Initial Problem
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_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<1 && Arg_0<0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<1 && 0<Arg_0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:1<Arg_0 && Arg_0<0
5:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:1<Arg_0 && 0<Arg_0
6:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=1 && 1<=Arg_0
7:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0
8:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0-2,Arg_1,Arg_2)
9:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2)
0:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)
Preprocessing
Cut unsatisfiable transition 3: eval_foo_bb1_in->eval_foo_bb2_in
Cut unsatisfiable transition 4: eval_foo_bb1_in->eval_foo_bb2_in
Eliminate variables {Arg_1} that do not contribute to the problem
Found invariant 0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_0<=1 && 0<=Arg_0 for location eval_foo_stop
Found invariant 0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_0<=1 && 0<=Arg_0 for location eval_foo_bb3_in
Found invariant Arg_0<=Arg_2 for location eval_foo_bb2_in
Found invariant Arg_0<=Arg_2 for location eval_foo_bb1_in
Problem after Preprocessing
Start: eval_foo_start
Program_Vars: Arg_0, Arg_2
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
22:eval_foo_bb0_in(Arg_0,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_2)
23:eval_foo_bb1_in(Arg_0,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_2):|:Arg_0<=Arg_2 && Arg_0<1 && Arg_0<0
24:eval_foo_bb1_in(Arg_0,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_2):|:Arg_0<=Arg_2 && 1<Arg_0 && 0<Arg_0
25:eval_foo_bb1_in(Arg_0,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_2):|:Arg_0<=Arg_2 && Arg_0<=1 && 1<=Arg_0
26:eval_foo_bb1_in(Arg_0,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_2):|:Arg_0<=Arg_2 && Arg_0<=0 && 0<=Arg_0
27:eval_foo_bb2_in(Arg_0,Arg_2) -> eval_foo_bb1_in(Arg_0-2,Arg_2):|:Arg_0<=Arg_2
28:eval_foo_bb3_in(Arg_0,Arg_2) -> eval_foo_stop(Arg_0,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_0<=1 && 0<=Arg_0
29:eval_foo_start(Arg_0,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_2)
MPRF for transition 24:eval_foo_bb1_in(Arg_0,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_2):|:Arg_0<=Arg_2 && 1<Arg_0 && 0<Arg_0 of depth 1:
new bound:
Arg_2+1 {O(n)}
MPRF:
eval_foo_bb2_in [Arg_0-3 ]
eval_foo_bb1_in [Arg_0-1 ]
Analysing control-flow refined program
Cut unsatisfiable transition 65: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___2
Cut unsatisfiable transition 82: n_eval_foo_bb1_in___5->eval_foo_bb3_in
Cut unsatisfiable transition 84: n_eval_foo_bb1_in___5->eval_foo_bb3_in
Cut unreachable locations [n_eval_foo_bb2_in___2] from the program graph
Found invariant 1+Arg_2<=0 && 4+Arg_0+Arg_2<=0 && 2+Arg_0<=Arg_2 && 3+Arg_0<=0 for location n_eval_foo_bb2_in___4
Found invariant 1+Arg_2<=0 && Arg_2<=Arg_0 && 2+Arg_0+Arg_2<=0 && Arg_0<=Arg_2 && 1+Arg_0<=0 for location n_eval_foo_bb2_in___7
Found invariant 0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_0<=1 && 0<=Arg_0 for location eval_foo_stop
Found invariant 2<=Arg_2 && 2<=Arg_0+Arg_2 && 2+Arg_0<=Arg_2 && 0<=Arg_0 for location n_eval_foo_bb1_in___3
Found invariant 0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_0<=1 && 0<=Arg_0 for location eval_foo_bb3_in
Found invariant 1+Arg_2<=0 && 4+Arg_0+Arg_2<=0 && 2+Arg_0<=Arg_2 && 3+Arg_0<=0 for location n_eval_foo_bb1_in___5
Found invariant 4<=Arg_2 && 6<=Arg_0+Arg_2 && 2+Arg_0<=Arg_2 && 2<=Arg_0 for location n_eval_foo_bb2_in___1
Found invariant Arg_2<=Arg_0 && Arg_0<=Arg_2 for location eval_foo_bb1_in
Found invariant Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 2<=Arg_0 for location n_eval_foo_bb2_in___6
MPRF for transition 64:n_eval_foo_bb1_in___3(Arg_0,Arg_2) -> n_eval_foo_bb2_in___1(Arg_0,Arg_2):|:2<=Arg_2 && 2<=Arg_0+Arg_2 && 2+Arg_0<=Arg_2 && 0<=Arg_0 && Arg_0<=Arg_2 && 2+Arg_0<=Arg_2 && 1<Arg_0 && Arg_0<=Arg_2 of depth 1:
new bound:
Arg_2+1 {O(n)}
MPRF:
n_eval_foo_bb2_in___1 [Arg_0-1 ]
n_eval_foo_bb1_in___3 [Arg_0+1 ]
MPRF for transition 69:n_eval_foo_bb2_in___1(Arg_0,Arg_2) -> n_eval_foo_bb1_in___3(Arg_0-2,Arg_2):|:4<=Arg_2 && 6<=Arg_0+Arg_2 && 2+Arg_0<=Arg_2 && 2<=Arg_0 && 2+Arg_0<=Arg_2 && 1<Arg_0 && Arg_0<=Arg_2 of depth 1:
new bound:
Arg_2+1 {O(n)}
MPRF:
n_eval_foo_bb2_in___1 [Arg_0-1 ]
n_eval_foo_bb1_in___3 [Arg_0-1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
22: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
23: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
24: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+1 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
26: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
27: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
28: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
29: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
22: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
23: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
24: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+1 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
26: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
27: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
28: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
29: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
Sizebounds
22: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
23: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_2 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_2 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 1 {O(1)}
25: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 3*Arg_2 {O(n)}
26: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 0 {O(1)}
26: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 3*Arg_2 {O(n)}
27: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 2*Arg_2 {O(n)}
28: eval_foo_bb3_in->eval_foo_stop, Arg_0: 1 {O(1)}
28: eval_foo_bb3_in->eval_foo_stop, Arg_2: 6*Arg_2 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}