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_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_2,Arg_3,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,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_0+Arg_1 && Arg_0<=Arg_4
3:eval_foo_bb1_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_0+Arg_1<0
4:eval_foo_bb1_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_4<Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(2*Arg_0+Arg_1,Arg_1+1,Arg_2,Arg_3,Arg_4)
6:eval_foo_bb3_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

Found invariant Arg_3<=Arg_1 for location eval_foo_stop

Found invariant Arg_3<=Arg_1 for location eval_foo_bb3_in

Found invariant 0<=Arg_1+Arg_4 && Arg_0<=Arg_4 && Arg_3<=Arg_1 && 0<=Arg_0+Arg_1 for location eval_foo_bb2_in

Found invariant Arg_3<=Arg_1 for location eval_foo_bb1_in

Problem after Preprocessing

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_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_2,Arg_3,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,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_4
3:eval_foo_bb1_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_3<=Arg_1 && Arg_0+Arg_1<0
4:eval_foo_bb1_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_3<=Arg_1 && Arg_4<Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(2*Arg_0+Arg_1,Arg_1+1,Arg_2,Arg_3,Arg_4):|:0<=Arg_1+Arg_4 && Arg_0<=Arg_4 && Arg_3<=Arg_1 && 0<=Arg_0+Arg_1
6:eval_foo_bb3_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_3<=Arg_1
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 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_3<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_4 of depth 2:

new bound:

16*Arg_2+8*Arg_3+8*Arg_4+9 {O(n)}

MPRF:

eval_foo_bb2_in [-Arg_0-Arg_1 ; Arg_4-2*Arg_0-Arg_1 ]
eval_foo_bb1_in [1-Arg_0-Arg_1 ; Arg_4-Arg_0 ]

MPRF for transition 5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(2*Arg_0+Arg_1,Arg_1+1,Arg_2,Arg_3,Arg_4):|:0<=Arg_1+Arg_4 && Arg_0<=Arg_4 && Arg_3<=Arg_1 && 0<=Arg_0+Arg_1 of depth 2:

new bound:

16*Arg_2+8*Arg_3+8*Arg_4+9 {O(n)}

MPRF:

eval_foo_bb2_in [1-Arg_0-Arg_1 ; Arg_4-Arg_0 ]
eval_foo_bb1_in [1-Arg_0-Arg_1 ; Arg_4-Arg_0 ]

All Bounds

Timebounds

Overall timebound:16*Arg_3+16*Arg_4+32*Arg_2+23 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: 16*Arg_2+8*Arg_3+8*Arg_4+9 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb1_in: 16*Arg_2+8*Arg_3+8*Arg_4+9 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 16*Arg_3+16*Arg_4+32*Arg_2+23 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: 16*Arg_2+8*Arg_3+8*Arg_4+9 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb1_in: 16*Arg_2+8*Arg_3+8*Arg_4+9 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {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_0: 136*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_3*Arg_4+152*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_4+162*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_3+256*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_2+256*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_4+272*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_3+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*305*Arg_2+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*64*Arg_4*Arg_4+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*72*Arg_3*Arg_3+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*90 {O(EXP)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 16*Arg_2+8*Arg_4+9*Arg_3+9 {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)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: Arg_2 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 136*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_3*Arg_4+152*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_4+162*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_3+256*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_2+256*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_4+272*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_3+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*305*Arg_2+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*64*Arg_4*Arg_4+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*72*Arg_3*Arg_3+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*90+Arg_2 {O(EXP)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 10*Arg_3+16*Arg_2+8*Arg_4+9 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 136*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_3*Arg_4+152*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_4+162*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_3+256*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_2+256*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_4+272*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_3+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*305*Arg_2+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*64*Arg_4*Arg_4+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*72*Arg_3*Arg_3+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*90 {O(EXP)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 16*Arg_2+8*Arg_4+9*Arg_3+9 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_0: 136*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_3*Arg_4+152*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_4+162*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_3+256*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_2+256*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_4+272*2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*Arg_2*Arg_3+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*305*Arg_2+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*64*Arg_4*Arg_4+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*72*Arg_3*Arg_3+2^(16*Arg_2+8*Arg_3+8*Arg_4+9)*90+2*Arg_2 {O(EXP)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_1: 11*Arg_3+16*Arg_2+8*Arg_4+9 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_2: 3*Arg_2 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_3: 3*Arg_3 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_4: 3*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)}