Initial Problem
Start: evalspeedpldi3start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: evalspeedpldi3bb2in, evalspeedpldi3bb3in, evalspeedpldi3bb4in, evalspeedpldi3bb5in, evalspeedpldi3entryin, evalspeedpldi3returnin, evalspeedpldi3start, evalspeedpldi3stop
Transitions:
6:evalspeedpldi3bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb3in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2+1<=Arg_0
7:evalspeedpldi3bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb4in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_2
8:evalspeedpldi3bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb5in(Arg_0,Arg_1,Arg_2+1,Arg_3)
9:evalspeedpldi3bb4in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb5in(Arg_0,Arg_1,0,Arg_3+1)
4:evalspeedpldi3bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb2in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3+1<=Arg_1
5:evalspeedpldi3bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3
3:evalspeedpldi3entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb5in(Arg_0,Arg_1,0,0):|:1<=Arg_0 && Arg_0+1<=Arg_1
1:evalspeedpldi3entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
2:evalspeedpldi3entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_0
10:evalspeedpldi3returnin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:evalspeedpldi3start(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3entryin(Arg_0,Arg_1,Arg_2,Arg_3)
Preprocessing
Found invariant 1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location evalspeedpldi3bb2in
Found invariant 1+Arg_3<=Arg_1 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location evalspeedpldi3bb4in
Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location evalspeedpldi3bb5in
Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location evalspeedpldi3bb3in
Problem after Preprocessing
Start: evalspeedpldi3start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: evalspeedpldi3bb2in, evalspeedpldi3bb3in, evalspeedpldi3bb4in, evalspeedpldi3bb5in, evalspeedpldi3entryin, evalspeedpldi3returnin, evalspeedpldi3start, evalspeedpldi3stop
Transitions:
6:evalspeedpldi3bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb3in(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2+1<=Arg_0
7:evalspeedpldi3bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb4in(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2
8:evalspeedpldi3bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb5in(Arg_0,Arg_1,Arg_2+1,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0
9:evalspeedpldi3bb4in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb5in(Arg_0,Arg_1,0,Arg_3+1):|:1+Arg_3<=Arg_1 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0
4:evalspeedpldi3bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb2in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3+1<=Arg_1
5:evalspeedpldi3bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_1<=Arg_3
3:evalspeedpldi3entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb5in(Arg_0,Arg_1,0,0):|:1<=Arg_0 && Arg_0+1<=Arg_1
1:evalspeedpldi3entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
2:evalspeedpldi3entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_0
10:evalspeedpldi3returnin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:evalspeedpldi3start(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3entryin(Arg_0,Arg_1,Arg_2,Arg_3)
MPRF for transition 7:evalspeedpldi3bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb4in(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalspeedpldi3bb3in [Arg_1-Arg_3 ]
evalspeedpldi3bb4in [Arg_1-Arg_3-1 ]
evalspeedpldi3bb5in [Arg_1-Arg_3 ]
evalspeedpldi3bb2in [Arg_1-Arg_3 ]
MPRF for transition 9:evalspeedpldi3bb4in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb5in(Arg_0,Arg_1,0,Arg_3+1):|:1+Arg_3<=Arg_1 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalspeedpldi3bb3in [Arg_1-Arg_3 ]
evalspeedpldi3bb4in [Arg_1-Arg_3 ]
evalspeedpldi3bb5in [Arg_1-Arg_3 ]
evalspeedpldi3bb2in [Arg_1-Arg_3 ]
MPRF for transition 6:evalspeedpldi3bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb3in(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2+1<=Arg_0 of depth 1:
new bound:
Arg_1*Arg_1+Arg_1 {O(n^2)}
MPRF:
evalspeedpldi3bb4in [Arg_1-Arg_2 ]
evalspeedpldi3bb3in [Arg_1-Arg_2-1 ]
evalspeedpldi3bb5in [Arg_1-Arg_2 ]
evalspeedpldi3bb2in [Arg_1-Arg_2 ]
MPRF for transition 8:evalspeedpldi3bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb5in(Arg_0,Arg_1,Arg_2+1,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_0*Arg_1+Arg_0 {O(n^2)}
MPRF:
evalspeedpldi3bb4in [Arg_0-Arg_2 ]
evalspeedpldi3bb3in [Arg_0-Arg_2 ]
evalspeedpldi3bb5in [Arg_0-Arg_2 ]
evalspeedpldi3bb2in [Arg_0-Arg_2 ]
MPRF for transition 4:evalspeedpldi3bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalspeedpldi3bb2in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3+1<=Arg_1 of depth 1:
new bound:
Arg_0*Arg_1+Arg_0+Arg_1+1 {O(n^2)}
MPRF:
evalspeedpldi3bb4in [Arg_0-Arg_2 ]
evalspeedpldi3bb3in [Arg_0-Arg_2 ]
evalspeedpldi3bb5in [Arg_0+1-Arg_2 ]
evalspeedpldi3bb2in [Arg_0-Arg_2 ]
All Bounds
Timebounds
Overall timebound:2*Arg_0*Arg_1+Arg_1*Arg_1+2*Arg_0+4*Arg_1+7 {O(n^2)}
6: evalspeedpldi3bb2in->evalspeedpldi3bb3in: Arg_1*Arg_1+Arg_1 {O(n^2)}
7: evalspeedpldi3bb2in->evalspeedpldi3bb4in: Arg_1 {O(n)}
8: evalspeedpldi3bb3in->evalspeedpldi3bb5in: Arg_0*Arg_1+Arg_0 {O(n^2)}
9: evalspeedpldi3bb4in->evalspeedpldi3bb5in: Arg_1 {O(n)}
4: evalspeedpldi3bb5in->evalspeedpldi3bb2in: Arg_0*Arg_1+Arg_0+Arg_1+1 {O(n^2)}
5: evalspeedpldi3bb5in->evalspeedpldi3returnin: 1 {O(1)}
1: evalspeedpldi3entryin->evalspeedpldi3returnin: 1 {O(1)}
2: evalspeedpldi3entryin->evalspeedpldi3returnin: 1 {O(1)}
3: evalspeedpldi3entryin->evalspeedpldi3bb5in: 1 {O(1)}
10: evalspeedpldi3returnin->evalspeedpldi3stop: 1 {O(1)}
0: evalspeedpldi3start->evalspeedpldi3entryin: 1 {O(1)}
Costbounds
Overall costbound: 2*Arg_0*Arg_1+Arg_1*Arg_1+2*Arg_0+4*Arg_1+7 {O(n^2)}
6: evalspeedpldi3bb2in->evalspeedpldi3bb3in: Arg_1*Arg_1+Arg_1 {O(n^2)}
7: evalspeedpldi3bb2in->evalspeedpldi3bb4in: Arg_1 {O(n)}
8: evalspeedpldi3bb3in->evalspeedpldi3bb5in: Arg_0*Arg_1+Arg_0 {O(n^2)}
9: evalspeedpldi3bb4in->evalspeedpldi3bb5in: Arg_1 {O(n)}
4: evalspeedpldi3bb5in->evalspeedpldi3bb2in: Arg_0*Arg_1+Arg_0+Arg_1+1 {O(n^2)}
5: evalspeedpldi3bb5in->evalspeedpldi3returnin: 1 {O(1)}
1: evalspeedpldi3entryin->evalspeedpldi3returnin: 1 {O(1)}
2: evalspeedpldi3entryin->evalspeedpldi3returnin: 1 {O(1)}
3: evalspeedpldi3entryin->evalspeedpldi3bb5in: 1 {O(1)}
10: evalspeedpldi3returnin->evalspeedpldi3stop: 1 {O(1)}
0: evalspeedpldi3start->evalspeedpldi3entryin: 1 {O(1)}
Sizebounds
6: evalspeedpldi3bb2in->evalspeedpldi3bb3in, Arg_0: Arg_0 {O(n)}
6: evalspeedpldi3bb2in->evalspeedpldi3bb3in, Arg_1: Arg_1 {O(n)}
6: evalspeedpldi3bb2in->evalspeedpldi3bb3in, Arg_2: Arg_0*Arg_1+Arg_0 {O(n^2)}
6: evalspeedpldi3bb2in->evalspeedpldi3bb3in, Arg_3: Arg_1 {O(n)}
7: evalspeedpldi3bb2in->evalspeedpldi3bb4in, Arg_0: Arg_0 {O(n)}
7: evalspeedpldi3bb2in->evalspeedpldi3bb4in, Arg_1: Arg_1 {O(n)}
7: evalspeedpldi3bb2in->evalspeedpldi3bb4in, Arg_2: Arg_0*Arg_1+Arg_0 {O(n^2)}
7: evalspeedpldi3bb2in->evalspeedpldi3bb4in, Arg_3: Arg_1 {O(n)}
8: evalspeedpldi3bb3in->evalspeedpldi3bb5in, Arg_0: Arg_0 {O(n)}
8: evalspeedpldi3bb3in->evalspeedpldi3bb5in, Arg_1: Arg_1 {O(n)}
8: evalspeedpldi3bb3in->evalspeedpldi3bb5in, Arg_2: Arg_0*Arg_1+Arg_0 {O(n^2)}
8: evalspeedpldi3bb3in->evalspeedpldi3bb5in, Arg_3: Arg_1 {O(n)}
9: evalspeedpldi3bb4in->evalspeedpldi3bb5in, Arg_0: Arg_0 {O(n)}
9: evalspeedpldi3bb4in->evalspeedpldi3bb5in, Arg_1: Arg_1 {O(n)}
9: evalspeedpldi3bb4in->evalspeedpldi3bb5in, Arg_2: 0 {O(1)}
9: evalspeedpldi3bb4in->evalspeedpldi3bb5in, Arg_3: Arg_1 {O(n)}
4: evalspeedpldi3bb5in->evalspeedpldi3bb2in, Arg_0: Arg_0 {O(n)}
4: evalspeedpldi3bb5in->evalspeedpldi3bb2in, Arg_1: Arg_1 {O(n)}
4: evalspeedpldi3bb5in->evalspeedpldi3bb2in, Arg_2: Arg_0*Arg_1+Arg_0 {O(n^2)}
4: evalspeedpldi3bb5in->evalspeedpldi3bb2in, Arg_3: Arg_1 {O(n)}
5: evalspeedpldi3bb5in->evalspeedpldi3returnin, Arg_0: 2*Arg_0 {O(n)}
5: evalspeedpldi3bb5in->evalspeedpldi3returnin, Arg_1: 2*Arg_1 {O(n)}
5: evalspeedpldi3bb5in->evalspeedpldi3returnin, Arg_2: Arg_0*Arg_1+Arg_0 {O(n^2)}
5: evalspeedpldi3bb5in->evalspeedpldi3returnin, Arg_3: 2*Arg_1 {O(n)}
1: evalspeedpldi3entryin->evalspeedpldi3returnin, Arg_0: Arg_0 {O(n)}
1: evalspeedpldi3entryin->evalspeedpldi3returnin, Arg_1: Arg_1 {O(n)}
1: evalspeedpldi3entryin->evalspeedpldi3returnin, Arg_2: Arg_2 {O(n)}
1: evalspeedpldi3entryin->evalspeedpldi3returnin, Arg_3: Arg_3 {O(n)}
2: evalspeedpldi3entryin->evalspeedpldi3returnin, Arg_0: Arg_0 {O(n)}
2: evalspeedpldi3entryin->evalspeedpldi3returnin, Arg_1: Arg_1 {O(n)}
2: evalspeedpldi3entryin->evalspeedpldi3returnin, Arg_2: Arg_2 {O(n)}
2: evalspeedpldi3entryin->evalspeedpldi3returnin, Arg_3: Arg_3 {O(n)}
3: evalspeedpldi3entryin->evalspeedpldi3bb5in, Arg_0: Arg_0 {O(n)}
3: evalspeedpldi3entryin->evalspeedpldi3bb5in, Arg_1: Arg_1 {O(n)}
3: evalspeedpldi3entryin->evalspeedpldi3bb5in, Arg_2: 0 {O(1)}
3: evalspeedpldi3entryin->evalspeedpldi3bb5in, Arg_3: 0 {O(1)}
10: evalspeedpldi3returnin->evalspeedpldi3stop, Arg_0: 4*Arg_0 {O(n)}
10: evalspeedpldi3returnin->evalspeedpldi3stop, Arg_1: 4*Arg_1 {O(n)}
10: evalspeedpldi3returnin->evalspeedpldi3stop, Arg_2: Arg_0*Arg_1+2*Arg_2+Arg_0 {O(n^2)}
10: evalspeedpldi3returnin->evalspeedpldi3stop, Arg_3: 2*Arg_1+2*Arg_3 {O(n)}
0: evalspeedpldi3start->evalspeedpldi3entryin, Arg_0: Arg_0 {O(n)}
0: evalspeedpldi3start->evalspeedpldi3entryin, Arg_1: Arg_1 {O(n)}
0: evalspeedpldi3start->evalspeedpldi3entryin, Arg_2: Arg_2 {O(n)}
0: evalspeedpldi3start->evalspeedpldi3entryin, Arg_3: Arg_3 {O(n)}