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_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) -> eval_foo_bb1_in(Arg_3,Arg_4,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_1,1,Arg_3,Arg_4):|:0<=Arg_0 && 0<Arg_1
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=0
5:eval_foo_bb2_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_2<Arg_0 && 0<Arg_2
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_2
7:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=0
8:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,2*Arg_2,Arg_3,Arg_4)
9:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_2,Arg_3,Arg_4)
10:eval_foo_bb5_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_0<=Arg_3 for location eval_foo_bb5_in
Found invariant Arg_0<=Arg_3 for location eval_foo_stop
Found invariant 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb3_in
Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb2_in
Found invariant Arg_0<=Arg_3 for location eval_foo_bb1_in
Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb4_in
Cut unsatisfiable transition 7: eval_foo_bb2_in->eval_foo_bb4_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_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) -> eval_foo_bb1_in(Arg_3,Arg_4,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_1,1,Arg_3,Arg_4):|:Arg_0<=Arg_3 && 0<=Arg_0 && 0<Arg_1
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_3 && Arg_0<0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_3 && Arg_1<=0
5:eval_foo_bb2_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):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<Arg_0 && 0<Arg_2
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_2
8:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,2*Arg_2,Arg_3,Arg_4):|:2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
9:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0
10:eval_foo_bb5_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_0<=Arg_3
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_1,1,Arg_3,Arg_4):|:Arg_0<=Arg_3 && 0<=Arg_0 && 0<Arg_1 of depth 1:
new bound:
Arg_3+1 {O(n)}
MPRF:
eval_foo_bb3_in [Arg_0 ]
eval_foo_bb2_in [Arg_0 ]
eval_foo_bb4_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]
MPRF for transition 6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_2 of depth 1:
new bound:
Arg_3+1 {O(n)}
MPRF:
eval_foo_bb3_in [Arg_0+1 ]
eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]
MPRF for transition 9:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:
new bound:
Arg_3+1 {O(n)}
MPRF:
eval_foo_bb3_in [Arg_0+1 ]
eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_0+1 ]
eval_foo_bb1_in [Arg_0+1 ]
MPRF for transition 5:eval_foo_bb2_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):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<Arg_0 && 0<Arg_2 of depth 1:
new bound:
Arg_3*Arg_3+2*Arg_3 {O(n^2)}
MPRF:
eval_foo_bb1_in [Arg_3 ]
eval_foo_bb4_in [-Arg_2 ]
eval_foo_bb3_in [Arg_3-2*Arg_2 ]
eval_foo_bb2_in [Arg_3-Arg_2 ]
MPRF for transition 8:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,2*Arg_2,Arg_3,Arg_4):|:2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:
new bound:
Arg_3*Arg_3+3*Arg_3+1 {O(n^2)}
MPRF:
eval_foo_bb1_in [Arg_0 ]
eval_foo_bb4_in [Arg_0-Arg_2 ]
eval_foo_bb3_in [Arg_0-Arg_2 ]
eval_foo_bb2_in [Arg_0-Arg_2 ]
All Bounds
Timebounds
Overall timebound:2*Arg_3*Arg_3+8*Arg_3+9 {O(n^2)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3*Arg_3+2*Arg_3 {O(n^2)}
6: eval_foo_bb2_in->eval_foo_bb4_in: Arg_3+1 {O(n)}
8: eval_foo_bb3_in->eval_foo_bb2_in: Arg_3*Arg_3+3*Arg_3+1 {O(n^2)}
9: eval_foo_bb4_in->eval_foo_bb1_in: Arg_3+1 {O(n)}
10: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: 2*Arg_3*Arg_3+8*Arg_3+9 {O(n^2)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3*Arg_3+2*Arg_3 {O(n^2)}
6: eval_foo_bb2_in->eval_foo_bb4_in: Arg_3+1 {O(n)}
8: eval_foo_bb3_in->eval_foo_bb2_in: Arg_3*Arg_3+3*Arg_3+1 {O(n^2)}
9: eval_foo_bb4_in->eval_foo_bb1_in: Arg_3+1 {O(n)}
10: eval_foo_bb5_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_3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_4 {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: Arg_3+1 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+Arg_4+1 {O(EXP)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 1 {O(1)}
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_bb5_in, Arg_0: 2*Arg_3+1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+Arg_4+1 {O(EXP)}
3: eval_foo_bb1_in->eval_foo_bb5_in, Arg_2: 2^(Arg_3*Arg_3+3*Arg_3+1)+Arg_2+1 {O(EXP)}
3: eval_foo_bb1_in->eval_foo_bb5_in, Arg_3: 2*Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb5_in, Arg_4: 2*Arg_4 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: Arg_3 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: Arg_4 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb5_in, Arg_2: Arg_2 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb5_in, Arg_3: Arg_3 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb5_in, Arg_4: Arg_4 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_3+1 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+Arg_4+1 {O(EXP)}
5: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: 2^(Arg_3*Arg_3+3*Arg_3+1) {O(EXP)}
5: eval_foo_bb2_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
6: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: Arg_3+1 {O(n)}
6: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 2*2^(Arg_3*Arg_3+3*Arg_3+1)+2*Arg_4+2 {O(EXP)}
6: eval_foo_bb2_in->eval_foo_bb4_in, Arg_2: 2^(Arg_3*Arg_3+3*Arg_3+1)+1 {O(EXP)}
6: eval_foo_bb2_in->eval_foo_bb4_in, Arg_3: Arg_3 {O(n)}
6: eval_foo_bb2_in->eval_foo_bb4_in, Arg_4: Arg_4 {O(n)}
8: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: Arg_3+1 {O(n)}
8: eval_foo_bb3_in->eval_foo_bb2_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+Arg_4+1 {O(EXP)}
8: eval_foo_bb3_in->eval_foo_bb2_in, Arg_2: 2^(Arg_3*Arg_3+3*Arg_3+1) {O(EXP)}
8: eval_foo_bb3_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
8: eval_foo_bb3_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
9: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: Arg_3+1 {O(n)}
9: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+1 {O(EXP)}
9: eval_foo_bb4_in->eval_foo_bb1_in, Arg_2: 2^(Arg_3*Arg_3+3*Arg_3+1)+1 {O(EXP)}
9: eval_foo_bb4_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
9: eval_foo_bb4_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
10: eval_foo_bb5_in->eval_foo_stop, Arg_0: 3*Arg_3+1 {O(n)}
10: eval_foo_bb5_in->eval_foo_stop, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+2*Arg_4+1 {O(EXP)}
10: eval_foo_bb5_in->eval_foo_stop, Arg_2: 2^(Arg_3*Arg_3+3*Arg_3+1)+2*Arg_2+1 {O(EXP)}
10: eval_foo_bb5_in->eval_foo_stop, Arg_3: 3*Arg_3 {O(n)}
10: eval_foo_bb5_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)}