Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
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,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_4,Arg_5,Arg_6,Arg_3,Arg_4,Arg_5,Arg_6)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<=Arg_0+Arg_1 && Arg_0<=Arg_3
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_0+Arg_1<0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_3<Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(2*Arg_0+Arg_1,Arg_2,Arg_2+1,Arg_3,Arg_4,Arg_5,Arg_6)
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)

Preprocessing

Found invariant Arg_6<=Arg_2 for location eval_foo_stop

Found invariant Arg_6<=Arg_2 for location eval_foo_bb3_in

Found invariant Arg_6<=Arg_2 && 0<=Arg_1+Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0+Arg_1 for location eval_foo_bb2_in

Found invariant Arg_6<=Arg_2 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, Arg_5, Arg_6
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,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_4,Arg_5,Arg_6,Arg_3,Arg_4,Arg_5,Arg_6)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_2 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_3
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_2 && Arg_0+Arg_1<0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_2 && Arg_3<Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(2*Arg_0+Arg_1,Arg_2,Arg_2+1,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_2 && 0<=Arg_1+Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0+Arg_1
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_2
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)

MPRF for transition 2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_2 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_3 of depth 3:

new bound:

54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82 {O(n)}

MPRF:

eval_foo_bb2_in [1-Arg_0-Arg_2 ; Arg_3+2-2*Arg_0-Arg_1 ; Arg_2+Arg_3 ]
eval_foo_bb1_in [2-Arg_0-Arg_2 ; Arg_2+Arg_3+1-Arg_0-Arg_1 ; Arg_1+Arg_3 ]

MPRF for transition 5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(2*Arg_0+Arg_1,Arg_2,Arg_2+1,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_2 && 0<=Arg_1+Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0+Arg_1 of depth 3:

new bound:

54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82 {O(n)}

MPRF:

eval_foo_bb2_in [2-Arg_0-Arg_2 ; Arg_2+Arg_3+1-Arg_0-Arg_1 ; Arg_1+Arg_3 ]
eval_foo_bb1_in [2-Arg_0-Arg_2 ; Arg_2+Arg_3+1-Arg_0-Arg_1 ; Arg_1+Arg_3 ]

All Bounds

Timebounds

Overall timebound:108*Arg_3+108*Arg_4+108*Arg_5+108*Arg_6+169 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: 54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82 {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: 54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82 {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: 108*Arg_3+108*Arg_4+108*Arg_5+108*Arg_6+169 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: 54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82 {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: 54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82 {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_4 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_5 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_6 {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)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2916*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_3*Arg_3+2916*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_4*Arg_4+2970*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_5*Arg_5+2970*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_6*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5832*Arg_3*Arg_4+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_3*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_3*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_4*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_4*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5940*Arg_5*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*6806+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8910*Arg_3+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8911*Arg_4+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8993*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8993*Arg_6 {O(EXP)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 54*Arg_3+54*Arg_4+55*Arg_5+55*Arg_6+82 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 54*Arg_3+54*Arg_4+54*Arg_5+55*Arg_6+82 {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)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_5: Arg_5 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_6: Arg_6 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2916*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_3*Arg_3+2916*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_4*Arg_4+2970*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_5*Arg_5+2970*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_6*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5832*Arg_3*Arg_4+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_3*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_3*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_4*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_4*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5940*Arg_5*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*6806+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8910*Arg_3+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8911*Arg_4+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8993*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8993*Arg_6+Arg_4 {O(EXP)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 54*Arg_3+54*Arg_4+55*Arg_5+55*Arg_6+82 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 54*Arg_3+54*Arg_4+54*Arg_5+56*Arg_6+82 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_5: 2*Arg_5 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_6: 2*Arg_6 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2916*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_3*Arg_3+2916*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_4*Arg_4+2970*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_5*Arg_5+2970*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_6*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5832*Arg_3*Arg_4+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_3*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_3*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_4*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_4*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5940*Arg_5*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*6806+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8910*Arg_3+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8911*Arg_4+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8993*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8993*Arg_6+Arg_4 {O(EXP)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 54*Arg_3+54*Arg_4+55*Arg_5+55*Arg_6+82 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 54*Arg_3+54*Arg_4+54*Arg_5+56*Arg_6+82 {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)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_5: 2*Arg_5 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_6: 2*Arg_6 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2916*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_3*Arg_3+2916*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_4*Arg_4+2970*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_5*Arg_5+2970*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_6*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5832*Arg_3*Arg_4+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_3*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_3*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_4*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5886*Arg_4*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5940*Arg_5*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*6806+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8910*Arg_3+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8911*Arg_4+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8993*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*8993*Arg_6 {O(EXP)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 54*Arg_3+54*Arg_4+54*Arg_5+55*Arg_6+82 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 54*Arg_3+54*Arg_4+54*Arg_5+55*Arg_6+82 {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)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_0: 11664*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_3*Arg_4+11772*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_3*Arg_5+11772*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_3*Arg_6+11772*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_4*Arg_5+11772*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_4*Arg_6+11880*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_5*Arg_6+13612*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)+17820*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_3+17822*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_4+17986*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_5+17986*2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*Arg_6+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5832*Arg_3*Arg_3+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5832*Arg_4*Arg_4+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5940*Arg_5*Arg_5+2^(54*Arg_3+54*Arg_4+54*Arg_5+54*Arg_6+82)*5940*Arg_6*Arg_6+2*Arg_4 {O(EXP)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_1: 108*Arg_3+108*Arg_4+110*Arg_5+110*Arg_6+164 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_2: 108*Arg_3+108*Arg_4+108*Arg_5+112*Arg_6+164 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_3: 4*Arg_3 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_4: 4*Arg_4 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_5: 4*Arg_5 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_6: 4*Arg_6 {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)}
0: eval_foo_start->eval_foo_bb0_in, Arg_5: Arg_5 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_6: Arg_6 {O(n)}