]
MPRF for transition 24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_1<=0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0 of depth 1:
new bound:
Arg_2+1 {O(n)}
MPRF:
eval_foo_bb3_in [1-Arg_0 ]
eval_foo_bb2_in [1-Arg_0 ]
eval_foo_bb4_in [1-Arg_0 ]
eval_foo_bb1_in [1-Arg_0 ]
Analysing control-flow refined program
Found invariant Arg_2<=Arg_0 && 10<=Arg_2 && 20<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 10<=Arg_0 for location eval_foo_bb5_in
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0 for location n_eval_foo_bb4_in___7
Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_1+Arg_2<=1 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb3_in___2
Found invariant Arg_2<=Arg_0 && 10<=Arg_2 && 20<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 10<=Arg_0 for location eval_foo_stop
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_1<=0 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=1 && Arg_0<=1+Arg_1 && Arg_0<=1 for location n_eval_foo_bb1_in___4
Found invariant Arg_2<=9 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=9 && 1<=Arg_0 for location n_eval_foo_bb3_in___5
Found invariant 1+Arg_2<=0 && 1+Arg_2<=Arg_1 && 1+Arg_1+Arg_2<=0 && 1+Arg_2<=Arg_0 && 1+Arg_0+Arg_2<=0 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0 for location n_eval_foo_bb4_in___1
Found invariant Arg_2<=9 && Arg_2<=Arg_1 && Arg_1+Arg_2<=18 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=9 && Arg_1<=Arg_0 && Arg_0+Arg_1<=18 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=9 && 1<=Arg_0 for location n_eval_foo_bb3_in___8
Found invariant Arg_2<=Arg_0 && Arg_0<=Arg_2 for location eval_foo_bb1_in
Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_1+Arg_2<=1 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && Arg_0<=Arg_1 && Arg_0<=1 for location n_eval_foo_bb2_in___3
Found invariant Arg_2<=9 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=9 && 1<=Arg_0 for location n_eval_foo_bb2_in___6
Found invariant Arg_2<=9 && Arg_2<=Arg_1 && Arg_1+Arg_2<=18 && Arg_2<=Arg_0 && Arg_0+Arg_2<=18 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=9 && Arg_1<=Arg_0 && Arg_0+Arg_1<=18 && Arg_0<=Arg_1 && Arg_0<=9 for location n_eval_foo_bb2_in___9
MPRF for transition 70:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___3(Arg_0,Arg_0,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_1<=0 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=1 && Arg_0<=1+Arg_1 && Arg_0<=1 && Arg_0<=9 && Arg_2<=Arg_0 && Arg_0<10 && Arg_2<=Arg_0 && Arg_0<=9 && 1+Arg_2<=Arg_0 && Arg_0<=1+Arg_1 && Arg_1<=0 && Arg_2<=Arg_0 && Arg_0<10 of depth 1:
new bound:
Arg_2+1 {O(n)}
MPRF:
n_eval_foo_bb2_in___3 [1-Arg_0 ]
n_eval_foo_bb4_in___1 [1-Arg_1 ]
n_eval_foo_bb1_in___4 [1-Arg_1 ]
MPRF for transition 72:n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb4_in___1(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_1+Arg_2<=1 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && Arg_0<=Arg_1 && Arg_0<=1 && Arg_0<=9 && Arg_0<=Arg_1 && Arg_2<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_0 && Arg_0<=9 && Arg_1<=0 && Arg_0<=Arg_1 && Arg_2<=Arg_0 of depth 1:
new bound:
Arg_2+11 {O(n)}
MPRF:
n_eval_foo_bb2_in___3 [10-Arg_0 ]
n_eval_foo_bb4_in___1 [9-Arg_0 ]
n_eval_foo_bb1_in___4 [10-Arg_0 ]
MPRF for transition 79:n_eval_foo_bb4_in___1(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1,Arg_2):|:1+Arg_2<=0 && 1+Arg_2<=Arg_1 && 1+Arg_1+Arg_2<=0 && 1+Arg_2<=Arg_0 && 1+Arg_0+Arg_2<=0 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0 && Arg_0<=0 && Arg_2<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_1<=0 && Arg_0<=Arg_1 && Arg_2<=Arg_0 of depth 1:
new bound:
Arg_2+2 {O(n)}
MPRF:
n_eval_foo_bb2_in___3 [1-Arg_1 ]
n_eval_foo_bb4_in___1 [1-Arg_1 ]
n_eval_foo_bb1_in___4 [1-Arg_0 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+10 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: inf {Infinity}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+10 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: inf {Infinity}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_2+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: inf {Infinity}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+10 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: inf {Infinity}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+10 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: inf {Infinity}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_2+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_2 {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_2: Arg_2 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_2+1 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_2+1 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: Arg_2 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: Arg_1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_2: Arg_2 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_2+1 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: Arg_2+1 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 2*Arg_2+1 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_2: Arg_2 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: Arg_2+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: Arg_2+1 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: 2*Arg_2+1 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: Arg_2 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: Arg_1 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_2: Arg_2 {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)}