Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_f0, n_f14___1, n_f14___2, n_f14___3, n_f14___6, n_f14___7, n_f14___8, n_f6___4, n_f6___5, n_f6___9
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___9(Arg_1,Arg_1,Arg_3,Arg_3)
1:n_f6___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___1(0,Arg_1,Arg_2,Arg_1):|:0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=Arg_3 && Arg_3<=Arg_1
2:n_f6___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___2(0,Arg_1,Arg_2,Arg_3):|:0<=Arg_0 && 1+Arg_3<=Arg_1 && Arg_0<=0 && 0<=Arg_0
3:n_f6___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___3(0,Arg_1,Arg_2,Arg_3):|:0<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=0 && 0<=Arg_0
4:n_f6___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___4(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:0<=Arg_0 && 1<=Arg_0
5:n_f6___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___5(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:1+Arg_0<=0 && 1+Arg_0<=0 && 2+Arg_0<=0 && 1+Arg_0<=0
6:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___6(0,Arg_1,Arg_2,Arg_1):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=Arg_3 && Arg_3<=Arg_1
7:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___7(0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && Arg_0<=0 && 0<=Arg_0
8:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___8(0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_3 && Arg_0<=0 && 0<=Arg_0
9:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___4(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1<=Arg_0
10:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___5(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1+Arg_0<=0

Preprocessing

Found invariant 1+Arg_3<=Arg_1 && 1+Arg_2<=Arg_3 && 2+Arg_2<=Arg_1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f14___2

Found invariant 1+Arg_2<=Arg_3 && 1+Arg_1<=0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=Arg_1 && 2+Arg_0<=0 for location n_f6___5

Found invariant 1+Arg_2<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location n_f6___4

Found invariant 1+Arg_3<=0 && Arg_3<=Arg_2 && 2+Arg_2+Arg_3<=0 && 1+Arg_3<=Arg_1 && 1+Arg_1+Arg_3<=0 && 1+Arg_3<=Arg_0 && 1+Arg_0+Arg_3<=0 && Arg_2<=Arg_3 && 1+Arg_2<=0 && 1+Arg_2<=Arg_1 && 1+Arg_1+Arg_2<=0 && 1+Arg_2<=Arg_0 && 1+Arg_0+Arg_2<=0 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f14___7

Found invariant Arg_3<=Arg_2 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_0<=Arg_1 for location n_f6___9

Found invariant Arg_3<=Arg_1 && 1<=Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f14___1

Found invariant 2<=Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f14___3

Found invariant Arg_3<=0 && Arg_3<=Arg_2 && Arg_2+Arg_3<=0 && Arg_3<=Arg_1 && Arg_1+Arg_3<=0 && Arg_3<=Arg_0 && Arg_0+Arg_3<=0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f14___6

Found invariant Arg_3<=Arg_2 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f14___8

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_f0, n_f14___1, n_f14___2, n_f14___3, n_f14___6, n_f14___7, n_f14___8, n_f6___4, n_f6___5, n_f6___9
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___9(Arg_1,Arg_1,Arg_3,Arg_3)
1:n_f6___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___1(0,Arg_1,Arg_2,Arg_1):|:1+Arg_2<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=Arg_3 && Arg_3<=Arg_1
2:n_f6___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___2(0,Arg_1,Arg_2,Arg_3):|:1+Arg_2<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_3<=Arg_1 && Arg_0<=0 && 0<=Arg_0
3:n_f6___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___3(0,Arg_1,Arg_2,Arg_3):|:1+Arg_2<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=0 && 0<=Arg_0
4:n_f6___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___4(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:1+Arg_2<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
5:n_f6___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___5(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:1+Arg_2<=Arg_3 && 1+Arg_1<=0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=Arg_1 && 2+Arg_0<=0 && 1+Arg_0<=0 && 1+Arg_0<=0 && 2+Arg_0<=0 && 1+Arg_0<=0
6:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___6(0,Arg_1,Arg_2,Arg_1):|:Arg_3<=Arg_2 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=Arg_3 && Arg_3<=Arg_1
7:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___7(0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && Arg_0<=0 && 0<=Arg_0
8:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f14___8(0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1+Arg_1<=Arg_3 && Arg_0<=0 && 0<=Arg_0
9:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___4(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:Arg_3<=Arg_2 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1<=Arg_0
10:n_f6___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___5(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:Arg_3<=Arg_2 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1+Arg_0<=0

MPRF for transition 4:n_f6___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f6___4(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:1+Arg_2<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f6___4 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_f0->n_f6___9: 1 {O(1)}
1: n_f6___4->n_f14___1: 1 {O(1)}
2: n_f6___4->n_f14___2: 1 {O(1)}
3: n_f6___4->n_f14___3: 1 {O(1)}
4: n_f6___4->n_f6___4: Arg_1+1 {O(n)}
5: n_f6___5->n_f6___5: inf {Infinity}
6: n_f6___9->n_f14___6: 1 {O(1)}
7: n_f6___9->n_f14___7: 1 {O(1)}
8: n_f6___9->n_f14___8: 1 {O(1)}
9: n_f6___9->n_f6___4: 1 {O(1)}
10: n_f6___9->n_f6___5: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: n_f0->n_f6___9: 1 {O(1)}
1: n_f6___4->n_f14___1: 1 {O(1)}
2: n_f6___4->n_f14___2: 1 {O(1)}
3: n_f6___4->n_f14___3: 1 {O(1)}
4: n_f6___4->n_f6___4: Arg_1+1 {O(n)}
5: n_f6___5->n_f6___5: inf {Infinity}
6: n_f6___9->n_f14___6: 1 {O(1)}
7: n_f6___9->n_f14___7: 1 {O(1)}
8: n_f6___9->n_f14___8: 1 {O(1)}
9: n_f6___9->n_f6___4: 1 {O(1)}
10: n_f6___9->n_f6___5: 1 {O(1)}

Sizebounds

0: n_f0->n_f6___9, Arg_0: Arg_1 {O(n)}
0: n_f0->n_f6___9, Arg_1: Arg_1 {O(n)}
0: n_f0->n_f6___9, Arg_2: Arg_3 {O(n)}
0: n_f0->n_f6___9, Arg_3: Arg_3 {O(n)}
1: n_f6___4->n_f14___1, Arg_0: 0 {O(1)}
1: n_f6___4->n_f14___1, Arg_1: 2*Arg_1 {O(n)}
1: n_f6___4->n_f14___1, Arg_2: 2*Arg_3+Arg_1+3 {O(n)}
1: n_f6___4->n_f14___1, Arg_3: 2*Arg_1 {O(n)}
2: n_f6___4->n_f14___2, Arg_0: 0 {O(1)}
2: n_f6___4->n_f14___2, Arg_1: 2*Arg_1 {O(n)}
2: n_f6___4->n_f14___2, Arg_2: 2*Arg_3+Arg_1+3 {O(n)}
2: n_f6___4->n_f14___2, Arg_3: 2*Arg_3 {O(n)}
3: n_f6___4->n_f14___3, Arg_0: 0 {O(1)}
3: n_f6___4->n_f14___3, Arg_1: 2*Arg_1 {O(n)}
3: n_f6___4->n_f14___3, Arg_2: 2*Arg_3+Arg_1+3 {O(n)}
3: n_f6___4->n_f14___3, Arg_3: 2*Arg_3 {O(n)}
4: n_f6___4->n_f6___4, Arg_0: Arg_1 {O(n)}
4: n_f6___4->n_f6___4, Arg_1: Arg_1 {O(n)}
4: n_f6___4->n_f6___4, Arg_2: Arg_1+Arg_3+2 {O(n)}
4: n_f6___4->n_f6___4, Arg_3: Arg_3 {O(n)}
5: n_f6___5->n_f6___5, Arg_1: Arg_1 {O(n)}
5: n_f6___5->n_f6___5, Arg_3: Arg_3 {O(n)}
6: n_f6___9->n_f14___6, Arg_0: 0 {O(1)}
6: n_f6___9->n_f14___6, Arg_1: 0 {O(1)}
6: n_f6___9->n_f14___6, Arg_2: 0 {O(1)}
6: n_f6___9->n_f14___6, Arg_3: 0 {O(1)}
7: n_f6___9->n_f14___7, Arg_0: 0 {O(1)}
7: n_f6___9->n_f14___7, Arg_1: 0 {O(1)}
7: n_f6___9->n_f14___7, Arg_2: Arg_3 {O(n)}
7: n_f6___9->n_f14___7, Arg_3: Arg_3 {O(n)}
8: n_f6___9->n_f14___8, Arg_0: 0 {O(1)}
8: n_f6___9->n_f14___8, Arg_1: 0 {O(1)}
8: n_f6___9->n_f14___8, Arg_2: Arg_3 {O(n)}
8: n_f6___9->n_f14___8, Arg_3: Arg_3 {O(n)}
9: n_f6___9->n_f6___4, Arg_0: Arg_1 {O(n)}
9: n_f6___9->n_f6___4, Arg_1: Arg_1 {O(n)}
9: n_f6___9->n_f6___4, Arg_2: Arg_3+1 {O(n)}
9: n_f6___9->n_f6___4, Arg_3: Arg_3 {O(n)}
10: n_f6___9->n_f6___5, Arg_0: Arg_1+1 {O(n)}
10: n_f6___9->n_f6___5, Arg_1: Arg_1 {O(n)}
10: n_f6___9->n_f6___5, Arg_2: Arg_3+1 {O(n)}
10: n_f6___9->n_f6___5, Arg_3: Arg_3 {O(n)}