Initial Problem

Start: eval_ndecr_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval_ndecr_bb0_in, eval_ndecr_bb1_in, eval_ndecr_bb2_in, eval_ndecr_bb3_in, eval_ndecr_start, eval_ndecr_stop
Transitions:
1:eval_ndecr_bb0_in(Arg_0,Arg_1) -> eval_ndecr_bb1_in(Arg_1-1,Arg_1)
2:eval_ndecr_bb1_in(Arg_0,Arg_1) -> eval_ndecr_bb2_in(Arg_0,Arg_1):|:1<Arg_0
3:eval_ndecr_bb1_in(Arg_0,Arg_1) -> eval_ndecr_bb3_in(Arg_0,Arg_1):|:Arg_0<=1
4:eval_ndecr_bb2_in(Arg_0,Arg_1) -> eval_ndecr_bb1_in(Arg_0-1,Arg_1)
5:eval_ndecr_bb3_in(Arg_0,Arg_1) -> eval_ndecr_stop(Arg_0,Arg_1)
0:eval_ndecr_start(Arg_0,Arg_1) -> eval_ndecr_bb0_in(Arg_0,Arg_1)

Preprocessing

Found invariant 1+Arg_0<=Arg_1 && Arg_0<=1 for location eval_ndecr_stop

Found invariant 3<=Arg_1 && 5<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 2<=Arg_0 for location eval_ndecr_bb2_in

Found invariant 1+Arg_0<=Arg_1 for location eval_ndecr_bb1_in

Found invariant 1+Arg_0<=Arg_1 && Arg_0<=1 for location eval_ndecr_bb3_in

Problem after Preprocessing

Start: eval_ndecr_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval_ndecr_bb0_in, eval_ndecr_bb1_in, eval_ndecr_bb2_in, eval_ndecr_bb3_in, eval_ndecr_start, eval_ndecr_stop
Transitions:
1:eval_ndecr_bb0_in(Arg_0,Arg_1) -> eval_ndecr_bb1_in(Arg_1-1,Arg_1)
2:eval_ndecr_bb1_in(Arg_0,Arg_1) -> eval_ndecr_bb2_in(Arg_0,Arg_1):|:1+Arg_0<=Arg_1 && 1<Arg_0
3:eval_ndecr_bb1_in(Arg_0,Arg_1) -> eval_ndecr_bb3_in(Arg_0,Arg_1):|:1+Arg_0<=Arg_1 && Arg_0<=1
4:eval_ndecr_bb2_in(Arg_0,Arg_1) -> eval_ndecr_bb1_in(Arg_0-1,Arg_1):|:3<=Arg_1 && 5<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 2<=Arg_0
5:eval_ndecr_bb3_in(Arg_0,Arg_1) -> eval_ndecr_stop(Arg_0,Arg_1):|:1+Arg_0<=Arg_1 && Arg_0<=1
0:eval_ndecr_start(Arg_0,Arg_1) -> eval_ndecr_bb0_in(Arg_0,Arg_1)

MPRF for transition 2:eval_ndecr_bb1_in(Arg_0,Arg_1) -> eval_ndecr_bb2_in(Arg_0,Arg_1):|:1+Arg_0<=Arg_1 && 1<Arg_0 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

eval_ndecr_bb2_in [Arg_0-2 ]
eval_ndecr_bb1_in [Arg_0-1 ]

MPRF for transition 4:eval_ndecr_bb2_in(Arg_0,Arg_1) -> eval_ndecr_bb1_in(Arg_0-1,Arg_1):|:3<=Arg_1 && 5<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

eval_ndecr_bb2_in [Arg_0-1 ]
eval_ndecr_bb1_in [Arg_0-1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1+8 {O(n)}
1: eval_ndecr_bb0_in->eval_ndecr_bb1_in: 1 {O(1)}
2: eval_ndecr_bb1_in->eval_ndecr_bb2_in: Arg_1+2 {O(n)}
3: eval_ndecr_bb1_in->eval_ndecr_bb3_in: 1 {O(1)}
4: eval_ndecr_bb2_in->eval_ndecr_bb1_in: Arg_1+2 {O(n)}
5: eval_ndecr_bb3_in->eval_ndecr_stop: 1 {O(1)}
0: eval_ndecr_start->eval_ndecr_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1+8 {O(n)}
1: eval_ndecr_bb0_in->eval_ndecr_bb1_in: 1 {O(1)}
2: eval_ndecr_bb1_in->eval_ndecr_bb2_in: Arg_1+2 {O(n)}
3: eval_ndecr_bb1_in->eval_ndecr_bb3_in: 1 {O(1)}
4: eval_ndecr_bb2_in->eval_ndecr_bb1_in: Arg_1+2 {O(n)}
5: eval_ndecr_bb3_in->eval_ndecr_stop: 1 {O(1)}
0: eval_ndecr_start->eval_ndecr_bb0_in: 1 {O(1)}

Sizebounds

1: eval_ndecr_bb0_in->eval_ndecr_bb1_in, Arg_0: Arg_1+1 {O(n)}
1: eval_ndecr_bb0_in->eval_ndecr_bb1_in, Arg_1: Arg_1 {O(n)}
2: eval_ndecr_bb1_in->eval_ndecr_bb2_in, Arg_0: Arg_1+1 {O(n)}
2: eval_ndecr_bb1_in->eval_ndecr_bb2_in, Arg_1: Arg_1 {O(n)}
3: eval_ndecr_bb1_in->eval_ndecr_bb3_in, Arg_0: 2*Arg_1+2 {O(n)}
3: eval_ndecr_bb1_in->eval_ndecr_bb3_in, Arg_1: 2*Arg_1 {O(n)}
4: eval_ndecr_bb2_in->eval_ndecr_bb1_in, Arg_0: Arg_1+1 {O(n)}
4: eval_ndecr_bb2_in->eval_ndecr_bb1_in, Arg_1: Arg_1 {O(n)}
5: eval_ndecr_bb3_in->eval_ndecr_stop, Arg_0: 2*Arg_1+2 {O(n)}
5: eval_ndecr_bb3_in->eval_ndecr_stop, Arg_1: 2*Arg_1 {O(n)}
0: eval_ndecr_start->eval_ndecr_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_ndecr_start->eval_ndecr_bb0_in, Arg_1: Arg_1 {O(n)}