Initial Problem
Start: eval_jama_ex7_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_jama_ex7_bb0_in, eval_jama_ex7_bb1_in, eval_jama_ex7_bb2_in, eval_jama_ex7_bb3_in, eval_jama_ex7_bb4_in, eval_jama_ex7_bb5_in, eval_jama_ex7_start, eval_jama_ex7_stop
Transitions:
1:eval_jama_ex7_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb1_in(Arg_3,Arg_1,Arg_2,Arg_3)
2:eval_jama_ex7_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb2_in(Arg_0,Arg_2,Arg_2,Arg_3):|:1<=Arg_0
3:eval_jama_ex7_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<1
4:eval_jama_ex7_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_1
5:eval_jama_ex7_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<1
6:eval_jama_ex7_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb2_in(Arg_0,Arg_1-1,Arg_2,Arg_3)
7:eval_jama_ex7_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3)
8:eval_jama_ex7_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_jama_ex7_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)
Preprocessing
Found invariant 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_jama_ex7_bb3_in
Found invariant Arg_0<=Arg_3 for location eval_jama_ex7_bb1_in
Found invariant 1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_2 && 1<=Arg_0 for location eval_jama_ex7_bb2_in
Found invariant Arg_0<=Arg_3 && Arg_0<=0 for location eval_jama_ex7_bb5_in
Found invariant 1<=Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 for location eval_jama_ex7_bb4_in
Found invariant Arg_0<=Arg_3 && Arg_0<=0 for location eval_jama_ex7_stop
Problem after Preprocessing
Start: eval_jama_ex7_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_jama_ex7_bb0_in, eval_jama_ex7_bb1_in, eval_jama_ex7_bb2_in, eval_jama_ex7_bb3_in, eval_jama_ex7_bb4_in, eval_jama_ex7_bb5_in, eval_jama_ex7_start, eval_jama_ex7_stop
Transitions:
1:eval_jama_ex7_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb1_in(Arg_3,Arg_1,Arg_2,Arg_3)
2:eval_jama_ex7_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb2_in(Arg_0,Arg_2,Arg_2,Arg_3):|:Arg_0<=Arg_3 && 1<=Arg_0
3:eval_jama_ex7_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_0<1
4:eval_jama_ex7_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_2 && 1<=Arg_0 && 1<=Arg_1
5:eval_jama_ex7_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_2 && 1<=Arg_0 && Arg_1<1
6:eval_jama_ex7_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb2_in(Arg_0,Arg_1-1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
7:eval_jama_ex7_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0
8:eval_jama_ex7_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_0<=0
0:eval_jama_ex7_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)
MPRF for transition 2:eval_jama_ex7_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb2_in(Arg_0,Arg_2,Arg_2,Arg_3):|:Arg_0<=Arg_3 && 1<=Arg_0 of depth 1:
new bound:
Arg_3 {O(n)}
MPRF:
eval_jama_ex7_bb3_in [Arg_0-1 ]
eval_jama_ex7_bb2_in [Arg_0-1 ]
eval_jama_ex7_bb4_in [Arg_0-1 ]
eval_jama_ex7_bb1_in [Arg_0 ]
MPRF for transition 5:eval_jama_ex7_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_2 && 1<=Arg_0 && Arg_1<1 of depth 1:
new bound:
Arg_3 {O(n)}
MPRF:
eval_jama_ex7_bb3_in [Arg_0 ]
eval_jama_ex7_bb2_in [Arg_0 ]
eval_jama_ex7_bb4_in [Arg_0-1 ]
eval_jama_ex7_bb1_in [Arg_0 ]
MPRF for transition 7:eval_jama_ex7_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 of depth 1:
new bound:
Arg_3 {O(n)}
MPRF:
eval_jama_ex7_bb3_in [Arg_0 ]
eval_jama_ex7_bb2_in [Arg_0 ]
eval_jama_ex7_bb4_in [Arg_0 ]
eval_jama_ex7_bb1_in [Arg_0 ]
MPRF for transition 4:eval_jama_ex7_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=Arg_2 && 1<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
Arg_2*Arg_3+Arg_2 {O(n^2)}
MPRF:
eval_jama_ex7_bb1_in [Arg_2 ]
eval_jama_ex7_bb4_in [Arg_1 ]
eval_jama_ex7_bb3_in [Arg_1-1 ]
eval_jama_ex7_bb2_in [Arg_1 ]
MPRF for transition 6:eval_jama_ex7_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_jama_ex7_bb2_in(Arg_0,Arg_1-1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_2*Arg_3+Arg_2 {O(n^2)}
MPRF:
eval_jama_ex7_bb1_in [Arg_2 ]
eval_jama_ex7_bb4_in [Arg_1 ]
eval_jama_ex7_bb3_in [Arg_1 ]
eval_jama_ex7_bb2_in [Arg_1 ]
All Bounds
Timebounds
Overall timebound:2*Arg_2*Arg_3+2*Arg_2+3*Arg_3+4 {O(n^2)}
1: eval_jama_ex7_bb0_in->eval_jama_ex7_bb1_in: 1 {O(1)}
2: eval_jama_ex7_bb1_in->eval_jama_ex7_bb2_in: Arg_3 {O(n)}
3: eval_jama_ex7_bb1_in->eval_jama_ex7_bb5_in: 1 {O(1)}
4: eval_jama_ex7_bb2_in->eval_jama_ex7_bb3_in: Arg_2*Arg_3+Arg_2 {O(n^2)}
5: eval_jama_ex7_bb2_in->eval_jama_ex7_bb4_in: Arg_3 {O(n)}
6: eval_jama_ex7_bb3_in->eval_jama_ex7_bb2_in: Arg_2*Arg_3+Arg_2 {O(n^2)}
7: eval_jama_ex7_bb4_in->eval_jama_ex7_bb1_in: Arg_3 {O(n)}
8: eval_jama_ex7_bb5_in->eval_jama_ex7_stop: 1 {O(1)}
0: eval_jama_ex7_start->eval_jama_ex7_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: 2*Arg_2*Arg_3+2*Arg_2+3*Arg_3+4 {O(n^2)}
1: eval_jama_ex7_bb0_in->eval_jama_ex7_bb1_in: 1 {O(1)}
2: eval_jama_ex7_bb1_in->eval_jama_ex7_bb2_in: Arg_3 {O(n)}
3: eval_jama_ex7_bb1_in->eval_jama_ex7_bb5_in: 1 {O(1)}
4: eval_jama_ex7_bb2_in->eval_jama_ex7_bb3_in: Arg_2*Arg_3+Arg_2 {O(n^2)}
5: eval_jama_ex7_bb2_in->eval_jama_ex7_bb4_in: Arg_3 {O(n)}
6: eval_jama_ex7_bb3_in->eval_jama_ex7_bb2_in: Arg_2*Arg_3+Arg_2 {O(n^2)}
7: eval_jama_ex7_bb4_in->eval_jama_ex7_bb1_in: Arg_3 {O(n)}
8: eval_jama_ex7_bb5_in->eval_jama_ex7_stop: 1 {O(1)}
0: eval_jama_ex7_start->eval_jama_ex7_bb0_in: 1 {O(1)}
Sizebounds
1: eval_jama_ex7_bb0_in->eval_jama_ex7_bb1_in, Arg_0: Arg_3 {O(n)}
1: eval_jama_ex7_bb0_in->eval_jama_ex7_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_jama_ex7_bb0_in->eval_jama_ex7_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_jama_ex7_bb0_in->eval_jama_ex7_bb1_in, Arg_3: Arg_3 {O(n)}
2: eval_jama_ex7_bb1_in->eval_jama_ex7_bb2_in, Arg_0: Arg_3 {O(n)}
2: eval_jama_ex7_bb1_in->eval_jama_ex7_bb2_in, Arg_1: 2*Arg_2 {O(n)}
2: eval_jama_ex7_bb1_in->eval_jama_ex7_bb2_in, Arg_2: Arg_2 {O(n)}
2: eval_jama_ex7_bb1_in->eval_jama_ex7_bb2_in, Arg_3: Arg_3 {O(n)}
3: eval_jama_ex7_bb1_in->eval_jama_ex7_bb5_in, Arg_0: 2*Arg_3 {O(n)}
3: eval_jama_ex7_bb1_in->eval_jama_ex7_bb5_in, Arg_1: 4*Arg_2+Arg_1 {O(n)}
3: eval_jama_ex7_bb1_in->eval_jama_ex7_bb5_in, Arg_2: 2*Arg_2 {O(n)}
3: eval_jama_ex7_bb1_in->eval_jama_ex7_bb5_in, Arg_3: 2*Arg_3 {O(n)}
4: eval_jama_ex7_bb2_in->eval_jama_ex7_bb3_in, Arg_0: Arg_3 {O(n)}
4: eval_jama_ex7_bb2_in->eval_jama_ex7_bb3_in, Arg_1: 2*Arg_2 {O(n)}
4: eval_jama_ex7_bb2_in->eval_jama_ex7_bb3_in, Arg_2: Arg_2 {O(n)}
4: eval_jama_ex7_bb2_in->eval_jama_ex7_bb3_in, Arg_3: Arg_3 {O(n)}
5: eval_jama_ex7_bb2_in->eval_jama_ex7_bb4_in, Arg_0: Arg_3 {O(n)}
5: eval_jama_ex7_bb2_in->eval_jama_ex7_bb4_in, Arg_1: 4*Arg_2 {O(n)}
5: eval_jama_ex7_bb2_in->eval_jama_ex7_bb4_in, Arg_2: Arg_2 {O(n)}
5: eval_jama_ex7_bb2_in->eval_jama_ex7_bb4_in, Arg_3: Arg_3 {O(n)}
6: eval_jama_ex7_bb3_in->eval_jama_ex7_bb2_in, Arg_0: Arg_3 {O(n)}
6: eval_jama_ex7_bb3_in->eval_jama_ex7_bb2_in, Arg_1: 2*Arg_2 {O(n)}
6: eval_jama_ex7_bb3_in->eval_jama_ex7_bb2_in, Arg_2: Arg_2 {O(n)}
6: eval_jama_ex7_bb3_in->eval_jama_ex7_bb2_in, Arg_3: Arg_3 {O(n)}
7: eval_jama_ex7_bb4_in->eval_jama_ex7_bb1_in, Arg_0: Arg_3 {O(n)}
7: eval_jama_ex7_bb4_in->eval_jama_ex7_bb1_in, Arg_1: 4*Arg_2 {O(n)}
7: eval_jama_ex7_bb4_in->eval_jama_ex7_bb1_in, Arg_2: Arg_2 {O(n)}
7: eval_jama_ex7_bb4_in->eval_jama_ex7_bb1_in, Arg_3: Arg_3 {O(n)}
8: eval_jama_ex7_bb5_in->eval_jama_ex7_stop, Arg_0: 2*Arg_3 {O(n)}
8: eval_jama_ex7_bb5_in->eval_jama_ex7_stop, Arg_1: 4*Arg_2+Arg_1 {O(n)}
8: eval_jama_ex7_bb5_in->eval_jama_ex7_stop, Arg_2: 2*Arg_2 {O(n)}
8: eval_jama_ex7_bb5_in->eval_jama_ex7_stop, Arg_3: 2*Arg_3 {O(n)}
0: eval_jama_ex7_start->eval_jama_ex7_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_jama_ex7_start->eval_jama_ex7_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_jama_ex7_start->eval_jama_ex7_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_jama_ex7_start->eval_jama_ex7_bb0_in, Arg_3: Arg_3 {O(n)}