Initial Problem
Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
6:evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_2-1)
4:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2
5:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_2<=0
7:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1-1,Arg_2)
2:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1<=Arg_1
3:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
1:evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_1,Arg_0,Arg_2)
8:evalfreturnin(Arg_0,Arg_1,Arg_2) -> evalfstop(Arg_0,Arg_1,Arg_2)
0:evalfstart(Arg_0,Arg_1,Arg_2) -> evalfentryin(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant Arg_1<=0 for location evalfreturnin
Found invariant Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalfbb1in
Found invariant Arg_2<=Arg_0 && 1<=Arg_1 for location evalfbb2in
Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1 for location evalfbb3in
Found invariant Arg_1<=0 for location evalfstop
Problem after Preprocessing
Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
6:evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
4:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_1 && 1<=Arg_2
5:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=0
7:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1
2:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1<=Arg_1
3:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
1:evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_1,Arg_0,Arg_2)
8:evalfreturnin(Arg_0,Arg_1,Arg_2) -> evalfstop(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
0:evalfstart(Arg_0,Arg_1,Arg_2) -> evalfentryin(Arg_0,Arg_1,Arg_2)
MPRF for transition 5:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
evalfbb1in [Arg_1 ]
evalfbb3in [Arg_1-1 ]
evalfbb4in [Arg_1 ]
evalfbb2in [Arg_1 ]
MPRF for transition 7:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
evalfbb1in [Arg_1 ]
evalfbb3in [Arg_1 ]
evalfbb4in [Arg_1 ]
evalfbb2in [Arg_1 ]
MPRF for transition 2:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1<=Arg_1 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
evalfbb1in [Arg_1-1 ]
evalfbb3in [Arg_1-1 ]
evalfbb4in [Arg_1 ]
evalfbb2in [Arg_1-1 ]
MPRF for transition 6:evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_0 && 1<=Arg_2 && 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:
2*Arg_0*Arg_1 {O(n^2)}
MPRF:
evalfbb1in [Arg_2 ]
evalfbb2in [Arg_2 ]
evalfbb3in [Arg_2 ]
evalfbb4in [Arg_2 ]
MPRF for transition 4:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_1 && 1<=Arg_2 of depth 1:
new bound:
2*Arg_0*Arg_1 {O(n^2)}
MPRF:
evalfbb1in [Arg_2-1 ]
evalfbb2in [Arg_2 ]
evalfbb3in [Arg_2 ]
evalfbb4in [Arg_2 ]
Analysing control-flow refined program
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 for location n_evalfbb4in___2
Found invariant Arg_1<=0 for location evalfreturnin
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalfbb4in___4
Found invariant Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalfbb1in___9
Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_0<=Arg_2 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 for location n_evalfbb2in___1
Found invariant Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalfbb2in___3
Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalfbb3in___5
Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_0<=Arg_2 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 for location n_evalfbb3in___8
Found invariant Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 for location n_evalfbb2in___10
Found invariant 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalfbb2in___7
Found invariant Arg_1<=0 for location evalfstop
Found invariant 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_evalfbb1in___6
MPRF for transition 70:n_evalfbb1in___9(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___7(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_2<=Arg_0 && 1<=Arg_1 && 1<=Arg_2 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_evalfbb1in___9 [Arg_1 ]
n_evalfbb1in___6 [Arg_1-1 ]
n_evalfbb2in___7 [Arg_1-1 ]
n_evalfbb3in___5 [Arg_1-1 ]
n_evalfbb4in___4 [Arg_1 ]
n_evalfbb2in___3 [Arg_1 ]
MPRF for transition 74:n_evalfbb2in___3(Arg_0,Arg_1,Arg_2) -> n_evalfbb1in___9(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1 && 1<=Arg_2 of depth 1:
new bound:
Arg_0+1 {O(n)}
MPRF:
n_evalfbb1in___9 [Arg_1-1 ]
n_evalfbb1in___6 [Arg_1-1 ]
n_evalfbb2in___7 [Arg_1-1 ]
n_evalfbb3in___5 [Arg_1-1 ]
n_evalfbb4in___4 [Arg_1 ]
n_evalfbb2in___3 [Arg_1 ]
MPRF for transition 76:n_evalfbb2in___7(Arg_0,Arg_1,Arg_2) -> n_evalfbb3in___5(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 1+Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_evalfbb1in___9 [Arg_1 ]
n_evalfbb1in___6 [Arg_1 ]
n_evalfbb2in___7 [Arg_1 ]
n_evalfbb3in___5 [Arg_1-1 ]
n_evalfbb4in___4 [Arg_1 ]
n_evalfbb2in___3 [Arg_1 ]
MPRF for transition 77:n_evalfbb3in___5(Arg_0,Arg_1,Arg_2) -> n_evalfbb4in___4(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && Arg_2<=0 && 0<=Arg_2 && 1<=Arg_1 && Arg_2<=Arg_0 && Arg_2<=0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_evalfbb1in___9 [Arg_1 ]
n_evalfbb1in___6 [Arg_1 ]
n_evalfbb2in___7 [Arg_1 ]
n_evalfbb3in___5 [Arg_1 ]
n_evalfbb4in___4 [Arg_1 ]
n_evalfbb2in___3 [Arg_1 ]
MPRF for transition 81:n_evalfbb4in___4(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___3(Arg_0,Arg_1,Arg_0):|:Arg_2<=0 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_2<=Arg_0 && 0<=Arg_1 && Arg_2<=0 && 1<=Arg_1 of depth 1:
new bound:
Arg_0+1 {O(n)}
MPRF:
n_evalfbb1in___9 [Arg_1-1 ]
n_evalfbb1in___6 [Arg_1-1 ]
n_evalfbb2in___7 [Arg_1-1 ]
n_evalfbb3in___5 [Arg_1-1 ]
n_evalfbb4in___4 [Arg_1 ]
n_evalfbb2in___3 [Arg_1-1 ]
MPRF for transition 69:n_evalfbb1in___6(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___7(Arg_0,Arg_1,Arg_2-1):|:1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_1 && 1<=Arg_2 of depth 1:
new bound:
Arg_0*Arg_1+2*Arg_1 {O(n^2)}
MPRF:
n_evalfbb2in___3 [Arg_2 ]
n_evalfbb1in___9 [Arg_2 ]
n_evalfbb1in___6 [Arg_2 ]
n_evalfbb2in___7 [Arg_2 ]
n_evalfbb3in___5 [0 ]
n_evalfbb4in___4 [0 ]
MPRF for transition 75:n_evalfbb2in___7(Arg_0,Arg_1,Arg_2) -> n_evalfbb1in___6(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && Arg_2<=Arg_0 && 0<=Arg_2 && 1+Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1 && 1<=Arg_2 of depth 1:
new bound:
Arg_0*Arg_1+2*Arg_1 {O(n^2)}
MPRF:
n_evalfbb2in___3 [Arg_2 ]
n_evalfbb1in___9 [Arg_2 ]
n_evalfbb1in___6 [Arg_2 ]
n_evalfbb2in___7 [Arg_2+1 ]
n_evalfbb3in___5 [0 ]
n_evalfbb4in___4 [0 ]
MPRF for transition 71:n_evalfbb2in___1(Arg_0,Arg_1,Arg_2) -> n_evalfbb3in___8(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_0<=Arg_2 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 1<=Arg_1 && Arg_2<=Arg_0 && Arg_2<=0 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=0 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=0 of depth 1:
new bound:
Arg_0+1 {O(n)}
MPRF:
n_evalfbb3in___8 [Arg_1-1 ]
n_evalfbb4in___2 [Arg_1 ]
n_evalfbb2in___1 [Arg_1 ]
MPRF for transition 78:n_evalfbb3in___8(Arg_0,Arg_1,Arg_2) -> n_evalfbb4in___2(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_0<=Arg_2 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && Arg_0<=0 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=Arg_0 && Arg_2<=0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_evalfbb3in___8 [Arg_1 ]
n_evalfbb4in___2 [Arg_1 ]
n_evalfbb2in___1 [Arg_1 ]
MPRF for transition 80:n_evalfbb4in___2(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___1(Arg_0,Arg_1,Arg_0):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && Arg_0<=0 && Arg_2<=Arg_0 && 0<=Arg_1 && Arg_2<=0 && 1<=Arg_1 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_evalfbb3in___8 [Arg_1 ]
n_evalfbb4in___2 [Arg_1+1 ]
n_evalfbb2in___1 [Arg_1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4*Arg_0*Arg_1+3*Arg_0+4 {O(n^2)}
6: evalfbb1in->evalfbb2in: 2*Arg_0*Arg_1 {O(n^2)}
4: evalfbb2in->evalfbb1in: 2*Arg_0*Arg_1 {O(n^2)}
5: evalfbb2in->evalfbb3in: Arg_0 {O(n)}
7: evalfbb3in->evalfbb4in: Arg_0 {O(n)}
2: evalfbb4in->evalfbb2in: Arg_0 {O(n)}
3: evalfbb4in->evalfreturnin: 1 {O(1)}
1: evalfentryin->evalfbb4in: 1 {O(1)}
8: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}
Costbounds
Overall costbound: 4*Arg_0*Arg_1+3*Arg_0+4 {O(n^2)}
6: evalfbb1in->evalfbb2in: 2*Arg_0*Arg_1 {O(n^2)}
4: evalfbb2in->evalfbb1in: 2*Arg_0*Arg_1 {O(n^2)}
5: evalfbb2in->evalfbb3in: Arg_0 {O(n)}
7: evalfbb3in->evalfbb4in: Arg_0 {O(n)}
2: evalfbb4in->evalfbb2in: Arg_0 {O(n)}
3: evalfbb4in->evalfreturnin: 1 {O(1)}
1: evalfentryin->evalfbb4in: 1 {O(1)}
8: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}
Sizebounds
6: evalfbb1in->evalfbb2in, Arg_0: Arg_1 {O(n)}
6: evalfbb1in->evalfbb2in, Arg_1: Arg_0 {O(n)}
6: evalfbb1in->evalfbb2in, Arg_2: 2*Arg_1 {O(n)}
4: evalfbb2in->evalfbb1in, Arg_0: Arg_1 {O(n)}
4: evalfbb2in->evalfbb1in, Arg_1: Arg_0 {O(n)}
4: evalfbb2in->evalfbb1in, Arg_2: 2*Arg_1 {O(n)}
5: evalfbb2in->evalfbb3in, Arg_0: Arg_1 {O(n)}
5: evalfbb2in->evalfbb3in, Arg_1: Arg_0 {O(n)}
5: evalfbb2in->evalfbb3in, Arg_2: 4*Arg_1 {O(n)}
7: evalfbb3in->evalfbb4in, Arg_0: Arg_1 {O(n)}
7: evalfbb3in->evalfbb4in, Arg_1: Arg_0 {O(n)}
7: evalfbb3in->evalfbb4in, Arg_2: 4*Arg_1 {O(n)}
2: evalfbb4in->evalfbb2in, Arg_0: Arg_1 {O(n)}
2: evalfbb4in->evalfbb2in, Arg_1: Arg_0 {O(n)}
2: evalfbb4in->evalfbb2in, Arg_2: 2*Arg_1 {O(n)}
3: evalfbb4in->evalfreturnin, Arg_0: 2*Arg_1 {O(n)}
3: evalfbb4in->evalfreturnin, Arg_1: 2*Arg_0 {O(n)}
3: evalfbb4in->evalfreturnin, Arg_2: 4*Arg_1+Arg_2 {O(n)}
1: evalfentryin->evalfbb4in, Arg_0: Arg_1 {O(n)}
1: evalfentryin->evalfbb4in, Arg_1: Arg_0 {O(n)}
1: evalfentryin->evalfbb4in, Arg_2: Arg_2 {O(n)}
8: evalfreturnin->evalfstop, Arg_0: 2*Arg_1 {O(n)}
8: evalfreturnin->evalfstop, Arg_1: 2*Arg_0 {O(n)}
8: evalfreturnin->evalfstop, Arg_2: 4*Arg_1+Arg_2 {O(n)}
0: evalfstart->evalfentryin, Arg_0: Arg_0 {O(n)}
0: evalfstart->evalfentryin, Arg_1: Arg_1 {O(n)}
0: evalfstart->evalfentryin, Arg_2: Arg_2 {O(n)}