Initial Problem

Start: eval_easy2_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval_easy2_0, eval_easy2_1, eval_easy2_2, eval_easy2_3, eval_easy2_4, eval_easy2_5, eval_easy2_6, eval_easy2_bb0_in, eval_easy2_bb1_in, eval_easy2_bb2_in, eval_easy2_bb3_in, eval_easy2_start, eval_easy2_stop
Transitions:
2:eval_easy2_0(Arg_0,Arg_1) -> eval_easy2_1(Arg_0,Arg_1)
3:eval_easy2_1(Arg_0,Arg_1) -> eval_easy2_2(Arg_0,Arg_1)
4:eval_easy2_2(Arg_0,Arg_1) -> eval_easy2_3(Arg_0,Arg_1)
5:eval_easy2_3(Arg_0,Arg_1) -> eval_easy2_4(Arg_0,Arg_1)
6:eval_easy2_4(Arg_0,Arg_1) -> eval_easy2_5(Arg_0,Arg_1)
7:eval_easy2_5(Arg_0,Arg_1) -> eval_easy2_6(Arg_0,Arg_1)
8:eval_easy2_6(Arg_0,Arg_1) -> eval_easy2_bb1_in(Arg_1,Arg_1)
1:eval_easy2_bb0_in(Arg_0,Arg_1) -> eval_easy2_0(Arg_0,Arg_1)
9:eval_easy2_bb1_in(Arg_0,Arg_1) -> eval_easy2_bb2_in(Arg_0,Arg_1):|:0<Arg_0
10:eval_easy2_bb1_in(Arg_0,Arg_1) -> eval_easy2_bb3_in(Arg_0,Arg_1):|:Arg_0<=0
11:eval_easy2_bb2_in(Arg_0,Arg_1) -> eval_easy2_bb1_in(Arg_0-1,Arg_1)
12:eval_easy2_bb3_in(Arg_0,Arg_1) -> eval_easy2_stop(Arg_0,Arg_1)
0:eval_easy2_start(Arg_0,Arg_1) -> eval_easy2_bb0_in(Arg_0,Arg_1)

Preprocessing

Found invariant 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location eval_easy2_bb2_in

Found invariant Arg_0<=Arg_1 for location eval_easy2_bb1_in

Found invariant Arg_0<=Arg_1 && Arg_0<=0 for location eval_easy2_bb3_in

Found invariant Arg_0<=Arg_1 && Arg_0<=0 for location eval_easy2_stop

Problem after Preprocessing

Start: eval_easy2_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval_easy2_0, eval_easy2_1, eval_easy2_2, eval_easy2_3, eval_easy2_4, eval_easy2_5, eval_easy2_6, eval_easy2_bb0_in, eval_easy2_bb1_in, eval_easy2_bb2_in, eval_easy2_bb3_in, eval_easy2_start, eval_easy2_stop
Transitions:
2:eval_easy2_0(Arg_0,Arg_1) -> eval_easy2_1(Arg_0,Arg_1)
3:eval_easy2_1(Arg_0,Arg_1) -> eval_easy2_2(Arg_0,Arg_1)
4:eval_easy2_2(Arg_0,Arg_1) -> eval_easy2_3(Arg_0,Arg_1)
5:eval_easy2_3(Arg_0,Arg_1) -> eval_easy2_4(Arg_0,Arg_1)
6:eval_easy2_4(Arg_0,Arg_1) -> eval_easy2_5(Arg_0,Arg_1)
7:eval_easy2_5(Arg_0,Arg_1) -> eval_easy2_6(Arg_0,Arg_1)
8:eval_easy2_6(Arg_0,Arg_1) -> eval_easy2_bb1_in(Arg_1,Arg_1)
1:eval_easy2_bb0_in(Arg_0,Arg_1) -> eval_easy2_0(Arg_0,Arg_1)
9:eval_easy2_bb1_in(Arg_0,Arg_1) -> eval_easy2_bb2_in(Arg_0,Arg_1):|:Arg_0<=Arg_1 && 0<Arg_0
10:eval_easy2_bb1_in(Arg_0,Arg_1) -> eval_easy2_bb3_in(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_0<=0
11:eval_easy2_bb2_in(Arg_0,Arg_1) -> eval_easy2_bb1_in(Arg_0-1,Arg_1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0
12:eval_easy2_bb3_in(Arg_0,Arg_1) -> eval_easy2_stop(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_0<=0
0:eval_easy2_start(Arg_0,Arg_1) -> eval_easy2_bb0_in(Arg_0,Arg_1)

MPRF for transition 9:eval_easy2_bb1_in(Arg_0,Arg_1) -> eval_easy2_bb2_in(Arg_0,Arg_1):|:Arg_0<=Arg_1 && 0<Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_easy2_bb2_in [Arg_0-1 ]
eval_easy2_bb1_in [Arg_0 ]

MPRF for transition 11:eval_easy2_bb2_in(Arg_0,Arg_1) -> eval_easy2_bb1_in(Arg_0-1,Arg_1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_easy2_bb2_in [Arg_0 ]
eval_easy2_bb1_in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1+11 {O(n)}
2: eval_easy2_0->eval_easy2_1: 1 {O(1)}
3: eval_easy2_1->eval_easy2_2: 1 {O(1)}
4: eval_easy2_2->eval_easy2_3: 1 {O(1)}
5: eval_easy2_3->eval_easy2_4: 1 {O(1)}
6: eval_easy2_4->eval_easy2_5: 1 {O(1)}
7: eval_easy2_5->eval_easy2_6: 1 {O(1)}
8: eval_easy2_6->eval_easy2_bb1_in: 1 {O(1)}
1: eval_easy2_bb0_in->eval_easy2_0: 1 {O(1)}
9: eval_easy2_bb1_in->eval_easy2_bb2_in: Arg_1 {O(n)}
10: eval_easy2_bb1_in->eval_easy2_bb3_in: 1 {O(1)}
11: eval_easy2_bb2_in->eval_easy2_bb1_in: Arg_1 {O(n)}
12: eval_easy2_bb3_in->eval_easy2_stop: 1 {O(1)}
0: eval_easy2_start->eval_easy2_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1+11 {O(n)}
2: eval_easy2_0->eval_easy2_1: 1 {O(1)}
3: eval_easy2_1->eval_easy2_2: 1 {O(1)}
4: eval_easy2_2->eval_easy2_3: 1 {O(1)}
5: eval_easy2_3->eval_easy2_4: 1 {O(1)}
6: eval_easy2_4->eval_easy2_5: 1 {O(1)}
7: eval_easy2_5->eval_easy2_6: 1 {O(1)}
8: eval_easy2_6->eval_easy2_bb1_in: 1 {O(1)}
1: eval_easy2_bb0_in->eval_easy2_0: 1 {O(1)}
9: eval_easy2_bb1_in->eval_easy2_bb2_in: Arg_1 {O(n)}
10: eval_easy2_bb1_in->eval_easy2_bb3_in: 1 {O(1)}
11: eval_easy2_bb2_in->eval_easy2_bb1_in: Arg_1 {O(n)}
12: eval_easy2_bb3_in->eval_easy2_stop: 1 {O(1)}
0: eval_easy2_start->eval_easy2_bb0_in: 1 {O(1)}

Sizebounds

2: eval_easy2_0->eval_easy2_1, Arg_0: Arg_0 {O(n)}
2: eval_easy2_0->eval_easy2_1, Arg_1: Arg_1 {O(n)}
3: eval_easy2_1->eval_easy2_2, Arg_0: Arg_0 {O(n)}
3: eval_easy2_1->eval_easy2_2, Arg_1: Arg_1 {O(n)}
4: eval_easy2_2->eval_easy2_3, Arg_0: Arg_0 {O(n)}
4: eval_easy2_2->eval_easy2_3, Arg_1: Arg_1 {O(n)}
5: eval_easy2_3->eval_easy2_4, Arg_0: Arg_0 {O(n)}
5: eval_easy2_3->eval_easy2_4, Arg_1: Arg_1 {O(n)}
6: eval_easy2_4->eval_easy2_5, Arg_0: Arg_0 {O(n)}
6: eval_easy2_4->eval_easy2_5, Arg_1: Arg_1 {O(n)}
7: eval_easy2_5->eval_easy2_6, Arg_0: Arg_0 {O(n)}
7: eval_easy2_5->eval_easy2_6, Arg_1: Arg_1 {O(n)}
8: eval_easy2_6->eval_easy2_bb1_in, Arg_0: Arg_1 {O(n)}
8: eval_easy2_6->eval_easy2_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_easy2_bb0_in->eval_easy2_0, Arg_0: Arg_0 {O(n)}
1: eval_easy2_bb0_in->eval_easy2_0, Arg_1: Arg_1 {O(n)}
9: eval_easy2_bb1_in->eval_easy2_bb2_in, Arg_0: Arg_1 {O(n)}
9: eval_easy2_bb1_in->eval_easy2_bb2_in, Arg_1: Arg_1 {O(n)}
10: eval_easy2_bb1_in->eval_easy2_bb3_in, Arg_0: 2*Arg_1 {O(n)}
10: eval_easy2_bb1_in->eval_easy2_bb3_in, Arg_1: 2*Arg_1 {O(n)}
11: eval_easy2_bb2_in->eval_easy2_bb1_in, Arg_0: Arg_1 {O(n)}
11: eval_easy2_bb2_in->eval_easy2_bb1_in, Arg_1: Arg_1 {O(n)}
12: eval_easy2_bb3_in->eval_easy2_stop, Arg_0: 2*Arg_1 {O(n)}
12: eval_easy2_bb3_in->eval_easy2_stop, Arg_1: 2*Arg_1 {O(n)}
0: eval_easy2_start->eval_easy2_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_easy2_start->eval_easy2_bb0_in, Arg_1: Arg_1 {O(n)}