Initial Problem

Start: eval_wise_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_wise_0, eval_wise_1, eval_wise_2, eval_wise__critedge_in, eval_wise_bb0_in, eval_wise_bb1_in, eval_wise_bb2_in, eval_wise_start, eval_wise_stop
Transitions:
2:eval_wise_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_wise_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_2(Arg_0,Arg_1,Arg_2,Arg_3)
6:eval_wise_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3):|:0<=Arg_2 && 0<=Arg_3
4:eval_wise_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<0
5:eval_wise_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<0
10:eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3):|:Arg_0<Arg_1 && Arg_0<Arg_1
11:eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<Arg_1 && Arg_1<=Arg_0
12:eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3):|:Arg_1<=Arg_0 && Arg_0<Arg_1
13:eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_1<=Arg_0 && Arg_1<=Arg_0
1:eval_wise_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_0(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_wise_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3):|:2+Arg_1<Arg_0
8:eval_wise_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3):|:2+Arg_0<Arg_1
9:eval_wise_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_1+2 && Arg_1<=Arg_0+2
14:eval_wise_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_wise_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Cut unsatisfiable transition 11: eval_wise__critedge_in->eval_wise_bb1_in

Cut unsatisfiable transition 12: eval_wise__critedge_in->eval_wise_bb1_in

Found invariant Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_wise__critedge_in

Found invariant Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_wise_bb1_in

Problem after Preprocessing

Start: eval_wise_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_wise_0, eval_wise_1, eval_wise_2, eval_wise__critedge_in, eval_wise_bb0_in, eval_wise_bb1_in, eval_wise_bb2_in, eval_wise_start, eval_wise_stop
Transitions:
2:eval_wise_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_wise_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_2(Arg_0,Arg_1,Arg_2,Arg_3)
6:eval_wise_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3):|:0<=Arg_2 && 0<=Arg_3
4:eval_wise_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<0
5:eval_wise_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<0
10:eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<Arg_1 && Arg_0<Arg_1
13:eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=Arg_0 && Arg_1<=Arg_0
1:eval_wise_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_0(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_wise_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 2+Arg_1<Arg_0
8:eval_wise_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 2+Arg_0<Arg_1
9:eval_wise_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1+2 && Arg_1<=Arg_0+2
14:eval_wise_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_wise_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 10:eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<Arg_1 && Arg_0<Arg_1 of depth 1:

new bound:

Arg_2+Arg_3 {O(n)}

MPRF:

eval_wise_bb1_in [Arg_1-Arg_0 ]
eval_wise__critedge_in [Arg_1-Arg_0 ]

MPRF for transition 13:eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=Arg_0 && Arg_1<=Arg_0 of depth 1:

new bound:

Arg_2+Arg_3+1 {O(n)}

MPRF:

eval_wise_bb1_in [Arg_0+1-Arg_1 ]
eval_wise__critedge_in [Arg_0+1-Arg_1 ]

MPRF for transition 7:eval_wise_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 2+Arg_1<Arg_0 of depth 1:

new bound:

Arg_2+Arg_3+2 {O(n)}

MPRF:

eval_wise_bb1_in [Arg_0-Arg_1-2 ]
eval_wise__critedge_in [Arg_0-Arg_1-3 ]

MPRF for transition 8:eval_wise_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_wise__critedge_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 2+Arg_0<Arg_1 of depth 1:

new bound:

Arg_2+Arg_3+4 {O(n)}

MPRF:

eval_wise_bb1_in [Arg_1+4-Arg_0 ]
eval_wise__critedge_in [Arg_1+3-Arg_0 ]

All Bounds

Timebounds

Overall timebound:4*Arg_2+4*Arg_3+16 {O(n)}
2: eval_wise_0->eval_wise_1: 1 {O(1)}
3: eval_wise_1->eval_wise_2: 1 {O(1)}
4: eval_wise_2->eval_wise_bb2_in: 1 {O(1)}
5: eval_wise_2->eval_wise_bb2_in: 1 {O(1)}
6: eval_wise_2->eval_wise_bb1_in: 1 {O(1)}
10: eval_wise__critedge_in->eval_wise_bb1_in: Arg_2+Arg_3 {O(n)}
13: eval_wise__critedge_in->eval_wise_bb1_in: Arg_2+Arg_3+1 {O(n)}
1: eval_wise_bb0_in->eval_wise_0: 1 {O(1)}
7: eval_wise_bb1_in->eval_wise__critedge_in: Arg_2+Arg_3+2 {O(n)}
8: eval_wise_bb1_in->eval_wise__critedge_in: Arg_2+Arg_3+4 {O(n)}
9: eval_wise_bb1_in->eval_wise_bb2_in: 1 {O(1)}
14: eval_wise_bb2_in->eval_wise_stop: 1 {O(1)}
0: eval_wise_start->eval_wise_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_2+4*Arg_3+16 {O(n)}
2: eval_wise_0->eval_wise_1: 1 {O(1)}
3: eval_wise_1->eval_wise_2: 1 {O(1)}
4: eval_wise_2->eval_wise_bb2_in: 1 {O(1)}
5: eval_wise_2->eval_wise_bb2_in: 1 {O(1)}
6: eval_wise_2->eval_wise_bb1_in: 1 {O(1)}
10: eval_wise__critedge_in->eval_wise_bb1_in: Arg_2+Arg_3 {O(n)}
13: eval_wise__critedge_in->eval_wise_bb1_in: Arg_2+Arg_3+1 {O(n)}
1: eval_wise_bb0_in->eval_wise_0: 1 {O(1)}
7: eval_wise_bb1_in->eval_wise__critedge_in: Arg_2+Arg_3+2 {O(n)}
8: eval_wise_bb1_in->eval_wise__critedge_in: Arg_2+Arg_3+4 {O(n)}
9: eval_wise_bb1_in->eval_wise_bb2_in: 1 {O(1)}
14: eval_wise_bb2_in->eval_wise_stop: 1 {O(1)}
0: eval_wise_start->eval_wise_bb0_in: 1 {O(1)}

Sizebounds

2: eval_wise_0->eval_wise_1, Arg_0: Arg_0 {O(n)}
2: eval_wise_0->eval_wise_1, Arg_1: Arg_1 {O(n)}
2: eval_wise_0->eval_wise_1, Arg_2: Arg_2 {O(n)}
2: eval_wise_0->eval_wise_1, Arg_3: Arg_3 {O(n)}
3: eval_wise_1->eval_wise_2, Arg_0: Arg_0 {O(n)}
3: eval_wise_1->eval_wise_2, Arg_1: Arg_1 {O(n)}
3: eval_wise_1->eval_wise_2, Arg_2: Arg_2 {O(n)}
3: eval_wise_1->eval_wise_2, Arg_3: Arg_3 {O(n)}
4: eval_wise_2->eval_wise_bb2_in, Arg_0: Arg_0 {O(n)}
4: eval_wise_2->eval_wise_bb2_in, Arg_1: Arg_1 {O(n)}
4: eval_wise_2->eval_wise_bb2_in, Arg_2: Arg_2 {O(n)}
4: eval_wise_2->eval_wise_bb2_in, Arg_3: Arg_3 {O(n)}
5: eval_wise_2->eval_wise_bb2_in, Arg_0: Arg_0 {O(n)}
5: eval_wise_2->eval_wise_bb2_in, Arg_1: Arg_1 {O(n)}
5: eval_wise_2->eval_wise_bb2_in, Arg_2: Arg_2 {O(n)}
5: eval_wise_2->eval_wise_bb2_in, Arg_3: Arg_3 {O(n)}
6: eval_wise_2->eval_wise_bb1_in, Arg_0: Arg_2 {O(n)}
6: eval_wise_2->eval_wise_bb1_in, Arg_1: Arg_3 {O(n)}
6: eval_wise_2->eval_wise_bb1_in, Arg_2: Arg_2 {O(n)}
6: eval_wise_2->eval_wise_bb1_in, Arg_3: Arg_3 {O(n)}
10: eval_wise__critedge_in->eval_wise_bb1_in, Arg_0: 2*Arg_2+Arg_3 {O(n)}
10: eval_wise__critedge_in->eval_wise_bb1_in, Arg_1: Arg_3 {O(n)}
10: eval_wise__critedge_in->eval_wise_bb1_in, Arg_2: Arg_2 {O(n)}
10: eval_wise__critedge_in->eval_wise_bb1_in, Arg_3: Arg_3 {O(n)}
13: eval_wise__critedge_in->eval_wise_bb1_in, Arg_0: Arg_2 {O(n)}
13: eval_wise__critedge_in->eval_wise_bb1_in, Arg_1: 2*Arg_3+Arg_2+1 {O(n)}
13: eval_wise__critedge_in->eval_wise_bb1_in, Arg_2: Arg_2 {O(n)}
13: eval_wise__critedge_in->eval_wise_bb1_in, Arg_3: Arg_3 {O(n)}
1: eval_wise_bb0_in->eval_wise_0, Arg_0: Arg_0 {O(n)}
1: eval_wise_bb0_in->eval_wise_0, Arg_1: Arg_1 {O(n)}
1: eval_wise_bb0_in->eval_wise_0, Arg_2: Arg_2 {O(n)}
1: eval_wise_bb0_in->eval_wise_0, Arg_3: Arg_3 {O(n)}
7: eval_wise_bb1_in->eval_wise__critedge_in, Arg_0: Arg_2 {O(n)}
7: eval_wise_bb1_in->eval_wise__critedge_in, Arg_1: 2*Arg_3+Arg_2+1 {O(n)}
7: eval_wise_bb1_in->eval_wise__critedge_in, Arg_2: Arg_2 {O(n)}
7: eval_wise_bb1_in->eval_wise__critedge_in, Arg_3: Arg_3 {O(n)}
8: eval_wise_bb1_in->eval_wise__critedge_in, Arg_0: 2*Arg_2+Arg_3 {O(n)}
8: eval_wise_bb1_in->eval_wise__critedge_in, Arg_1: Arg_3 {O(n)}
8: eval_wise_bb1_in->eval_wise__critedge_in, Arg_2: Arg_2 {O(n)}
8: eval_wise_bb1_in->eval_wise__critedge_in, Arg_3: Arg_3 {O(n)}
9: eval_wise_bb1_in->eval_wise_bb2_in, Arg_0: 4*Arg_2+Arg_3 {O(n)}
9: eval_wise_bb1_in->eval_wise_bb2_in, Arg_1: 4*Arg_3+Arg_2+1 {O(n)}
9: eval_wise_bb1_in->eval_wise_bb2_in, Arg_2: 3*Arg_2 {O(n)}
9: eval_wise_bb1_in->eval_wise_bb2_in, Arg_3: 3*Arg_3 {O(n)}
14: eval_wise_bb2_in->eval_wise_stop, Arg_0: 2*Arg_0+4*Arg_2+Arg_3 {O(n)}
14: eval_wise_bb2_in->eval_wise_stop, Arg_1: 2*Arg_1+4*Arg_3+Arg_2+1 {O(n)}
14: eval_wise_bb2_in->eval_wise_stop, Arg_2: 5*Arg_2 {O(n)}
14: eval_wise_bb2_in->eval_wise_stop, Arg_3: 5*Arg_3 {O(n)}
0: eval_wise_start->eval_wise_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_wise_start->eval_wise_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_wise_start->eval_wise_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_wise_start->eval_wise_bb0_in, Arg_3: Arg_3 {O(n)}