Initial Problem
Start: evalspeedpldi4start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: evalspeedpldi4bb2in, evalspeedpldi4bb3in, evalspeedpldi4bb4in, evalspeedpldi4bb5in, evalspeedpldi4entryin, evalspeedpldi4returnin, evalspeedpldi4start, evalspeedpldi4stop
Transitions:
6:evalspeedpldi4bb2in(Arg_0,Arg_1) -> evalspeedpldi4bb3in(Arg_0,Arg_1):|:Arg_1+1<=Arg_0
7:evalspeedpldi4bb2in(Arg_0,Arg_1) -> evalspeedpldi4bb4in(Arg_0,Arg_1):|:Arg_0<=Arg_1
8:evalspeedpldi4bb3in(Arg_0,Arg_1) -> evalspeedpldi4bb5in(Arg_0,Arg_1-1)
9:evalspeedpldi4bb4in(Arg_0,Arg_1) -> evalspeedpldi4bb5in(Arg_0,Arg_1-Arg_0)
4:evalspeedpldi4bb5in(Arg_0,Arg_1) -> evalspeedpldi4bb2in(Arg_0,Arg_1):|:1<=Arg_1
5:evalspeedpldi4bb5in(Arg_0,Arg_1) -> evalspeedpldi4returnin(Arg_0,Arg_1):|:Arg_1<=0
3:evalspeedpldi4entryin(Arg_0,Arg_1) -> evalspeedpldi4bb5in(Arg_0,Arg_1):|:1<=Arg_0 && Arg_0+1<=Arg_1
1:evalspeedpldi4entryin(Arg_0,Arg_1) -> evalspeedpldi4returnin(Arg_0,Arg_1):|:Arg_0<=0
2:evalspeedpldi4entryin(Arg_0,Arg_1) -> evalspeedpldi4returnin(Arg_0,Arg_1):|:Arg_1<=Arg_0
10:evalspeedpldi4returnin(Arg_0,Arg_1) -> evalspeedpldi4stop(Arg_0,Arg_1)
0:evalspeedpldi4start(Arg_0,Arg_1) -> evalspeedpldi4entryin(Arg_0,Arg_1)
Preprocessing
Found invariant 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location evalspeedpldi4bb3in
Found invariant 1<=Arg_0+Arg_1 && 1<=Arg_0 for location evalspeedpldi4bb5in
Found invariant 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location evalspeedpldi4bb4in
Found invariant 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalspeedpldi4bb2in
Problem after Preprocessing
Start: evalspeedpldi4start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: evalspeedpldi4bb2in, evalspeedpldi4bb3in, evalspeedpldi4bb4in, evalspeedpldi4bb5in, evalspeedpldi4entryin, evalspeedpldi4returnin, evalspeedpldi4start, evalspeedpldi4stop
Transitions:
6:evalspeedpldi4bb2in(Arg_0,Arg_1) -> evalspeedpldi4bb3in(Arg_0,Arg_1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1+1<=Arg_0
7:evalspeedpldi4bb2in(Arg_0,Arg_1) -> evalspeedpldi4bb4in(Arg_0,Arg_1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1
8:evalspeedpldi4bb3in(Arg_0,Arg_1) -> evalspeedpldi4bb5in(Arg_0,Arg_1-1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
9:evalspeedpldi4bb4in(Arg_0,Arg_1) -> evalspeedpldi4bb5in(Arg_0,Arg_1-Arg_0):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0
4:evalspeedpldi4bb5in(Arg_0,Arg_1) -> evalspeedpldi4bb2in(Arg_0,Arg_1):|:1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1
5:evalspeedpldi4bb5in(Arg_0,Arg_1) -> evalspeedpldi4returnin(Arg_0,Arg_1):|:1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=0
3:evalspeedpldi4entryin(Arg_0,Arg_1) -> evalspeedpldi4bb5in(Arg_0,Arg_1):|:1<=Arg_0 && Arg_0+1<=Arg_1
1:evalspeedpldi4entryin(Arg_0,Arg_1) -> evalspeedpldi4returnin(Arg_0,Arg_1):|:Arg_0<=0
2:evalspeedpldi4entryin(Arg_0,Arg_1) -> evalspeedpldi4returnin(Arg_0,Arg_1):|:Arg_1<=Arg_0
10:evalspeedpldi4returnin(Arg_0,Arg_1) -> evalspeedpldi4stop(Arg_0,Arg_1)
0:evalspeedpldi4start(Arg_0,Arg_1) -> evalspeedpldi4entryin(Arg_0,Arg_1)
MPRF for transition 6:evalspeedpldi4bb2in(Arg_0,Arg_1) -> evalspeedpldi4bb3in(Arg_0,Arg_1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1+1<=Arg_0 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalspeedpldi4bb3in [Arg_1-1 ]
evalspeedpldi4bb4in [Arg_1-Arg_0 ]
evalspeedpldi4bb5in [Arg_1 ]
evalspeedpldi4bb2in [Arg_1 ]
MPRF for transition 7:evalspeedpldi4bb2in(Arg_0,Arg_1) -> evalspeedpldi4bb4in(Arg_0,Arg_1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalspeedpldi4bb3in [Arg_1-1 ]
evalspeedpldi4bb4in [Arg_1-1 ]
evalspeedpldi4bb5in [Arg_1 ]
evalspeedpldi4bb2in [Arg_1 ]
MPRF for transition 8:evalspeedpldi4bb3in(Arg_0,Arg_1) -> evalspeedpldi4bb5in(Arg_0,Arg_1-1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalspeedpldi4bb3in [Arg_1 ]
evalspeedpldi4bb4in [Arg_1 ]
evalspeedpldi4bb5in [Arg_1 ]
evalspeedpldi4bb2in [Arg_1 ]
MPRF for transition 9:evalspeedpldi4bb4in(Arg_0,Arg_1) -> evalspeedpldi4bb5in(Arg_0,Arg_1-Arg_0):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalspeedpldi4bb3in [Arg_1 ]
evalspeedpldi4bb4in [Arg_1 ]
evalspeedpldi4bb5in [Arg_1 ]
evalspeedpldi4bb2in [Arg_1 ]
MPRF for transition 4:evalspeedpldi4bb5in(Arg_0,Arg_1) -> evalspeedpldi4bb2in(Arg_0,Arg_1):|:1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalspeedpldi4bb3in [Arg_1-1 ]
evalspeedpldi4bb4in [Arg_1-1 ]
evalspeedpldi4bb5in [Arg_1 ]
evalspeedpldi4bb2in [Arg_1-1 ]
All Bounds
Timebounds
Overall timebound:5*Arg_1+6 {O(n)}
6: evalspeedpldi4bb2in->evalspeedpldi4bb3in: Arg_1 {O(n)}
7: evalspeedpldi4bb2in->evalspeedpldi4bb4in: Arg_1 {O(n)}
8: evalspeedpldi4bb3in->evalspeedpldi4bb5in: Arg_1 {O(n)}
9: evalspeedpldi4bb4in->evalspeedpldi4bb5in: Arg_1 {O(n)}
4: evalspeedpldi4bb5in->evalspeedpldi4bb2in: Arg_1 {O(n)}
5: evalspeedpldi4bb5in->evalspeedpldi4returnin: 1 {O(1)}
1: evalspeedpldi4entryin->evalspeedpldi4returnin: 1 {O(1)}
2: evalspeedpldi4entryin->evalspeedpldi4returnin: 1 {O(1)}
3: evalspeedpldi4entryin->evalspeedpldi4bb5in: 1 {O(1)}
10: evalspeedpldi4returnin->evalspeedpldi4stop: 1 {O(1)}
0: evalspeedpldi4start->evalspeedpldi4entryin: 1 {O(1)}
Costbounds
Overall costbound: 5*Arg_1+6 {O(n)}
6: evalspeedpldi4bb2in->evalspeedpldi4bb3in: Arg_1 {O(n)}
7: evalspeedpldi4bb2in->evalspeedpldi4bb4in: Arg_1 {O(n)}
8: evalspeedpldi4bb3in->evalspeedpldi4bb5in: Arg_1 {O(n)}
9: evalspeedpldi4bb4in->evalspeedpldi4bb5in: Arg_1 {O(n)}
4: evalspeedpldi4bb5in->evalspeedpldi4bb2in: Arg_1 {O(n)}
5: evalspeedpldi4bb5in->evalspeedpldi4returnin: 1 {O(1)}
1: evalspeedpldi4entryin->evalspeedpldi4returnin: 1 {O(1)}
2: evalspeedpldi4entryin->evalspeedpldi4returnin: 1 {O(1)}
3: evalspeedpldi4entryin->evalspeedpldi4bb5in: 1 {O(1)}
10: evalspeedpldi4returnin->evalspeedpldi4stop: 1 {O(1)}
0: evalspeedpldi4start->evalspeedpldi4entryin: 1 {O(1)}
Sizebounds
6: evalspeedpldi4bb2in->evalspeedpldi4bb3in, Arg_0: Arg_0 {O(n)}
6: evalspeedpldi4bb2in->evalspeedpldi4bb3in, Arg_1: Arg_1 {O(n)}
7: evalspeedpldi4bb2in->evalspeedpldi4bb4in, Arg_0: Arg_0 {O(n)}
7: evalspeedpldi4bb2in->evalspeedpldi4bb4in, Arg_1: Arg_1 {O(n)}
8: evalspeedpldi4bb3in->evalspeedpldi4bb5in, Arg_0: Arg_0 {O(n)}
8: evalspeedpldi4bb3in->evalspeedpldi4bb5in, Arg_1: Arg_1 {O(n)}
9: evalspeedpldi4bb4in->evalspeedpldi4bb5in, Arg_0: Arg_0 {O(n)}
9: evalspeedpldi4bb4in->evalspeedpldi4bb5in, Arg_1: Arg_1 {O(n)}
4: evalspeedpldi4bb5in->evalspeedpldi4bb2in, Arg_0: Arg_0 {O(n)}
4: evalspeedpldi4bb5in->evalspeedpldi4bb2in, Arg_1: Arg_1 {O(n)}
5: evalspeedpldi4bb5in->evalspeedpldi4returnin, Arg_0: 2*Arg_0 {O(n)}
5: evalspeedpldi4bb5in->evalspeedpldi4returnin, Arg_1: 2*Arg_1 {O(n)}
1: evalspeedpldi4entryin->evalspeedpldi4returnin, Arg_0: Arg_0 {O(n)}
1: evalspeedpldi4entryin->evalspeedpldi4returnin, Arg_1: Arg_1 {O(n)}
2: evalspeedpldi4entryin->evalspeedpldi4returnin, Arg_0: Arg_0 {O(n)}
2: evalspeedpldi4entryin->evalspeedpldi4returnin, Arg_1: Arg_1 {O(n)}
3: evalspeedpldi4entryin->evalspeedpldi4bb5in, Arg_0: Arg_0 {O(n)}
3: evalspeedpldi4entryin->evalspeedpldi4bb5in, Arg_1: Arg_1 {O(n)}
10: evalspeedpldi4returnin->evalspeedpldi4stop, Arg_0: 4*Arg_0 {O(n)}
10: evalspeedpldi4returnin->evalspeedpldi4stop, Arg_1: 4*Arg_1 {O(n)}
0: evalspeedpldi4start->evalspeedpldi4entryin, Arg_0: Arg_0 {O(n)}
0: evalspeedpldi4start->evalspeedpldi4entryin, Arg_1: Arg_1 {O(n)}