Initial Problem
Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef.0
Locations: eval_foo_.critedge_in, eval_foo_2, eval_foo_3, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_start, eval_foo_stop
Transitions:
9:eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
7:eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_3(Arg_0,Arg_1,nondef.0,Arg_3,Arg_4)
8:eval_foo_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_2,Arg_0,Arg_2,Arg_3,Arg_4)
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_4,Arg_3,Arg_2,Arg_3,Arg_4)
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<2*Arg_0
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1<Arg_0 && 2*Arg_0<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_2(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
Found invariant 4<=Arg_3 && 8<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 4<=Arg_1 && 6<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 2<=Arg_0 for location eval_foo_2
Found invariant Arg_1<=Arg_3 for location eval_foo_stop
Found invariant 4<=Arg_3 && 8<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 4<=Arg_1 && 6<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 2<=Arg_0 for location eval_foo_3
Found invariant 4<=Arg_3 && 8<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 4<=Arg_1 && 6<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 2<=Arg_0 for location eval_foo_bb2_in
Found invariant Arg_1<=Arg_3 for location eval_foo_bb1_in
Found invariant Arg_1<=Arg_3 for location eval_foo_.critedge_in
Problem after Preprocessing
Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef.0
Locations: eval_foo_.critedge_in, eval_foo_2, eval_foo_3, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_start, eval_foo_stop
Transitions:
9:eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_3
7:eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_3(Arg_0,Arg_1,nondef.0,Arg_3,Arg_4):|:4<=Arg_3 && 8<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 4<=Arg_1 && 6<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 2<=Arg_0
8:eval_foo_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_2,Arg_0,Arg_2,Arg_3,Arg_4):|:4<=Arg_3 && 8<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 4<=Arg_1 && 6<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 2<=Arg_0
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_4,Arg_3,Arg_2,Arg_3,Arg_4)
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_3 && Arg_0<=1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_3 && Arg_1<2*Arg_0
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_3 && 1<Arg_0 && 2*Arg_0<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:4<=Arg_3 && 8<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 4<=Arg_1 && 6<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 2<=Arg_0
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)
MPRF for transition 7:eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_3(Arg_0,Arg_1,nondef.0,Arg_3,Arg_4):|:4<=Arg_3 && 8<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 4<=Arg_1 && 6<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 2<=Arg_0 of depth 1:
new bound:
Arg_3 {O(n)}
MPRF:
eval_foo_3 [Arg_0 ]
eval_foo_bb1_in [Arg_1 ]
eval_foo_bb2_in [2*Arg_0 ]
eval_foo_2 [Arg_0+2 ]
MPRF for transition 8:eval_foo_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_2,Arg_0,Arg_2,Arg_3,Arg_4):|:4<=Arg_3 && 8<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 4<=Arg_1 && 6<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 2<=Arg_0 of depth 1:
new bound:
Arg_3+3 {O(n)}
MPRF:
eval_foo_3 [Arg_1-3 ]
eval_foo_bb1_in [Arg_1-3 ]
eval_foo_bb2_in [Arg_1-3 ]
eval_foo_2 [Arg_1-3 ]
MPRF for transition 2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_3 && 1<Arg_0 && 2*Arg_0<=Arg_1 of depth 1:
new bound:
Arg_3+2 {O(n)}
MPRF:
eval_foo_3 [2*Arg_0-4 ]
eval_foo_bb1_in [Arg_1-2 ]
eval_foo_bb2_in [2*Arg_0-4 ]
eval_foo_2 [2*Arg_0-4 ]
MPRF for transition 5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:4<=Arg_3 && 8<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 4<=Arg_1 && 6<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 2<=Arg_0 of depth 1:
new bound:
Arg_3+3 {O(n)}
MPRF:
eval_foo_3 [Arg_0-3 ]
eval_foo_bb1_in [Arg_1-3 ]
eval_foo_bb2_in [Arg_1-3 ]
eval_foo_2 [Arg_1-5 ]
All Bounds
Timebounds
Overall timebound:4*Arg_3+13 {O(n)}
9: eval_foo_.critedge_in->eval_foo_stop: 1 {O(1)}
7: eval_foo_2->eval_foo_3: Arg_3 {O(n)}
8: eval_foo_3->eval_foo_bb1_in: Arg_3+3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+2 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_2: Arg_3+3 {O(n)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: 4*Arg_3+13 {O(n)}
9: eval_foo_.critedge_in->eval_foo_stop: 1 {O(1)}
7: eval_foo_2->eval_foo_3: Arg_3 {O(n)}
8: eval_foo_3->eval_foo_bb1_in: Arg_3+3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+2 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_2: Arg_3+3 {O(n)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
Sizebounds
9: eval_foo_.critedge_in->eval_foo_stop, Arg_3: 4*Arg_3 {O(n)}
9: eval_foo_.critedge_in->eval_foo_stop, Arg_4: 4*Arg_4 {O(n)}
7: eval_foo_2->eval_foo_3, Arg_3: Arg_3 {O(n)}
7: eval_foo_2->eval_foo_3, Arg_4: Arg_4 {O(n)}
8: eval_foo_3->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
8: eval_foo_3->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_4 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_3: 2*Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_4: 2*Arg_4 {O(n)}
4: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_3: 2*Arg_3 {O(n)}
4: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_4: 2*Arg_4 {O(n)}
5: eval_foo_bb2_in->eval_foo_2, Arg_3: Arg_3 {O(n)}
5: eval_foo_bb2_in->eval_foo_2, Arg_4: Arg_4 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}