Initial Problem

Start: eval_t47_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_t47_bb0_in, eval_t47_bb1_in, eval_t47_bb2_in, eval_t47_bb3_in, eval_t47_start, eval_t47_stop
Transitions:
1:eval_t47_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_2,1,Arg_2)
2:eval_t47_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb2_in(Arg_0,Arg_1,Arg_2):|:0<Arg_1
3:eval_t47_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
4:eval_t47_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_0-1,1,Arg_2):|:0<Arg_0 && 0<Arg_0
5:eval_t47_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_0,1,Arg_2):|:0<Arg_0 && Arg_0<=0
6:eval_t47_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_0-1,0,Arg_2):|:Arg_0<=0 && 0<Arg_0
7:eval_t47_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_0,0,Arg_2):|:Arg_0<=0 && Arg_0<=0
8:eval_t47_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_t47_stop(Arg_0,Arg_1,Arg_2)
0:eval_t47_start(Arg_0,Arg_1,Arg_2) -> eval_t47_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Cut unsatisfiable transition 5: eval_t47_bb2_in->eval_t47_bb1_in

Cut unsatisfiable transition 6: eval_t47_bb2_in->eval_t47_bb1_in

Found invariant Arg_0<=Arg_2 && Arg_1<=0 && 0<=Arg_1 for location eval_t47_stop

Found invariant Arg_0<=Arg_2 && Arg_1<=0 && 0<=Arg_1 for location eval_t47_bb3_in

Found invariant Arg_0<=Arg_2 && Arg_1<=1 && 0<=Arg_1 for location eval_t47_bb1_in

Found invariant Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 for location eval_t47_bb2_in

Problem after Preprocessing

Start: eval_t47_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_t47_bb0_in, eval_t47_bb1_in, eval_t47_bb2_in, eval_t47_bb3_in, eval_t47_start, eval_t47_stop
Transitions:
1:eval_t47_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_2,1,Arg_2)
2:eval_t47_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 0<=Arg_1 && 0<Arg_1
3:eval_t47_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 0<=Arg_1 && Arg_1<=0
4:eval_t47_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_0-1,1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && 0<Arg_0 && 0<Arg_0
7:eval_t47_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_0,0,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=0 && Arg_0<=0
8:eval_t47_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_t47_stop(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=0 && 0<=Arg_1
0:eval_t47_start(Arg_0,Arg_1,Arg_2) -> eval_t47_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 4:eval_t47_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_0-1,1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && 0<Arg_0 && 0<Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_t47_bb2_in [Arg_0 ]
eval_t47_bb1_in [Arg_0 ]

MPRF for transition 7:eval_t47_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb1_in(Arg_0,0,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=0 && Arg_0<=0 of depth 1:

new bound:

1 {O(1)}

MPRF:

eval_t47_bb2_in [1 ]
eval_t47_bb1_in [Arg_1 ]

knowledge_propagation leads to new time bound Arg_2+1 {O(n)} for transition 2:eval_t47_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_t47_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 0<=Arg_1 && 0<Arg_1

All Bounds

Timebounds

Overall timebound:2*Arg_2+6 {O(n)}
1: eval_t47_bb0_in->eval_t47_bb1_in: 1 {O(1)}
2: eval_t47_bb1_in->eval_t47_bb2_in: Arg_2+1 {O(n)}
3: eval_t47_bb1_in->eval_t47_bb3_in: 1 {O(1)}
4: eval_t47_bb2_in->eval_t47_bb1_in: Arg_2 {O(n)}
7: eval_t47_bb2_in->eval_t47_bb1_in: 1 {O(1)}
8: eval_t47_bb3_in->eval_t47_stop: 1 {O(1)}
0: eval_t47_start->eval_t47_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_2+6 {O(n)}
1: eval_t47_bb0_in->eval_t47_bb1_in: 1 {O(1)}
2: eval_t47_bb1_in->eval_t47_bb2_in: Arg_2+1 {O(n)}
3: eval_t47_bb1_in->eval_t47_bb3_in: 1 {O(1)}
4: eval_t47_bb2_in->eval_t47_bb1_in: Arg_2 {O(n)}
7: eval_t47_bb2_in->eval_t47_bb1_in: 1 {O(1)}
8: eval_t47_bb3_in->eval_t47_stop: 1 {O(1)}
0: eval_t47_start->eval_t47_bb0_in: 1 {O(1)}

Sizebounds

1: eval_t47_bb0_in->eval_t47_bb1_in, Arg_0: Arg_2 {O(n)}
1: eval_t47_bb0_in->eval_t47_bb1_in, Arg_1: 1 {O(1)}
1: eval_t47_bb0_in->eval_t47_bb1_in, Arg_2: Arg_2 {O(n)}
2: eval_t47_bb1_in->eval_t47_bb2_in, Arg_0: Arg_2 {O(n)}
2: eval_t47_bb1_in->eval_t47_bb2_in, Arg_1: 1 {O(1)}
2: eval_t47_bb1_in->eval_t47_bb2_in, Arg_2: Arg_2 {O(n)}
3: eval_t47_bb1_in->eval_t47_bb3_in, Arg_0: Arg_2 {O(n)}
3: eval_t47_bb1_in->eval_t47_bb3_in, Arg_1: 0 {O(1)}
3: eval_t47_bb1_in->eval_t47_bb3_in, Arg_2: Arg_2 {O(n)}
4: eval_t47_bb2_in->eval_t47_bb1_in, Arg_0: Arg_2 {O(n)}
4: eval_t47_bb2_in->eval_t47_bb1_in, Arg_1: 1 {O(1)}
4: eval_t47_bb2_in->eval_t47_bb1_in, Arg_2: Arg_2 {O(n)}
7: eval_t47_bb2_in->eval_t47_bb1_in, Arg_0: Arg_2 {O(n)}
7: eval_t47_bb2_in->eval_t47_bb1_in, Arg_1: 0 {O(1)}
7: eval_t47_bb2_in->eval_t47_bb1_in, Arg_2: Arg_2 {O(n)}
8: eval_t47_bb3_in->eval_t47_stop, Arg_0: Arg_2 {O(n)}
8: eval_t47_bb3_in->eval_t47_stop, Arg_1: 0 {O(1)}
8: eval_t47_bb3_in->eval_t47_stop, Arg_2: Arg_2 {O(n)}
0: eval_t47_start->eval_t47_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_t47_start->eval_t47_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_t47_start->eval_t47_bb0_in, Arg_2: Arg_2 {O(n)}