Initial Problem
Start: n_evalDis2start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_evalDis2bb1in___4, n_evalDis2bb2in___3, n_evalDis2bb3in___2, n_evalDis2bb3in___7, n_evalDis2bbin___6, n_evalDis2entryin___8, n_evalDis2returnin___5, n_evalDis2start, n_evalDis2stop___1
Transitions:
0:n_evalDis2bb1in___4(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb3in___7(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0
1:n_evalDis2bb2in___3(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb3in___2(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_2
2:n_evalDis2bb3in___2(Arg_0,Arg_1,Arg_2) -> n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0
3:n_evalDis2bb3in___7(Arg_0,Arg_1,Arg_2) -> n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0
4:n_evalDis2bb3in___7(Arg_0,Arg_1,Arg_2) -> n_evalDis2returnin___5(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2
5:n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb1in___4(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_1
6:n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb2in___3(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_2
7:n_evalDis2entryin___8(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb3in___7(Arg_1,Arg_2,Arg_0)
8:n_evalDis2returnin___5(Arg_0,Arg_1,Arg_2) -> n_evalDis2stop___1(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2
9:n_evalDis2start(Arg_0,Arg_1,Arg_2) -> n_evalDis2entryin___8(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 for location n_evalDis2bb1in___4
Found invariant 1+Arg_2<=Arg_0 && Arg_1<=1+Arg_2 && Arg_1<=Arg_0 for location n_evalDis2bb3in___2
Found invariant Arg_0<=Arg_2 for location n_evalDis2returnin___5
Found invariant 1+Arg_2<=Arg_0 for location n_evalDis2bbin___6
Found invariant 1+Arg_2<=Arg_0 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 for location n_evalDis2bb2in___3
Found invariant Arg_0<=Arg_2 for location n_evalDis2stop___1
Problem after Preprocessing
Start: n_evalDis2start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_evalDis2bb1in___4, n_evalDis2bb2in___3, n_evalDis2bb3in___2, n_evalDis2bb3in___7, n_evalDis2bbin___6, n_evalDis2entryin___8, n_evalDis2returnin___5, n_evalDis2start, n_evalDis2stop___1
Transitions:
0:n_evalDis2bb1in___4(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb3in___7(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0
1:n_evalDis2bb2in___3(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb3in___2(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_2
2:n_evalDis2bb3in___2(Arg_0,Arg_1,Arg_2) -> n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=1+Arg_2 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0
3:n_evalDis2bb3in___7(Arg_0,Arg_1,Arg_2) -> n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0
4:n_evalDis2bb3in___7(Arg_0,Arg_1,Arg_2) -> n_evalDis2returnin___5(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2
5:n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb1in___4(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_1
6:n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb2in___3(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_2
7:n_evalDis2entryin___8(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb3in___7(Arg_1,Arg_2,Arg_0)
8:n_evalDis2returnin___5(Arg_0,Arg_1,Arg_2) -> n_evalDis2stop___1(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_0<=Arg_2
9:n_evalDis2start(Arg_0,Arg_1,Arg_2) -> n_evalDis2entryin___8(Arg_0,Arg_1,Arg_2)
MPRF for transition 0:n_evalDis2bb1in___4(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb3in___7(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 of depth 1:
new bound:
Arg_0+Arg_1 {O(n)}
MPRF:
n_evalDis2bb3in___2 [Arg_0-Arg_2 ]
n_evalDis2bb3in___7 [Arg_0-Arg_2 ]
n_evalDis2bb1in___4 [Arg_0-Arg_2 ]
n_evalDis2bbin___6 [Arg_0-Arg_2 ]
n_evalDis2bb2in___3 [Arg_0-Arg_2 ]
MPRF for transition 1:n_evalDis2bb2in___3(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb3in___2(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_2 of depth 1:
new bound:
Arg_1+Arg_2 {O(n)}
MPRF:
n_evalDis2bb3in___2 [Arg_0-Arg_1 ]
n_evalDis2bb3in___7 [Arg_0-Arg_1 ]
n_evalDis2bb1in___4 [Arg_0-Arg_1 ]
n_evalDis2bbin___6 [Arg_0-Arg_1 ]
n_evalDis2bb2in___3 [Arg_0-Arg_1 ]
MPRF for transition 2:n_evalDis2bb3in___2(Arg_0,Arg_1,Arg_2) -> n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=1+Arg_2 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 of depth 1:
new bound:
Arg_1+Arg_2 {O(n)}
MPRF:
n_evalDis2bb3in___2 [Arg_0+1-Arg_1 ]
n_evalDis2bb3in___7 [Arg_0-Arg_1 ]
n_evalDis2bb1in___4 [Arg_0-Arg_1 ]
n_evalDis2bbin___6 [Arg_0-Arg_1 ]
n_evalDis2bb2in___3 [Arg_0-Arg_1 ]
MPRF for transition 3:n_evalDis2bb3in___7(Arg_0,Arg_1,Arg_2) -> n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 of depth 1:
new bound:
Arg_0+Arg_1 {O(n)}
MPRF:
n_evalDis2bb3in___2 [Arg_0-Arg_2-1 ]
n_evalDis2bb3in___7 [Arg_0-Arg_2 ]
n_evalDis2bb1in___4 [Arg_0-Arg_2-1 ]
n_evalDis2bbin___6 [Arg_0-Arg_2-1 ]
n_evalDis2bb2in___3 [Arg_0-Arg_2-1 ]
MPRF for transition 5:n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb1in___4(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_1 of depth 1:
new bound:
Arg_0+Arg_1+1 {O(n)}
MPRF:
n_evalDis2bb3in___2 [Arg_0+1-Arg_2 ]
n_evalDis2bb3in___7 [Arg_0+1-Arg_2 ]
n_evalDis2bb1in___4 [Arg_0-Arg_2 ]
n_evalDis2bbin___6 [Arg_0+1-Arg_2 ]
n_evalDis2bb2in___3 [Arg_0+1-Arg_2 ]
MPRF for transition 6:n_evalDis2bbin___6(Arg_0,Arg_1,Arg_2) -> n_evalDis2bb2in___3(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_2 of depth 1:
new bound:
Arg_1+Arg_2 {O(n)}
MPRF:
n_evalDis2bb3in___2 [Arg_0-Arg_1 ]
n_evalDis2bb3in___7 [Arg_0-Arg_1 ]
n_evalDis2bb1in___4 [Arg_0-Arg_1 ]
n_evalDis2bbin___6 [Arg_0-Arg_1 ]
n_evalDis2bb2in___3 [Arg_0-Arg_1-1 ]
All Bounds
Timebounds
Overall timebound:3*Arg_0+3*Arg_2+6*Arg_1+5 {O(n)}
0: n_evalDis2bb1in___4->n_evalDis2bb3in___7: Arg_0+Arg_1 {O(n)}
1: n_evalDis2bb2in___3->n_evalDis2bb3in___2: Arg_1+Arg_2 {O(n)}
2: n_evalDis2bb3in___2->n_evalDis2bbin___6: Arg_1+Arg_2 {O(n)}
3: n_evalDis2bb3in___7->n_evalDis2bbin___6: Arg_0+Arg_1 {O(n)}
4: n_evalDis2bb3in___7->n_evalDis2returnin___5: 1 {O(1)}
5: n_evalDis2bbin___6->n_evalDis2bb1in___4: Arg_0+Arg_1+1 {O(n)}
6: n_evalDis2bbin___6->n_evalDis2bb2in___3: Arg_1+Arg_2 {O(n)}
7: n_evalDis2entryin___8->n_evalDis2bb3in___7: 1 {O(1)}
8: n_evalDis2returnin___5->n_evalDis2stop___1: 1 {O(1)}
9: n_evalDis2start->n_evalDis2entryin___8: 1 {O(1)}
Costbounds
Overall costbound: 3*Arg_0+3*Arg_2+6*Arg_1+5 {O(n)}
0: n_evalDis2bb1in___4->n_evalDis2bb3in___7: Arg_0+Arg_1 {O(n)}
1: n_evalDis2bb2in___3->n_evalDis2bb3in___2: Arg_1+Arg_2 {O(n)}
2: n_evalDis2bb3in___2->n_evalDis2bbin___6: Arg_1+Arg_2 {O(n)}
3: n_evalDis2bb3in___7->n_evalDis2bbin___6: Arg_0+Arg_1 {O(n)}
4: n_evalDis2bb3in___7->n_evalDis2returnin___5: 1 {O(1)}
5: n_evalDis2bbin___6->n_evalDis2bb1in___4: Arg_0+Arg_1+1 {O(n)}
6: n_evalDis2bbin___6->n_evalDis2bb2in___3: Arg_1+Arg_2 {O(n)}
7: n_evalDis2entryin___8->n_evalDis2bb3in___7: 1 {O(1)}
8: n_evalDis2returnin___5->n_evalDis2stop___1: 1 {O(1)}
9: n_evalDis2start->n_evalDis2entryin___8: 1 {O(1)}
Sizebounds
0: n_evalDis2bb1in___4->n_evalDis2bb3in___7, Arg_0: Arg_1 {O(n)}
0: n_evalDis2bb1in___4->n_evalDis2bb3in___7, Arg_1: 2*Arg_2+Arg_1 {O(n)}
0: n_evalDis2bb1in___4->n_evalDis2bb3in___7, Arg_2: 2*Arg_0+Arg_1 {O(n)}
1: n_evalDis2bb2in___3->n_evalDis2bb3in___2, Arg_0: Arg_1 {O(n)}
1: n_evalDis2bb2in___3->n_evalDis2bb3in___2, Arg_1: 2*Arg_2+Arg_1 {O(n)}
1: n_evalDis2bb2in___3->n_evalDis2bb3in___2, Arg_2: 2*Arg_0+Arg_1 {O(n)}
2: n_evalDis2bb3in___2->n_evalDis2bbin___6, Arg_0: Arg_1 {O(n)}
2: n_evalDis2bb3in___2->n_evalDis2bbin___6, Arg_1: 2*Arg_2+Arg_1 {O(n)}
2: n_evalDis2bb3in___2->n_evalDis2bbin___6, Arg_2: 2*Arg_0+Arg_1 {O(n)}
3: n_evalDis2bb3in___7->n_evalDis2bbin___6, Arg_0: Arg_1 {O(n)}
3: n_evalDis2bb3in___7->n_evalDis2bbin___6, Arg_1: 2*Arg_2+Arg_1 {O(n)}
3: n_evalDis2bb3in___7->n_evalDis2bbin___6, Arg_2: 2*Arg_0+Arg_1 {O(n)}
4: n_evalDis2bb3in___7->n_evalDis2returnin___5, Arg_0: 2*Arg_1 {O(n)}
4: n_evalDis2bb3in___7->n_evalDis2returnin___5, Arg_1: 3*Arg_2+Arg_1 {O(n)}
4: n_evalDis2bb3in___7->n_evalDis2returnin___5, Arg_2: 3*Arg_0+Arg_1 {O(n)}
5: n_evalDis2bbin___6->n_evalDis2bb1in___4, Arg_0: Arg_1 {O(n)}
5: n_evalDis2bbin___6->n_evalDis2bb1in___4, Arg_1: 2*Arg_2+Arg_1 {O(n)}
5: n_evalDis2bbin___6->n_evalDis2bb1in___4, Arg_2: 2*Arg_0+Arg_1 {O(n)}
6: n_evalDis2bbin___6->n_evalDis2bb2in___3, Arg_0: Arg_1 {O(n)}
6: n_evalDis2bbin___6->n_evalDis2bb2in___3, Arg_1: 2*Arg_2+Arg_1 {O(n)}
6: n_evalDis2bbin___6->n_evalDis2bb2in___3, Arg_2: 2*Arg_0+Arg_1 {O(n)}
7: n_evalDis2entryin___8->n_evalDis2bb3in___7, Arg_0: Arg_1 {O(n)}
7: n_evalDis2entryin___8->n_evalDis2bb3in___7, Arg_1: Arg_2 {O(n)}
7: n_evalDis2entryin___8->n_evalDis2bb3in___7, Arg_2: Arg_0 {O(n)}
8: n_evalDis2returnin___5->n_evalDis2stop___1, Arg_0: 2*Arg_1 {O(n)}
8: n_evalDis2returnin___5->n_evalDis2stop___1, Arg_1: 3*Arg_2+Arg_1 {O(n)}
8: n_evalDis2returnin___5->n_evalDis2stop___1, Arg_2: 3*Arg_0+Arg_1 {O(n)}
9: n_evalDis2start->n_evalDis2entryin___8, Arg_0: Arg_0 {O(n)}
9: n_evalDis2start->n_evalDis2entryin___8, Arg_1: Arg_1 {O(n)}
9: n_evalDis2start->n_evalDis2entryin___8, Arg_2: Arg_2 {O(n)}