Initial Problem
Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_eval___5, n_start
Transitions:
0:n_eval___1(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
1:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1+1,Arg_2):|:1+Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
2:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1+1,Arg_2):|:1+Arg_1<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
3:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0,Arg_1,Arg_2+1):|:1+Arg_1<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
4:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2+1):|:Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
5:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
6:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0,Arg_1,Arg_2+1):|:1+Arg_1<=Arg_0 && Arg_2<=Arg_1
7:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0,Arg_1+1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
8:n_start(Arg_0,Arg_1,Arg_2) -> n_eval___5(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=Arg_0 for location n_eval___1
Found invariant Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 for location n_eval___2
Found invariant Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 for location n_eval___3
Found invariant Arg_1<=Arg_2 && Arg_1<=Arg_0 for location n_eval___4
Problem after Preprocessing
Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_eval___5, n_start
Transitions:
0:n_eval___1(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
1:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
2:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
3:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
4:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2+1):|:Arg_1<=Arg_2 && Arg_1<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
5:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=Arg_2 && Arg_1<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
6:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0,Arg_1,Arg_2+1):|:1+Arg_1<=Arg_0 && Arg_2<=Arg_1
7:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0,Arg_1+1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
8:n_start(Arg_0,Arg_1,Arg_2) -> n_eval___5(Arg_0,Arg_1,Arg_2)
MPRF for transition 5:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=Arg_2 && Arg_1<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 of depth 1:
new bound:
Arg_1+Arg_2+2 {O(n)}
MPRF:
n_eval___4 [Arg_2+1-Arg_1 ]
MPRF for transition 3:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 of depth 1:
new bound:
Arg_1+Arg_2+2 {O(n)}
MPRF:
n_eval___3 [Arg_1+1-Arg_2 ]
MPRF for transition 0:n_eval___1(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 of depth 1:
new bound:
4*Arg_0+4*Arg_1+4*Arg_2+9 {O(n)}
MPRF:
n_eval___2 [Arg_0-Arg_1 ]
n_eval___1 [Arg_0+1-Arg_2 ]
MPRF for transition 1:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 of depth 1:
new bound:
4*Arg_0+5*Arg_1+Arg_2+8 {O(n)}
MPRF:
n_eval___2 [Arg_0+1-Arg_1 ]
n_eval___1 [Arg_0+1-Arg_1 ]
All Bounds
Timebounds
Overall timebound:11*Arg_1+7*Arg_2+8*Arg_0+26 {O(n)}
0: n_eval___1->n_eval___2: 4*Arg_0+4*Arg_1+4*Arg_2+9 {O(n)}
1: n_eval___2->n_eval___1: 4*Arg_0+5*Arg_1+Arg_2+8 {O(n)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___3: Arg_1+Arg_2+2 {O(n)}
4: n_eval___4->n_eval___2: 1 {O(1)}
5: n_eval___4->n_eval___4: Arg_1+Arg_2+2 {O(n)}
6: n_eval___5->n_eval___3: 1 {O(1)}
7: n_eval___5->n_eval___4: 1 {O(1)}
8: n_start->n_eval___5: 1 {O(1)}
Costbounds
Overall costbound: 11*Arg_1+7*Arg_2+8*Arg_0+26 {O(n)}
0: n_eval___1->n_eval___2: 4*Arg_0+4*Arg_1+4*Arg_2+9 {O(n)}
1: n_eval___2->n_eval___1: 4*Arg_0+5*Arg_1+Arg_2+8 {O(n)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___3: Arg_1+Arg_2+2 {O(n)}
4: n_eval___4->n_eval___2: 1 {O(1)}
5: n_eval___4->n_eval___4: Arg_1+Arg_2+2 {O(n)}
6: n_eval___5->n_eval___3: 1 {O(1)}
7: n_eval___5->n_eval___4: 1 {O(1)}
8: n_start->n_eval___5: 1 {O(1)}
Sizebounds
0: n_eval___1->n_eval___2, Arg_0: 4*Arg_0 {O(n)}
0: n_eval___1->n_eval___2, Arg_1: 10*Arg_1+2*Arg_2+4*Arg_0+14 {O(n)}
0: n_eval___1->n_eval___2, Arg_2: 4*Arg_0+5*Arg_1+9*Arg_2+15 {O(n)}
1: n_eval___2->n_eval___1, Arg_0: 4*Arg_0 {O(n)}
1: n_eval___2->n_eval___1, Arg_1: 10*Arg_1+2*Arg_2+4*Arg_0+14 {O(n)}
1: n_eval___2->n_eval___1, Arg_2: 4*Arg_0+5*Arg_1+9*Arg_2+15 {O(n)}
2: n_eval___3->n_eval___1, Arg_0: 2*Arg_0 {O(n)}
2: n_eval___3->n_eval___1, Arg_1: 2*Arg_1+2 {O(n)}
2: n_eval___3->n_eval___1, Arg_2: 3*Arg_2+Arg_1+4 {O(n)}
3: n_eval___3->n_eval___3, Arg_0: Arg_0 {O(n)}
3: n_eval___3->n_eval___3, Arg_1: Arg_1 {O(n)}
3: n_eval___3->n_eval___3, Arg_2: 2*Arg_2+Arg_1+3 {O(n)}
4: n_eval___4->n_eval___2, Arg_0: 2*Arg_0 {O(n)}
4: n_eval___4->n_eval___2, Arg_1: 3*Arg_1+Arg_2+4 {O(n)}
4: n_eval___4->n_eval___2, Arg_2: 2*Arg_2+2 {O(n)}
5: n_eval___4->n_eval___4, Arg_0: Arg_0 {O(n)}
5: n_eval___4->n_eval___4, Arg_1: 2*Arg_1+Arg_2+3 {O(n)}
5: n_eval___4->n_eval___4, Arg_2: Arg_2 {O(n)}
6: n_eval___5->n_eval___3, Arg_0: Arg_0 {O(n)}
6: n_eval___5->n_eval___3, Arg_1: Arg_1 {O(n)}
6: n_eval___5->n_eval___3, Arg_2: Arg_2+1 {O(n)}
7: n_eval___5->n_eval___4, Arg_0: Arg_0 {O(n)}
7: n_eval___5->n_eval___4, Arg_1: Arg_1+1 {O(n)}
7: n_eval___5->n_eval___4, Arg_2: Arg_2 {O(n)}
8: n_start->n_eval___5, Arg_0: Arg_0 {O(n)}
8: n_start->n_eval___5, Arg_1: Arg_1 {O(n)}
8: n_start->n_eval___5, Arg_2: Arg_2 {O(n)}