Initial Problem
Start: eval_rsd_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: nondef.0
Locations: eval_rsd_3, eval_rsd_4, eval_rsd_bb0_in, eval_rsd_bb1_in, eval_rsd_bb2_in, eval_rsd_bb3_in, eval_rsd_bb4_in, eval_rsd_start, eval_rsd_stop
Transitions:
8:eval_rsd_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_4(nondef.0,Arg_1,Arg_2,Arg_3)
9:eval_rsd_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,Arg_1-1,Arg_2,Arg_3):|:0<Arg_0 && 0<Arg_0
10:eval_rsd_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,Arg_2-1,Arg_2,Arg_3):|:0<Arg_0 && Arg_0<=0
11:eval_rsd_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,Arg_1-1,Arg_1,Arg_3):|:Arg_0<=0 && 0<Arg_0
12:eval_rsd_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,Arg_2-1,Arg_1,Arg_3):|:Arg_0<=0 && Arg_0<=0
1:eval_rsd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3
2:eval_rsd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<0
3:eval_rsd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,2*Arg_3,2*Arg_3,Arg_3)
4:eval_rsd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1
5:eval_rsd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<Arg_3
6:eval_rsd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_3(Arg_0,Arg_1,Arg_2,Arg_3)
13:eval_rsd_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_rsd_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)
Preprocessing
Cut unsatisfiable transition 10: eval_rsd_4->eval_rsd_bb2_in
Cut unsatisfiable transition 11: eval_rsd_4->eval_rsd_bb2_in
Found invariant Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 0<=Arg_2 && 0<=1+Arg_1+Arg_2 && 0<=1+Arg_1 for location eval_rsd_bb2_in
Found invariant Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_rsd_4
Found invariant Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_rsd_3
Found invariant Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_rsd_bb3_in
Found invariant 0<=Arg_3 for location eval_rsd_bb1_in
Problem after Preprocessing
Start: eval_rsd_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: nondef.0
Locations: eval_rsd_3, eval_rsd_4, eval_rsd_bb0_in, eval_rsd_bb1_in, eval_rsd_bb2_in, eval_rsd_bb3_in, eval_rsd_bb4_in, eval_rsd_start, eval_rsd_stop
Transitions:
8:eval_rsd_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_4(nondef.0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1
9:eval_rsd_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,Arg_1-1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && 0<Arg_0 && 0<Arg_0
12:eval_rsd_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,Arg_2-1,Arg_1,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=0 && Arg_0<=0
1:eval_rsd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3
2:eval_rsd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<0
3:eval_rsd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,2*Arg_3,2*Arg_3,Arg_3):|:0<=Arg_3
4:eval_rsd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 0<=Arg_2 && 0<=1+Arg_1+Arg_2 && 0<=1+Arg_1 && Arg_3<=Arg_1
5:eval_rsd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 0<=Arg_2 && 0<=1+Arg_1+Arg_2 && 0<=1+Arg_1 && Arg_1<Arg_3
6:eval_rsd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1
13:eval_rsd_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_rsd_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)
MPRF for transition 8:eval_rsd_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_4(nondef.0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 of depth 1:
new bound:
4*Arg_3+1 {O(n)}
MPRF:
eval_rsd_4 [Arg_1+Arg_2 ]
eval_rsd_bb2_in [Arg_1+Arg_2+1 ]
eval_rsd_bb3_in [Arg_1+Arg_2+1 ]
eval_rsd_3 [Arg_1+Arg_2+1 ]
MPRF for transition 9:eval_rsd_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,Arg_1-1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && 0<Arg_0 && 0<Arg_0 of depth 1:
new bound:
4*Arg_3+1 {O(n)}
MPRF:
eval_rsd_4 [Arg_1+Arg_2+1 ]
eval_rsd_bb2_in [Arg_1+Arg_2+1 ]
eval_rsd_bb3_in [Arg_1+Arg_2+1 ]
eval_rsd_3 [Arg_1+Arg_2+1 ]
MPRF for transition 12:eval_rsd_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb2_in(Arg_0,Arg_2-1,Arg_1,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=0 && Arg_0<=0 of depth 1:
new bound:
4*Arg_3+1 {O(n)}
MPRF:
eval_rsd_4 [Arg_1+Arg_2+1 ]
eval_rsd_bb2_in [Arg_1+Arg_2+1 ]
eval_rsd_bb3_in [Arg_1+Arg_2+1 ]
eval_rsd_3 [Arg_1+Arg_2+1 ]
MPRF for transition 4:eval_rsd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 0<=Arg_2 && 0<=1+Arg_1+Arg_2 && 0<=1+Arg_1 && Arg_3<=Arg_1 of depth 1:
new bound:
4*Arg_3+2 {O(n)}
MPRF:
eval_rsd_4 [Arg_1+Arg_2+1 ]
eval_rsd_bb2_in [Arg_1+Arg_2+2 ]
eval_rsd_bb3_in [Arg_1+Arg_2+1 ]
eval_rsd_3 [Arg_1+Arg_2+1 ]
MPRF for transition 6:eval_rsd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_rsd_3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 of depth 1:
new bound:
4*Arg_3+1 {O(n)}
MPRF:
eval_rsd_4 [Arg_1+Arg_2 ]
eval_rsd_bb2_in [Arg_1+Arg_2+1 ]
eval_rsd_bb3_in [Arg_1+Arg_2+1 ]
eval_rsd_3 [Arg_1+Arg_2 ]
All Bounds
Timebounds
Overall timebound:20*Arg_3+12 {O(n)}
8: eval_rsd_3->eval_rsd_4: 4*Arg_3+1 {O(n)}
9: eval_rsd_4->eval_rsd_bb2_in: 4*Arg_3+1 {O(n)}
12: eval_rsd_4->eval_rsd_bb2_in: 4*Arg_3+1 {O(n)}
1: eval_rsd_bb0_in->eval_rsd_bb1_in: 1 {O(1)}
2: eval_rsd_bb0_in->eval_rsd_bb4_in: 1 {O(1)}
3: eval_rsd_bb1_in->eval_rsd_bb2_in: 1 {O(1)}
4: eval_rsd_bb2_in->eval_rsd_bb3_in: 4*Arg_3+2 {O(n)}
5: eval_rsd_bb2_in->eval_rsd_bb4_in: 1 {O(1)}
6: eval_rsd_bb3_in->eval_rsd_3: 4*Arg_3+1 {O(n)}
13: eval_rsd_bb4_in->eval_rsd_stop: 1 {O(1)}
0: eval_rsd_start->eval_rsd_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: 20*Arg_3+12 {O(n)}
8: eval_rsd_3->eval_rsd_4: 4*Arg_3+1 {O(n)}
9: eval_rsd_4->eval_rsd_bb2_in: 4*Arg_3+1 {O(n)}
12: eval_rsd_4->eval_rsd_bb2_in: 4*Arg_3+1 {O(n)}
1: eval_rsd_bb0_in->eval_rsd_bb1_in: 1 {O(1)}
2: eval_rsd_bb0_in->eval_rsd_bb4_in: 1 {O(1)}
3: eval_rsd_bb1_in->eval_rsd_bb2_in: 1 {O(1)}
4: eval_rsd_bb2_in->eval_rsd_bb3_in: 4*Arg_3+2 {O(n)}
5: eval_rsd_bb2_in->eval_rsd_bb4_in: 1 {O(1)}
6: eval_rsd_bb3_in->eval_rsd_3: 4*Arg_3+1 {O(n)}
13: eval_rsd_bb4_in->eval_rsd_stop: 1 {O(1)}
0: eval_rsd_start->eval_rsd_bb0_in: 1 {O(1)}
Sizebounds
8: eval_rsd_3->eval_rsd_4, Arg_1: 4*Arg_3+1 {O(n)}
8: eval_rsd_3->eval_rsd_4, Arg_2: 4*Arg_3+1 {O(n)}
8: eval_rsd_3->eval_rsd_4, Arg_3: Arg_3 {O(n)}
9: eval_rsd_4->eval_rsd_bb2_in, Arg_1: 4*Arg_3+1 {O(n)}
9: eval_rsd_4->eval_rsd_bb2_in, Arg_2: 4*Arg_3+1 {O(n)}
9: eval_rsd_4->eval_rsd_bb2_in, Arg_3: Arg_3 {O(n)}
12: eval_rsd_4->eval_rsd_bb2_in, Arg_1: 4*Arg_3+1 {O(n)}
12: eval_rsd_4->eval_rsd_bb2_in, Arg_2: 4*Arg_3+1 {O(n)}
12: eval_rsd_4->eval_rsd_bb2_in, Arg_3: Arg_3 {O(n)}
1: eval_rsd_bb0_in->eval_rsd_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_rsd_bb0_in->eval_rsd_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_rsd_bb0_in->eval_rsd_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_rsd_bb0_in->eval_rsd_bb1_in, Arg_3: Arg_3 {O(n)}
2: eval_rsd_bb0_in->eval_rsd_bb4_in, Arg_0: Arg_0 {O(n)}
2: eval_rsd_bb0_in->eval_rsd_bb4_in, Arg_1: Arg_1 {O(n)}
2: eval_rsd_bb0_in->eval_rsd_bb4_in, Arg_2: Arg_2 {O(n)}
2: eval_rsd_bb0_in->eval_rsd_bb4_in, Arg_3: Arg_3 {O(n)}
3: eval_rsd_bb1_in->eval_rsd_bb2_in, Arg_0: Arg_0 {O(n)}
3: eval_rsd_bb1_in->eval_rsd_bb2_in, Arg_1: 2*Arg_3 {O(n)}
3: eval_rsd_bb1_in->eval_rsd_bb2_in, Arg_2: 2*Arg_3 {O(n)}
3: eval_rsd_bb1_in->eval_rsd_bb2_in, Arg_3: Arg_3 {O(n)}
4: eval_rsd_bb2_in->eval_rsd_bb3_in, Arg_1: 4*Arg_3+1 {O(n)}
4: eval_rsd_bb2_in->eval_rsd_bb3_in, Arg_2: 4*Arg_3+1 {O(n)}
4: eval_rsd_bb2_in->eval_rsd_bb3_in, Arg_3: Arg_3 {O(n)}
5: eval_rsd_bb2_in->eval_rsd_bb4_in, Arg_1: 8*Arg_3+2 {O(n)}
5: eval_rsd_bb2_in->eval_rsd_bb4_in, Arg_2: 8*Arg_3+2 {O(n)}
5: eval_rsd_bb2_in->eval_rsd_bb4_in, Arg_3: 2*Arg_3 {O(n)}
6: eval_rsd_bb3_in->eval_rsd_3, Arg_1: 4*Arg_3+1 {O(n)}
6: eval_rsd_bb3_in->eval_rsd_3, Arg_2: 4*Arg_3+1 {O(n)}
6: eval_rsd_bb3_in->eval_rsd_3, Arg_3: Arg_3 {O(n)}
13: eval_rsd_bb4_in->eval_rsd_stop, Arg_1: 8*Arg_3+Arg_1+2 {O(n)}
13: eval_rsd_bb4_in->eval_rsd_stop, Arg_2: 8*Arg_3+Arg_2+2 {O(n)}
13: eval_rsd_bb4_in->eval_rsd_stop, Arg_3: 3*Arg_3 {O(n)}
0: eval_rsd_start->eval_rsd_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_rsd_start->eval_rsd_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_rsd_start->eval_rsd_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_rsd_start->eval_rsd_bb0_in, Arg_3: Arg_3 {O(n)}