Initial Problem
Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, 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:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_3,Arg_1,Arg_2,Arg_3,Arg_4)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,0,Arg_2,Arg_3,Arg_4):|:0<=Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1+1<=Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<1+Arg_1
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4)
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3,Arg_4)
8:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
Preprocessing
Eliminate variables {Arg_2,Arg_4} that do not contribute to the problem
Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_bb5_in
Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_stop
Found invariant 1<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_foo_bb3_in
Found invariant 0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb2_in
Found invariant Arg_0<=Arg_3 for location eval_foo_bb1_in
Found invariant 0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb4_in
Problem after Preprocessing
Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, 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:
18:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_3,Arg_1,Arg_3)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,0,Arg_3):|:Arg_0<=Arg_3 && 0<=Arg_0
20:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_3):|:Arg_0<=Arg_3 && Arg_0<0
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_0
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<1+Arg_1
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_3):|:1<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_3):|:0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
25:eval_foo_bb5_in(Arg_0,Arg_1,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_3):|:Arg_0<=Arg_3 && 1+Arg_0<=0
26:eval_foo_start(Arg_0,Arg_1,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_3)
MPRF for transition 19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,0,Arg_3):|:Arg_0<=Arg_3 && 0<=Arg_0 of depth 1:
new bound:
Arg_3+1 {O(n)}
MPRF:
eval_foo_bb3_in [Arg_0 ]
eval_foo_bb2_in [Arg_0 ]
eval_foo_bb4_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]
MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<1+Arg_1 of depth 1:
new bound:
Arg_3+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 24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_3):|:0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:
new bound:
Arg_3+1 {O(n)}
MPRF:
eval_foo_bb3_in [Arg_0+1 ]
eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_1+1 ]
eval_foo_bb1_in [Arg_0+1 ]
MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_0 of depth 1:
new bound:
Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
MPRF:
eval_foo_bb1_in [Arg_0+1 ]
eval_foo_bb4_in [1 ]
eval_foo_bb3_in [Arg_0-Arg_1 ]
eval_foo_bb2_in [Arg_0+1-Arg_1 ]
MPRF for transition 23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_3):|:1<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
MPRF:
eval_foo_bb1_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_0+1-Arg_1 ]
eval_foo_bb3_in [Arg_0+1-Arg_1 ]
eval_foo_bb2_in [Arg_0+1-Arg_1 ]
Analysing control-flow refined program
Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_bb5_in
Found invariant 1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_foo_bb2_in___2
Found invariant 2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_foo_bb3_in___1
Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_stop
Found invariant 1<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_foo_bb3_in___3
Found invariant 0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb2_in
Found invariant Arg_0<=Arg_3 for location eval_foo_bb1_in
Found invariant 0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb4_in
knowledge_propagation leads to new time bound Arg_3+1 {O(n)} for transition 60:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb3_in___3(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_3 && 0<=Arg_1 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_3 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_3
knowledge_propagation leads to new time bound Arg_3+1 {O(n)} for transition 62:n_eval_foo_bb3_in___3(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb2_in___2(Arg_0,Arg_1+1,Arg_3):|:1<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_3
MPRF for transition 59:n_eval_foo_bb2_in___2(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb3_in___1(Arg_0,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_3 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_3 of depth 1:
new bound:
Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
MPRF:
eval_foo_bb2_in [0 ]
n_eval_foo_bb3_in___3 [0 ]
eval_foo_bb1_in [0 ]
eval_foo_bb4_in [0 ]
n_eval_foo_bb3_in___1 [Arg_0-Arg_1 ]
n_eval_foo_bb2_in___2 [Arg_0+1-Arg_1 ]
MPRF for transition 67:n_eval_foo_bb2_in___2(Arg_0,Arg_1,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<1+Arg_1 of depth 1:
new bound:
Arg_3 {O(n)}
MPRF:
eval_foo_bb2_in [Arg_0 ]
eval_foo_bb1_in [Arg_0 ]
eval_foo_bb4_in [Arg_1-1 ]
n_eval_foo_bb3_in___1 [Arg_0 ]
n_eval_foo_bb3_in___3 [Arg_0 ]
n_eval_foo_bb2_in___2 [Arg_0 ]
MPRF for transition 61:n_eval_foo_bb3_in___1(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb2_in___2(Arg_0,Arg_1+1,Arg_3):|:2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_3 of depth 1:
new bound:
Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
MPRF:
eval_foo_bb2_in [0 ]
n_eval_foo_bb3_in___3 [0 ]
eval_foo_bb1_in [0 ]
eval_foo_bb4_in [0 ]
n_eval_foo_bb3_in___1 [Arg_0-Arg_1 ]
n_eval_foo_bb2_in___2 [Arg_0-Arg_1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:2*Arg_3*Arg_3+11*Arg_3+13 {O(n^2)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_3+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_3+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: 2*Arg_3*Arg_3+11*Arg_3+13 {O(n^2)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_3+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_3+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_3 {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_3: Arg_3 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3+1 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 0 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 2*Arg_3+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: Arg_3*Arg_3+4*Arg_3+Arg_1+3 {O(n^2)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_3: 2*Arg_3 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_3+1 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: Arg_3+1 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_3: Arg_3 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: Arg_3+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_1: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: Arg_3+1 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: 2*Arg_3+1 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: Arg_3*Arg_3+4*Arg_3+Arg_1+3 {O(n^2)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_3: 2*Arg_3 {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_3: Arg_3 {O(n)}