Initial Problem
Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
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) -> eval_foo_bb1_in(Arg_3,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:0<Arg_4 && 0<Arg_3
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4<=0
3:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_3<=0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:0<Arg_0
5:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_0,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=0
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
7:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_4
8:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4<=Arg_1
9:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5)
10:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
Preprocessing
Eliminate variables {Arg_2,Arg_5} that do not contribute to the problem
Found invariant 1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && 1<=Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location eval_foo_bb3_in
Found invariant 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 for location eval_foo_bb2_in
Found invariant 1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_0+Arg_4 && 1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0 for location eval_foo_bb1_in
Found invariant 1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && 1<=Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location eval_foo_bb4_in
Problem after Preprocessing
Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, 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:
22:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_3,Arg_1,Arg_3,Arg_4):|:0<Arg_4 && 0<Arg_3
23:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=0
24:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_3<=0
25:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_0+Arg_4 && 1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0 && 0<Arg_0
26:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_0,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_0+Arg_4 && 1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0 && Arg_0<=0
27:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0
28:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && 1<=Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_1<Arg_4
29:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && 1<=Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_4<=Arg_1
30:eval_foo_bb4_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1+1,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && 1<=Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0
31:eval_foo_bb5_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_3,Arg_4)
32:eval_foo_start(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4)
MPRF for transition 25:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_0+Arg_4 && 1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0 && 0<Arg_0 of depth 1:
new bound:
Arg_3+1 {O(n)}
MPRF:
eval_foo_bb2_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]
MPRF for transition 27:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 of depth 1:
new bound:
Arg_3 {O(n)}
MPRF:
eval_foo_bb2_in [Arg_0 ]
eval_foo_bb1_in [Arg_0 ]
MPRF for transition 28:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && 1<=Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_1<Arg_4 of depth 1:
new bound:
Arg_4+1 {O(n)}
MPRF:
eval_foo_bb4_in [Arg_4-Arg_1 ]
eval_foo_bb3_in [Arg_4+1-Arg_1 ]
MPRF for transition 30:eval_foo_bb4_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1+1,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_3+Arg_4 && 1<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && 1<=Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 of depth 1:
new bound:
Arg_4 {O(n)}
MPRF:
eval_foo_bb4_in [Arg_4-Arg_1 ]
eval_foo_bb3_in [Arg_4-Arg_1 ]
All Bounds
Timebounds
Overall timebound:2*Arg_3+2*Arg_4+9 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
23: eval_foo_bb0_in->eval_foo_bb5_in: 1 {O(1)}
24: eval_foo_bb0_in->eval_foo_bb5_in: 1 {O(1)}
25: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+1 {O(n)}
26: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
27: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3 {O(n)}
28: eval_foo_bb3_in->eval_foo_bb4_in: Arg_4+1 {O(n)}
29: eval_foo_bb3_in->eval_foo_bb5_in: 1 {O(1)}
30: eval_foo_bb4_in->eval_foo_bb3_in: Arg_4 {O(n)}
31: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
32: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: 2*Arg_3+2*Arg_4+9 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
23: eval_foo_bb0_in->eval_foo_bb5_in: 1 {O(1)}
24: eval_foo_bb0_in->eval_foo_bb5_in: 1 {O(1)}
25: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+1 {O(n)}
26: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
27: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3 {O(n)}
28: eval_foo_bb3_in->eval_foo_bb4_in: Arg_4+1 {O(n)}
29: eval_foo_bb3_in->eval_foo_bb5_in: 1 {O(1)}
30: eval_foo_bb4_in->eval_foo_bb3_in: Arg_4 {O(n)}
31: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
32: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
Sizebounds
22: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
23: eval_foo_bb0_in->eval_foo_bb5_in, Arg_0: Arg_0 {O(n)}
23: eval_foo_bb0_in->eval_foo_bb5_in, Arg_1: Arg_1 {O(n)}
23: eval_foo_bb0_in->eval_foo_bb5_in, Arg_3: Arg_3 {O(n)}
23: eval_foo_bb0_in->eval_foo_bb5_in, Arg_4: Arg_4 {O(n)}
24: eval_foo_bb0_in->eval_foo_bb5_in, Arg_0: Arg_0 {O(n)}
24: eval_foo_bb0_in->eval_foo_bb5_in, Arg_1: Arg_1 {O(n)}
24: eval_foo_bb0_in->eval_foo_bb5_in, Arg_3: Arg_3 {O(n)}
24: eval_foo_bb0_in->eval_foo_bb5_in, Arg_4: Arg_4 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_1 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {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_1: 0 {O(1)}
26: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
26: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
27: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
27: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
27: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
27: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
28: eval_foo_bb3_in->eval_foo_bb4_in, Arg_0: 0 {O(1)}
28: eval_foo_bb3_in->eval_foo_bb4_in, Arg_1: Arg_4 {O(n)}
28: eval_foo_bb3_in->eval_foo_bb4_in, Arg_3: Arg_3 {O(n)}
28: eval_foo_bb3_in->eval_foo_bb4_in, Arg_4: Arg_4 {O(n)}
29: eval_foo_bb3_in->eval_foo_bb5_in, Arg_0: 0 {O(1)}
29: eval_foo_bb3_in->eval_foo_bb5_in, Arg_1: Arg_4 {O(n)}
29: eval_foo_bb3_in->eval_foo_bb5_in, Arg_3: Arg_3 {O(n)}
29: eval_foo_bb3_in->eval_foo_bb5_in, Arg_4: Arg_4 {O(n)}
30: eval_foo_bb4_in->eval_foo_bb3_in, Arg_0: 0 {O(1)}
30: eval_foo_bb4_in->eval_foo_bb3_in, Arg_1: Arg_4 {O(n)}
30: eval_foo_bb4_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
30: eval_foo_bb4_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
31: eval_foo_bb5_in->eval_foo_stop, Arg_0: 2*Arg_0 {O(n)}
31: eval_foo_bb5_in->eval_foo_stop, Arg_1: 2*Arg_1+Arg_4 {O(n)}
31: eval_foo_bb5_in->eval_foo_stop, Arg_3: 3*Arg_3 {O(n)}
31: eval_foo_bb5_in->eval_foo_stop, Arg_4: 3*Arg_4 {O(n)}
32: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
32: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
32: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
32: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}