Initial Problem
Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval1___3, n_eval1___5, n_eval2___1, n_eval2___2, n_eval2___4, n_start
Transitions:
0:n_eval1___3(Arg_0,Arg_1,Arg_2) -> n_eval2___1(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && Arg_2<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0
1:n_eval1___5(Arg_0,Arg_1,Arg_2) -> n_eval2___4(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_0
2:n_eval2___1(Arg_0,Arg_1,Arg_2) -> n_eval1___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && Arg_2<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
3:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
4:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval2___2(Arg_0,Arg_1,Arg_2-1):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
5:n_eval2___4(Arg_0,Arg_1,Arg_2) -> n_eval1___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
6:n_eval2___4(Arg_0,Arg_1,Arg_2) -> n_eval2___2(Arg_0,Arg_1,Arg_2-1):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
7:n_start(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 for location n_eval2___2
Found invariant Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_1<=Arg_0 for location n_eval1___3
Found invariant 1+Arg_1<=Arg_0 for location n_eval2___4
Found invariant Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 for location n_eval2___1
Problem after Preprocessing
Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval1___3, n_eval1___5, n_eval2___1, n_eval2___2, n_eval2___4, n_start
Transitions:
0:n_eval1___3(Arg_0,Arg_1,Arg_2) -> n_eval2___1(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_1<=Arg_0 && Arg_2<=Arg_1 && Arg_2<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0
1:n_eval1___5(Arg_0,Arg_1,Arg_2) -> n_eval2___4(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_0
2:n_eval2___1(Arg_0,Arg_1,Arg_2) -> n_eval1___3(Arg_0-1,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
3:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___3(Arg_0-1,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
4:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval2___2(Arg_0,Arg_1,Arg_2-1):|:Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
5:n_eval2___4(Arg_0,Arg_1,Arg_2) -> n_eval1___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1
6:n_eval2___4(Arg_0,Arg_1,Arg_2) -> n_eval2___2(Arg_0,Arg_1,Arg_2-1):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
7:n_start(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2)
MPRF for transition 4:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval2___2(Arg_0,Arg_1,Arg_2-1):|:Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_2 && 1+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_eval2___2 [Arg_2+1-Arg_1 ]
MPRF for transition 0:n_eval1___3(Arg_0,Arg_1,Arg_2) -> n_eval2___1(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_1<=Arg_0 && Arg_2<=Arg_1 && Arg_2<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:
new bound:
3*Arg_0+4*Arg_2+Arg_1+9 {O(n)}
MPRF:
n_eval2___1 [Arg_0-Arg_2 ]
n_eval1___3 [Arg_0+1-Arg_2 ]
MPRF for transition 2:n_eval2___1(Arg_0,Arg_1,Arg_2) -> n_eval1___3(Arg_0-1,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 of depth 1:
new bound:
3*Arg_0+4*Arg_2+Arg_1+7 {O(n)}
MPRF:
n_eval2___1 [Arg_0-Arg_2 ]
n_eval1___3 [Arg_0-Arg_2 ]
All Bounds
Timebounds
Overall timebound:3*Arg_1+6*Arg_0+9*Arg_2+23 {O(n)}
0: n_eval1___3->n_eval2___1: 3*Arg_0+4*Arg_2+Arg_1+9 {O(n)}
1: n_eval1___5->n_eval2___4: 1 {O(1)}
2: n_eval2___1->n_eval1___3: 3*Arg_0+4*Arg_2+Arg_1+7 {O(n)}
3: n_eval2___2->n_eval1___3: 1 {O(1)}
4: n_eval2___2->n_eval2___2: Arg_1+Arg_2+2 {O(n)}
5: n_eval2___4->n_eval1___3: 1 {O(1)}
6: n_eval2___4->n_eval2___2: 1 {O(1)}
7: n_start->n_eval1___5: 1 {O(1)}
Costbounds
Overall costbound: 3*Arg_1+6*Arg_0+9*Arg_2+23 {O(n)}
0: n_eval1___3->n_eval2___1: 3*Arg_0+4*Arg_2+Arg_1+9 {O(n)}
1: n_eval1___5->n_eval2___4: 1 {O(1)}
2: n_eval2___1->n_eval1___3: 3*Arg_0+4*Arg_2+Arg_1+7 {O(n)}
3: n_eval2___2->n_eval1___3: 1 {O(1)}
4: n_eval2___2->n_eval2___2: Arg_1+Arg_2+2 {O(n)}
5: n_eval2___4->n_eval1___3: 1 {O(1)}
6: n_eval2___4->n_eval2___2: 1 {O(1)}
7: n_start->n_eval1___5: 1 {O(1)}
Sizebounds
0: n_eval1___3->n_eval2___1, Arg_0: 4*Arg_2+6*Arg_0+Arg_1+10 {O(n)}
0: n_eval1___3->n_eval2___1, Arg_1: 3*Arg_1 {O(n)}
0: n_eval1___3->n_eval2___1, Arg_2: 4*Arg_2+Arg_1+4 {O(n)}
1: n_eval1___5->n_eval2___4, Arg_0: Arg_0 {O(n)}
1: n_eval1___5->n_eval2___4, Arg_1: Arg_1 {O(n)}
1: n_eval1___5->n_eval2___4, Arg_2: Arg_2 {O(n)}
2: n_eval2___1->n_eval1___3, Arg_0: 4*Arg_2+6*Arg_0+Arg_1+10 {O(n)}
2: n_eval2___1->n_eval1___3, Arg_1: 3*Arg_1 {O(n)}
2: n_eval2___1->n_eval1___3, Arg_2: 4*Arg_2+Arg_1+4 {O(n)}
3: n_eval2___2->n_eval1___3, Arg_0: 2*Arg_0+2 {O(n)}
3: n_eval2___2->n_eval1___3, Arg_1: 2*Arg_1 {O(n)}
3: n_eval2___2->n_eval1___3, Arg_2: 3*Arg_2+Arg_1+4 {O(n)}
4: n_eval2___2->n_eval2___2, Arg_0: Arg_0 {O(n)}
4: n_eval2___2->n_eval2___2, Arg_1: Arg_1 {O(n)}
4: n_eval2___2->n_eval2___2, Arg_2: 2*Arg_2+Arg_1+3 {O(n)}
5: n_eval2___4->n_eval1___3, Arg_0: Arg_0+1 {O(n)}
5: n_eval2___4->n_eval1___3, Arg_1: Arg_1 {O(n)}
5: n_eval2___4->n_eval1___3, Arg_2: Arg_2 {O(n)}
6: n_eval2___4->n_eval2___2, Arg_0: Arg_0 {O(n)}
6: n_eval2___4->n_eval2___2, Arg_1: Arg_1 {O(n)}
6: n_eval2___4->n_eval2___2, Arg_2: Arg_2+1 {O(n)}
7: n_start->n_eval1___5, Arg_0: Arg_0 {O(n)}
7: n_start->n_eval1___5, Arg_1: Arg_1 {O(n)}
7: n_start->n_eval1___5, Arg_2: Arg_2 {O(n)}