Initial Problem
Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
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,Arg_3,Arg_4) -> n_eval___1(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4+1):|:Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_3
1:n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4+1):|:Arg_0<=Arg_1 && Arg_3<=Arg_2 && Arg_0<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_0<=Arg_1
2:n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___1(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4+1):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_3
3:n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4+1):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
4:n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___4(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4+1):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
5:n_eval___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4+1):|:1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_2 && Arg_0<=Arg_1
6:n_eval___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4+1):|:1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
7:n_eval___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___4(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4+1):|:1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
8:n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___1(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4+1):|:1+Arg_1<=Arg_0 && Arg_2<=Arg_3
9:n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4+1):|:1+Arg_3<=Arg_2 && Arg_0<=Arg_1
10:n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4+1):|:1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
11:n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___4(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4+1):|:1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
12:n_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
Preprocessing
Eliminate variables {Arg_4} that do not contribute to the problem
Found invariant Arg_2<=Arg_3 && Arg_1<=Arg_0 for location n_eval___1
Found invariant Arg_3<=Arg_2 && Arg_0<=Arg_1 for location n_eval___2
Found invariant Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 for location n_eval___3
Found invariant 1+Arg_3<=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, Arg_3
Temp_Vars:
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_eval___5, n_start
Transitions:
26:n_eval___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___1(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_3
27:n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_3<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_3<=Arg_2 && Arg_0<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_0<=Arg_1
28:n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___1(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_3
29:n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
30:n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___4(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
31:n_eval___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3+1):|:1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_2 && Arg_0<=Arg_1
32:n_eval___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3+1):|:1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
33:n_eval___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___4(Arg_0,Arg_1+1,Arg_2,Arg_3):|:1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
34:n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___1(Arg_0,Arg_1+1,Arg_2,Arg_3):|:1+Arg_1<=Arg_0 && Arg_2<=Arg_3
35:n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3+1):|:1+Arg_3<=Arg_2 && Arg_0<=Arg_1
36:n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3+1):|:1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
37:n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___4(Arg_0,Arg_1+1,Arg_2,Arg_3):|:1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2
38:n_start(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___5(Arg_0,Arg_1,Arg_2,Arg_3)
MPRF for transition 29:n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 of depth 1:
new bound:
2*Arg_2+2*Arg_3+2 {O(n)}
MPRF:
n_eval___3 [Arg_2+1-Arg_3 ]
n_eval___4 [Arg_2-Arg_3 ]
MPRF for transition 30:n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___4(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 of depth 1:
new bound:
2*Arg_2+2*Arg_3+2 {O(n)}
MPRF:
n_eval___3 [Arg_2+1-Arg_3 ]
n_eval___4 [Arg_2-Arg_3 ]
MPRF for transition 32:n_eval___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___3(Arg_0,Arg_1,Arg_2,Arg_3+1):|:1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 of depth 1:
new bound:
2*Arg_0+2*Arg_1+2 {O(n)}
MPRF:
n_eval___3 [Arg_0-Arg_1 ]
n_eval___4 [Arg_0+1-Arg_1 ]
MPRF for transition 33:n_eval___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___4(Arg_0,Arg_1+1,Arg_2,Arg_3):|:1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_3<=Arg_2 of depth 1:
new bound:
2*Arg_0+2*Arg_1+2 {O(n)}
MPRF:
n_eval___3 [Arg_0-Arg_1 ]
n_eval___4 [Arg_0+1-Arg_1 ]
MPRF for transition 27:n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___2(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_3<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_3<=Arg_2 && Arg_0<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_0<=Arg_1 of depth 1:
new bound:
14*Arg_2+14*Arg_3+4*Arg_0+4*Arg_1+18 {O(n)}
MPRF:
n_eval___2 [Arg_2+1-Arg_3 ]
MPRF for transition 26:n_eval___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval___1(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_3 of depth 1:
new bound:
14*Arg_0+14*Arg_1+4*Arg_2+4*Arg_3+18 {O(n)}
MPRF:
n_eval___1 [Arg_0+1-Arg_1 ]
All Bounds
Timebounds
Overall timebound:22*Arg_0+22*Arg_1+22*Arg_2+22*Arg_3+51 {O(n)}
26: n_eval___1->n_eval___1: 14*Arg_0+14*Arg_1+4*Arg_2+4*Arg_3+18 {O(n)}
27: n_eval___2->n_eval___2: 14*Arg_2+14*Arg_3+4*Arg_0+4*Arg_1+18 {O(n)}
28: n_eval___3->n_eval___1: 1 {O(1)}
29: n_eval___3->n_eval___3: 2*Arg_2+2*Arg_3+2 {O(n)}
30: n_eval___3->n_eval___4: 2*Arg_2+2*Arg_3+2 {O(n)}
31: n_eval___4->n_eval___2: 1 {O(1)}
32: n_eval___4->n_eval___3: 2*Arg_0+2*Arg_1+2 {O(n)}
33: n_eval___4->n_eval___4: 2*Arg_0+2*Arg_1+2 {O(n)}
34: n_eval___5->n_eval___1: 1 {O(1)}
35: n_eval___5->n_eval___2: 1 {O(1)}
36: n_eval___5->n_eval___3: 1 {O(1)}
37: n_eval___5->n_eval___4: 1 {O(1)}
38: n_start->n_eval___5: 1 {O(1)}
Costbounds
Overall costbound: 22*Arg_0+22*Arg_1+22*Arg_2+22*Arg_3+51 {O(n)}
26: n_eval___1->n_eval___1: 14*Arg_0+14*Arg_1+4*Arg_2+4*Arg_3+18 {O(n)}
27: n_eval___2->n_eval___2: 14*Arg_2+14*Arg_3+4*Arg_0+4*Arg_1+18 {O(n)}
28: n_eval___3->n_eval___1: 1 {O(1)}
29: n_eval___3->n_eval___3: 2*Arg_2+2*Arg_3+2 {O(n)}
30: n_eval___3->n_eval___4: 2*Arg_2+2*Arg_3+2 {O(n)}
31: n_eval___4->n_eval___2: 1 {O(1)}
32: n_eval___4->n_eval___3: 2*Arg_0+2*Arg_1+2 {O(n)}
33: n_eval___4->n_eval___4: 2*Arg_0+2*Arg_1+2 {O(n)}
34: n_eval___5->n_eval___1: 1 {O(1)}
35: n_eval___5->n_eval___2: 1 {O(1)}
36: n_eval___5->n_eval___3: 1 {O(1)}
37: n_eval___5->n_eval___4: 1 {O(1)}
38: n_start->n_eval___5: 1 {O(1)}
Sizebounds
26: n_eval___1->n_eval___1, Arg_0: 10*Arg_0 {O(n)}
26: n_eval___1->n_eval___1, Arg_1: 18*Arg_0+28*Arg_1+8*Arg_2+8*Arg_3+34 {O(n)}
26: n_eval___1->n_eval___1, Arg_2: 10*Arg_2 {O(n)}
26: n_eval___1->n_eval___1, Arg_3: 14*Arg_3+4*Arg_0+4*Arg_1+4*Arg_2+13 {O(n)}
27: n_eval___2->n_eval___2, Arg_0: 10*Arg_0 {O(n)}
27: n_eval___2->n_eval___2, Arg_1: 14*Arg_1+4*Arg_0+4*Arg_2+4*Arg_3+13 {O(n)}
27: n_eval___2->n_eval___2, Arg_2: 10*Arg_2 {O(n)}
27: n_eval___2->n_eval___2, Arg_3: 18*Arg_2+28*Arg_3+8*Arg_0+8*Arg_1+34 {O(n)}
28: n_eval___3->n_eval___1, Arg_0: 9*Arg_0 {O(n)}
28: n_eval___3->n_eval___1, Arg_1: 13*Arg_1+4*Arg_0+4*Arg_2+4*Arg_3+15 {O(n)}
28: n_eval___3->n_eval___1, Arg_2: 9*Arg_2 {O(n)}
28: n_eval___3->n_eval___1, Arg_3: 13*Arg_3+4*Arg_0+4*Arg_1+4*Arg_2+13 {O(n)}
29: n_eval___3->n_eval___3, Arg_0: 4*Arg_0 {O(n)}
29: n_eval___3->n_eval___3, Arg_1: 2*Arg_0+2*Arg_2+2*Arg_3+6*Arg_1+6 {O(n)}
29: n_eval___3->n_eval___3, Arg_2: 4*Arg_2 {O(n)}
29: n_eval___3->n_eval___3, Arg_3: 2*Arg_0+2*Arg_1+2*Arg_2+6*Arg_3+6 {O(n)}
30: n_eval___3->n_eval___4, Arg_0: 4*Arg_0 {O(n)}
30: n_eval___3->n_eval___4, Arg_1: 2*Arg_0+2*Arg_2+2*Arg_3+6*Arg_1+6 {O(n)}
30: n_eval___3->n_eval___4, Arg_2: 4*Arg_2 {O(n)}
30: n_eval___3->n_eval___4, Arg_3: 2*Arg_0+2*Arg_1+2*Arg_2+6*Arg_3+6 {O(n)}
31: n_eval___4->n_eval___2, Arg_0: 9*Arg_0 {O(n)}
31: n_eval___4->n_eval___2, Arg_1: 13*Arg_1+4*Arg_0+4*Arg_2+4*Arg_3+13 {O(n)}
31: n_eval___4->n_eval___2, Arg_2: 9*Arg_2 {O(n)}
31: n_eval___4->n_eval___2, Arg_3: 13*Arg_3+4*Arg_0+4*Arg_1+4*Arg_2+15 {O(n)}
32: n_eval___4->n_eval___3, Arg_0: 4*Arg_0 {O(n)}
32: n_eval___4->n_eval___3, Arg_1: 2*Arg_0+2*Arg_2+2*Arg_3+6*Arg_1+6 {O(n)}
32: n_eval___4->n_eval___3, Arg_2: 4*Arg_2 {O(n)}
32: n_eval___4->n_eval___3, Arg_3: 2*Arg_0+2*Arg_1+2*Arg_2+6*Arg_3+6 {O(n)}
33: n_eval___4->n_eval___4, Arg_0: 4*Arg_0 {O(n)}
33: n_eval___4->n_eval___4, Arg_1: 2*Arg_0+2*Arg_2+2*Arg_3+6*Arg_1+6 {O(n)}
33: n_eval___4->n_eval___4, Arg_2: 4*Arg_2 {O(n)}
33: n_eval___4->n_eval___4, Arg_3: 2*Arg_0+2*Arg_1+2*Arg_2+6*Arg_3+6 {O(n)}
34: n_eval___5->n_eval___1, Arg_0: Arg_0 {O(n)}
34: n_eval___5->n_eval___1, Arg_1: Arg_1+1 {O(n)}
34: n_eval___5->n_eval___1, Arg_2: Arg_2 {O(n)}
34: n_eval___5->n_eval___1, Arg_3: Arg_3 {O(n)}
35: n_eval___5->n_eval___2, Arg_0: Arg_0 {O(n)}
35: n_eval___5->n_eval___2, Arg_1: Arg_1 {O(n)}
35: n_eval___5->n_eval___2, Arg_2: Arg_2 {O(n)}
35: n_eval___5->n_eval___2, Arg_3: Arg_3+1 {O(n)}
36: n_eval___5->n_eval___3, Arg_0: Arg_0 {O(n)}
36: n_eval___5->n_eval___3, Arg_1: Arg_1 {O(n)}
36: n_eval___5->n_eval___3, Arg_2: Arg_2 {O(n)}
36: n_eval___5->n_eval___3, Arg_3: Arg_3+1 {O(n)}
37: n_eval___5->n_eval___4, Arg_0: Arg_0 {O(n)}
37: n_eval___5->n_eval___4, Arg_1: Arg_1+1 {O(n)}
37: n_eval___5->n_eval___4, Arg_2: Arg_2 {O(n)}
37: n_eval___5->n_eval___4, Arg_3: Arg_3 {O(n)}
38: n_start->n_eval___5, Arg_0: Arg_0 {O(n)}
38: n_start->n_eval___5, Arg_1: Arg_1 {O(n)}
38: n_start->n_eval___5, Arg_2: Arg_2 {O(n)}
38: n_start->n_eval___5, Arg_3: Arg_3 {O(n)}