Initial Problem

Start: eval_t15_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: eval_t15_bb0_in, eval_t15_bb1_in, eval_t15_bb2_in, eval_t15_bb3_in, eval_t15_bb4_in, eval_t15_bb5_in, eval_t15_start, eval_t15_stop
Transitions:
2:eval_t15_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb1_in(Arg_2,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3
1:eval_t15_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<0
3:eval_t15_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<Arg_0
4:eval_t15_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_3
5:eval_t15_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb3_in(Arg_0,Arg_0-Arg_3-1,Arg_2,Arg_3,Arg_3)
7:eval_t15_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb1_in(Arg_1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=0
6:eval_t15_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<Arg_4
8:eval_t15_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4-1)
9:eval_t15_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_t15_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Found invariant 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0 for location eval_t15_bb2_in

Found invariant Arg_4<=Arg_3 && 1+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 1<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_t15_bb3_in

Found invariant 0<=Arg_3 && Arg_0<=Arg_2 for location eval_t15_bb1_in

Found invariant Arg_4<=Arg_3 && 1+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 3<=Arg_2+Arg_4 && 3<=Arg_0+Arg_4 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_t15_bb4_in

Problem after Preprocessing

Start: eval_t15_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: eval_t15_bb0_in, eval_t15_bb1_in, eval_t15_bb2_in, eval_t15_bb3_in, eval_t15_bb4_in, eval_t15_bb5_in, eval_t15_start, eval_t15_stop
Transitions:
2:eval_t15_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb1_in(Arg_2,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3
1:eval_t15_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<0
3:eval_t15_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && Arg_0<=Arg_2 && Arg_3<Arg_0
4:eval_t15_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && Arg_0<=Arg_2 && Arg_0<=Arg_3
5:eval_t15_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb3_in(Arg_0,Arg_0-Arg_3-1,Arg_2,Arg_3,Arg_3):|:1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0
7:eval_t15_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb1_in(Arg_1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_3 && 1+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 1<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_4<=0
6:eval_t15_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_3 && 1+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 1<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<Arg_4
8:eval_t15_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4-1):|:Arg_4<=Arg_3 && 1+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 3<=Arg_2+Arg_4 && 3<=Arg_0+Arg_4 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0+Arg_1 && 2<=Arg_0
9:eval_t15_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_t15_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 3:eval_t15_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && Arg_0<=Arg_2 && Arg_3<Arg_0 of depth 1:

new bound:

Arg_2+Arg_3 {O(n)}

MPRF:

eval_t15_bb2_in [Arg_0-Arg_3-1 ]
eval_t15_bb1_in [Arg_0-Arg_3 ]
eval_t15_bb4_in [Arg_1 ]
eval_t15_bb3_in [Arg_1 ]

MPRF for transition 5:eval_t15_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb3_in(Arg_0,Arg_0-Arg_3-1,Arg_2,Arg_3,Arg_3):|:1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_t15_bb2_in [Arg_0 ]
eval_t15_bb1_in [Arg_0 ]
eval_t15_bb4_in [Arg_0-1 ]
eval_t15_bb3_in [Arg_0-1 ]

MPRF for transition 6:eval_t15_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_3 && 1+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 1<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<Arg_4 of depth 1:

new bound:

Arg_2+Arg_3+1 {O(n)}

MPRF:

eval_t15_bb2_in [Arg_0+Arg_3+1 ]
eval_t15_bb1_in [Arg_0+Arg_3+1 ]
eval_t15_bb4_in [Arg_1+Arg_3+Arg_4 ]
eval_t15_bb3_in [Arg_1+Arg_3+Arg_4+1 ]

MPRF for transition 7:eval_t15_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb1_in(Arg_1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_3 && 1+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 1<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_4<=0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_t15_bb2_in [Arg_0 ]
eval_t15_bb1_in [Arg_0 ]
eval_t15_bb4_in [Arg_0 ]
eval_t15_bb3_in [Arg_0 ]

MPRF for transition 8:eval_t15_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t15_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4-1):|:Arg_4<=Arg_3 && 1+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 3<=Arg_2+Arg_4 && 3<=Arg_0+Arg_4 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_2+Arg_3 {O(n)}

MPRF:

eval_t15_bb2_in [Arg_0+Arg_3 ]
eval_t15_bb1_in [Arg_0+Arg_3 ]
eval_t15_bb4_in [Arg_1+Arg_3+Arg_4 ]
eval_t15_bb3_in [Arg_1+Arg_3+Arg_4 ]

All Bounds

Timebounds

Overall timebound:3*Arg_3+5*Arg_2+6 {O(n)}
1: eval_t15_bb0_in->eval_t15_bb5_in: 1 {O(1)}
2: eval_t15_bb0_in->eval_t15_bb1_in: 1 {O(1)}
3: eval_t15_bb1_in->eval_t15_bb2_in: Arg_2+Arg_3 {O(n)}
4: eval_t15_bb1_in->eval_t15_bb5_in: 1 {O(1)}
5: eval_t15_bb2_in->eval_t15_bb3_in: Arg_2 {O(n)}
6: eval_t15_bb3_in->eval_t15_bb4_in: Arg_2+Arg_3+1 {O(n)}
7: eval_t15_bb3_in->eval_t15_bb1_in: Arg_2 {O(n)}
8: eval_t15_bb4_in->eval_t15_bb3_in: Arg_2+Arg_3 {O(n)}
9: eval_t15_bb5_in->eval_t15_stop: 1 {O(1)}
0: eval_t15_start->eval_t15_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 3*Arg_3+5*Arg_2+6 {O(n)}
1: eval_t15_bb0_in->eval_t15_bb5_in: 1 {O(1)}
2: eval_t15_bb0_in->eval_t15_bb1_in: 1 {O(1)}
3: eval_t15_bb1_in->eval_t15_bb2_in: Arg_2+Arg_3 {O(n)}
4: eval_t15_bb1_in->eval_t15_bb5_in: 1 {O(1)}
5: eval_t15_bb2_in->eval_t15_bb3_in: Arg_2 {O(n)}
6: eval_t15_bb3_in->eval_t15_bb4_in: Arg_2+Arg_3+1 {O(n)}
7: eval_t15_bb3_in->eval_t15_bb1_in: Arg_2 {O(n)}
8: eval_t15_bb4_in->eval_t15_bb3_in: Arg_2+Arg_3 {O(n)}
9: eval_t15_bb5_in->eval_t15_stop: 1 {O(1)}
0: eval_t15_start->eval_t15_bb0_in: 1 {O(1)}

Sizebounds

1: eval_t15_bb0_in->eval_t15_bb5_in, Arg_0: Arg_0 {O(n)}
1: eval_t15_bb0_in->eval_t15_bb5_in, Arg_1: Arg_1 {O(n)}
1: eval_t15_bb0_in->eval_t15_bb5_in, Arg_2: Arg_2 {O(n)}
1: eval_t15_bb0_in->eval_t15_bb5_in, Arg_3: Arg_3 {O(n)}
1: eval_t15_bb0_in->eval_t15_bb5_in, Arg_4: Arg_4 {O(n)}
2: eval_t15_bb0_in->eval_t15_bb1_in, Arg_0: Arg_2 {O(n)}
2: eval_t15_bb0_in->eval_t15_bb1_in, Arg_1: Arg_1 {O(n)}
2: eval_t15_bb0_in->eval_t15_bb1_in, Arg_2: Arg_2 {O(n)}
2: eval_t15_bb0_in->eval_t15_bb1_in, Arg_3: Arg_3 {O(n)}
2: eval_t15_bb0_in->eval_t15_bb1_in, Arg_4: Arg_4 {O(n)}
3: eval_t15_bb1_in->eval_t15_bb2_in, Arg_0: Arg_2 {O(n)}
3: eval_t15_bb1_in->eval_t15_bb2_in, Arg_1: 2*Arg_2+Arg_1 {O(n)}
3: eval_t15_bb1_in->eval_t15_bb2_in, Arg_2: Arg_2 {O(n)}
3: eval_t15_bb1_in->eval_t15_bb2_in, Arg_3: Arg_3 {O(n)}
3: eval_t15_bb1_in->eval_t15_bb2_in, Arg_4: Arg_4 {O(n)}
4: eval_t15_bb1_in->eval_t15_bb5_in, Arg_0: 2*Arg_2 {O(n)}
4: eval_t15_bb1_in->eval_t15_bb5_in, Arg_1: 2*Arg_2+Arg_1 {O(n)}
4: eval_t15_bb1_in->eval_t15_bb5_in, Arg_2: 2*Arg_2 {O(n)}
4: eval_t15_bb1_in->eval_t15_bb5_in, Arg_3: 2*Arg_3 {O(n)}
4: eval_t15_bb1_in->eval_t15_bb5_in, Arg_4: Arg_4 {O(n)}
5: eval_t15_bb2_in->eval_t15_bb3_in, Arg_0: Arg_2 {O(n)}
5: eval_t15_bb2_in->eval_t15_bb3_in, Arg_1: Arg_2 {O(n)}
5: eval_t15_bb2_in->eval_t15_bb3_in, Arg_2: Arg_2 {O(n)}
5: eval_t15_bb2_in->eval_t15_bb3_in, Arg_3: Arg_3 {O(n)}
5: eval_t15_bb2_in->eval_t15_bb3_in, Arg_4: Arg_3 {O(n)}
6: eval_t15_bb3_in->eval_t15_bb4_in, Arg_0: Arg_2 {O(n)}
6: eval_t15_bb3_in->eval_t15_bb4_in, Arg_1: Arg_2 {O(n)}
6: eval_t15_bb3_in->eval_t15_bb4_in, Arg_2: Arg_2 {O(n)}
6: eval_t15_bb3_in->eval_t15_bb4_in, Arg_3: Arg_3 {O(n)}
6: eval_t15_bb3_in->eval_t15_bb4_in, Arg_4: Arg_3 {O(n)}
7: eval_t15_bb3_in->eval_t15_bb1_in, Arg_0: Arg_2 {O(n)}
7: eval_t15_bb3_in->eval_t15_bb1_in, Arg_1: 2*Arg_2 {O(n)}
7: eval_t15_bb3_in->eval_t15_bb1_in, Arg_2: Arg_2 {O(n)}
7: eval_t15_bb3_in->eval_t15_bb1_in, Arg_3: Arg_3 {O(n)}
7: eval_t15_bb3_in->eval_t15_bb1_in, Arg_4: 0 {O(1)}
8: eval_t15_bb4_in->eval_t15_bb3_in, Arg_0: Arg_2 {O(n)}
8: eval_t15_bb4_in->eval_t15_bb3_in, Arg_1: Arg_2 {O(n)}
8: eval_t15_bb4_in->eval_t15_bb3_in, Arg_2: Arg_2 {O(n)}
8: eval_t15_bb4_in->eval_t15_bb3_in, Arg_3: Arg_3 {O(n)}
8: eval_t15_bb4_in->eval_t15_bb3_in, Arg_4: Arg_3 {O(n)}
9: eval_t15_bb5_in->eval_t15_stop, Arg_0: 2*Arg_2+Arg_0 {O(n)}
9: eval_t15_bb5_in->eval_t15_stop, Arg_1: 2*Arg_1+2*Arg_2 {O(n)}
9: eval_t15_bb5_in->eval_t15_stop, Arg_2: 3*Arg_2 {O(n)}
9: eval_t15_bb5_in->eval_t15_stop, Arg_3: 3*Arg_3 {O(n)}
9: eval_t15_bb5_in->eval_t15_stop, Arg_4: 2*Arg_4 {O(n)}
0: eval_t15_start->eval_t15_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_t15_start->eval_t15_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_t15_start->eval_t15_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_t15_start->eval_t15_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_t15_start->eval_t15_bb0_in, Arg_4: Arg_4 {O(n)}