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___1(Arg_0,Arg_1,Arg_2-1):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1
1:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2-1):|:Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1
2:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1,Arg_2-1):|:1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1
3:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0
4:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
5:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1,Arg_2-1):|:Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1
6:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
7:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0-1,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 1+Arg_1<=Arg_0
8:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2-1):|:1+Arg_1<=Arg_2 && Arg_0<=Arg_1
9:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
10:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0
11:n_start(Arg_0,Arg_1,Arg_2) -> n_eval___5(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_1 for location n_eval___1
Found invariant Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=Arg_1 for location n_eval___2
Found invariant 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 for location n_eval___3
Found invariant 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___1(Arg_0,Arg_1,Arg_2-1):|:Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1
1:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2-1):|:Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1
2:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1,Arg_2-1):|:1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1
3:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0
4:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
5:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1,Arg_2-1):|:Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1
6:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
7:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0-1,Arg_1,Arg_2):|:Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0
8:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2-1):|:1+Arg_1<=Arg_2 && Arg_0<=Arg_1
9:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2
10:n_eval___5(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0
11:n_start(Arg_0,Arg_1,Arg_2) -> n_eval___5(Arg_0,Arg_1,Arg_2)
MPRF for transition 7:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0-1,Arg_1,Arg_2):|:Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:
new bound:
Arg_0+Arg_1+2 {O(n)}
MPRF:
n_eval___4 [Arg_0+1-Arg_1 ]
MPRF for transition 3:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:
new bound:
4*Arg_0+4*Arg_1+9 {O(n)}
MPRF:
n_eval___3 [Arg_0+1-Arg_1 ]
MPRF for transition 4:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_2 of depth 1:
new bound:
4*Arg_0+4*Arg_1+9 {O(n)}
MPRF:
n_eval___3 [Arg_0+1-Arg_1 ]
MPRF for transition 1:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1,Arg_2-1):|:Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_1+Arg_2+2 {O(n)}
MPRF:
n_eval___2 [Arg_2+1-Arg_1 ]
MPRF for transition 0:n_eval___1(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1,Arg_2-1):|:Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_1 of depth 1:
new bound:
17*Arg_2+22*Arg_1+39*Arg_0+83 {O(n)}
MPRF:
n_eval___1 [Arg_2+1-Arg_0 ]
All Bounds
Timebounds
Overall timebound:18*Arg_2+32*Arg_1+48*Arg_0+112 {O(n)}
0: n_eval___1->n_eval___1: 17*Arg_2+22*Arg_1+39*Arg_0+83 {O(n)}
1: n_eval___2->n_eval___2: Arg_1+Arg_2+2 {O(n)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___3: 4*Arg_0+4*Arg_1+9 {O(n)}
4: n_eval___3->n_eval___3: 4*Arg_0+4*Arg_1+9 {O(n)}
5: n_eval___4->n_eval___1: 1 {O(1)}
6: n_eval___4->n_eval___3: 1 {O(1)}
7: n_eval___4->n_eval___4: Arg_0+Arg_1+2 {O(n)}
8: n_eval___5->n_eval___2: 1 {O(1)}
9: n_eval___5->n_eval___3: 1 {O(1)}
10: n_eval___5->n_eval___4: 1 {O(1)}
11: n_start->n_eval___5: 1 {O(1)}
Costbounds
Overall costbound: 18*Arg_2+32*Arg_1+48*Arg_0+112 {O(n)}
0: n_eval___1->n_eval___1: 17*Arg_2+22*Arg_1+39*Arg_0+83 {O(n)}
1: n_eval___2->n_eval___2: Arg_1+Arg_2+2 {O(n)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___3: 4*Arg_0+4*Arg_1+9 {O(n)}
4: n_eval___3->n_eval___3: 4*Arg_0+4*Arg_1+9 {O(n)}
5: n_eval___4->n_eval___1: 1 {O(1)}
6: n_eval___4->n_eval___3: 1 {O(1)}
7: n_eval___4->n_eval___4: Arg_0+Arg_1+2 {O(n)}
8: n_eval___5->n_eval___2: 1 {O(1)}
9: n_eval___5->n_eval___3: 1 {O(1)}
10: n_eval___5->n_eval___4: 1 {O(1)}
11: n_start->n_eval___5: 1 {O(1)}
Sizebounds
0: n_eval___1->n_eval___1, Arg_0: 22*Arg_1+39*Arg_0+75 {O(n)}
0: n_eval___1->n_eval___1, Arg_1: 17*Arg_1 {O(n)}
0: n_eval___1->n_eval___1, Arg_2: 22*Arg_1+34*Arg_2+39*Arg_0+89 {O(n)}
1: n_eval___2->n_eval___2, Arg_0: Arg_0 {O(n)}
1: n_eval___2->n_eval___2, Arg_1: Arg_1 {O(n)}
1: n_eval___2->n_eval___2, Arg_2: 2*Arg_2+Arg_1+3 {O(n)}
2: n_eval___3->n_eval___1, Arg_0: 21*Arg_1+36*Arg_0+71 {O(n)}
2: n_eval___3->n_eval___1, Arg_1: 15*Arg_1 {O(n)}
2: n_eval___3->n_eval___1, Arg_2: 15*Arg_2+4 {O(n)}
3: n_eval___3->n_eval___3, Arg_0: 10*Arg_1+16*Arg_0+32 {O(n)}
3: n_eval___3->n_eval___3, Arg_1: 6*Arg_1 {O(n)}
3: n_eval___3->n_eval___3, Arg_2: 6*Arg_2 {O(n)}
4: n_eval___3->n_eval___3, Arg_0: 10*Arg_1+16*Arg_0+32 {O(n)}
4: n_eval___3->n_eval___3, Arg_1: 6*Arg_1 {O(n)}
4: n_eval___3->n_eval___3, Arg_2: 6*Arg_2 {O(n)}
5: n_eval___4->n_eval___1, Arg_0: 3*Arg_0+Arg_1+4 {O(n)}
5: n_eval___4->n_eval___1, Arg_1: 2*Arg_1 {O(n)}
5: n_eval___4->n_eval___1, Arg_2: 2*Arg_2+2 {O(n)}
6: n_eval___4->n_eval___3, Arg_0: 3*Arg_0+Arg_1+6 {O(n)}
6: n_eval___4->n_eval___3, Arg_1: 2*Arg_1 {O(n)}
6: n_eval___4->n_eval___3, Arg_2: 2*Arg_2 {O(n)}
7: n_eval___4->n_eval___4, Arg_0: 2*Arg_0+Arg_1+3 {O(n)}
7: n_eval___4->n_eval___4, Arg_1: Arg_1 {O(n)}
7: n_eval___4->n_eval___4, Arg_2: Arg_2 {O(n)}
8: n_eval___5->n_eval___2, Arg_0: Arg_0 {O(n)}
8: n_eval___5->n_eval___2, Arg_1: Arg_1 {O(n)}
8: n_eval___5->n_eval___2, Arg_2: Arg_2+1 {O(n)}
9: n_eval___5->n_eval___3, Arg_0: Arg_0+1 {O(n)}
9: n_eval___5->n_eval___3, Arg_1: Arg_1 {O(n)}
9: n_eval___5->n_eval___3, Arg_2: Arg_2 {O(n)}
10: n_eval___5->n_eval___4, Arg_0: Arg_0+1 {O(n)}
10: n_eval___5->n_eval___4, Arg_1: Arg_1 {O(n)}
10: n_eval___5->n_eval___4, Arg_2: Arg_2 {O(n)}
11: n_start->n_eval___5, Arg_0: Arg_0 {O(n)}
11: n_start->n_eval___5, Arg_1: Arg_1 {O(n)}
11: n_start->n_eval___5, Arg_2: Arg_2 {O(n)}