Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_foo_0, eval_foo_1, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
7:eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,1,Arg_2,Arg_3):|:1<=Arg_0
9:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,0,Arg_2,Arg_3):|:Arg_0<1
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_3,Arg_2,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<Arg_1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=0 && 0<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3)
10:eval_foo_bb3_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

Found invariant Arg_0<=Arg_3 for location eval_foo_0

Found invariant Arg_0<=Arg_3 && Arg_1<=0 && 0<=Arg_1 for location eval_foo_stop

Found invariant Arg_0<=Arg_3 && Arg_1<=0 && 0<=Arg_1 for location eval_foo_bb3_in

Found invariant Arg_0<=Arg_3 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_3 for location eval_foo_1

Found invariant Arg_0<=Arg_3 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_foo_0, eval_foo_1, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
7:eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3
8:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && 1<=Arg_0
9:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,0,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_0<1
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_3,Arg_2,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_1<0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && 0<Arg_1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_1<=0 && 0<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3
10:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_1<=0 && 0<=Arg_1
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

knowledge_propagation leads to new time bound 1 {O(1)} for transition 2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_1<0

MPRF for transition 8:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && 1<=Arg_0 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

eval_foo_1 [Arg_0 ]
eval_foo_bb1_in [Arg_0 ]
eval_foo_bb2_in [Arg_0 ]
eval_foo_0 [Arg_0 ]

MPRF for transition 9:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,0,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_0<1 of depth 1:

new bound:

Arg_2+3 {O(n)}

MPRF:

eval_foo_1 [2 ]
eval_foo_bb1_in [Arg_1+1 ]
eval_foo_bb2_in [2 ]
eval_foo_0 [2 ]

knowledge_propagation leads to new time bound Arg_3+1 {O(n)} for transition 3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && 0<Arg_1

knowledge_propagation leads to new time bound Arg_3+2 {O(n)} for transition 5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3

knowledge_propagation leads to new time bound Arg_3+2 {O(n)} for transition 7:eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3

All Bounds

Timebounds

Overall timebound:4*Arg_3+Arg_2+13 {O(n)}
7: eval_foo_0->eval_foo_1: Arg_3+2 {O(n)}
8: eval_foo_1->eval_foo_bb1_in: Arg_3 {O(n)}
9: eval_foo_1->eval_foo_bb1_in: Arg_2+3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: 1 {O(1)}
3: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_0: Arg_3+2 {O(n)}
10: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_3+Arg_2+13 {O(n)}
7: eval_foo_0->eval_foo_1: Arg_3+2 {O(n)}
8: eval_foo_1->eval_foo_bb1_in: Arg_3 {O(n)}
9: eval_foo_1->eval_foo_bb1_in: Arg_2+3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: 1 {O(1)}
3: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_0: Arg_3+2 {O(n)}
10: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

7: eval_foo_0->eval_foo_1, Arg_0: 2*Arg_3 {O(n)}
7: eval_foo_0->eval_foo_1, Arg_1: 2*Arg_2+1 {O(n)}
7: eval_foo_0->eval_foo_1, Arg_2: 2*Arg_2 {O(n)}
7: eval_foo_0->eval_foo_1, Arg_3: 2*Arg_3 {O(n)}
8: eval_foo_1->eval_foo_bb1_in, Arg_0: 2*Arg_3 {O(n)}
8: eval_foo_1->eval_foo_bb1_in, Arg_1: 1 {O(1)}
8: eval_foo_1->eval_foo_bb1_in, Arg_2: 2*Arg_2 {O(n)}
8: eval_foo_1->eval_foo_bb1_in, Arg_3: 2*Arg_3 {O(n)}
9: eval_foo_1->eval_foo_bb1_in, Arg_0: 2*Arg_3+1 {O(n)}
9: eval_foo_1->eval_foo_bb1_in, Arg_1: 0 {O(1)}
9: eval_foo_1->eval_foo_bb1_in, Arg_2: 2*Arg_2 {O(n)}
9: eval_foo_1->eval_foo_bb1_in, Arg_3: 2*Arg_3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_2 {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)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_2 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_2+1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_2 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: 2*Arg_3 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 3*Arg_3+1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 0 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 3*Arg_2 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 3*Arg_3 {O(n)}
5: eval_foo_bb2_in->eval_foo_0, Arg_0: 2*Arg_3 {O(n)}
5: eval_foo_bb2_in->eval_foo_0, Arg_1: 2*Arg_2+1 {O(n)}
5: eval_foo_bb2_in->eval_foo_0, Arg_2: 2*Arg_2 {O(n)}
5: eval_foo_bb2_in->eval_foo_0, Arg_3: 2*Arg_3 {O(n)}
10: eval_foo_bb3_in->eval_foo_stop, Arg_0: 3*Arg_3+1 {O(n)}
10: eval_foo_bb3_in->eval_foo_stop, Arg_1: 0 {O(1)}
10: eval_foo_bb3_in->eval_foo_stop, Arg_2: 3*Arg_2 {O(n)}
10: eval_foo_bb3_in->eval_foo_stop, Arg_3: 3*Arg_3 {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)}