Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 100
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 100 ≤ X₀
t₁: l2(X₀, X₁) → l1(0, X₁)
t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ < 50
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 50 ≤ X₀
t₆: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Eliminate variables {X₁} that do not contribute to the problem

Found invariant 100 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant 100 ≤ X₀ for location l4

Found invariant X₀ ≤ 99 ∧ 0 ≤ X₀ for location l3

Cut unsatisfiable transition t₁₆: l1→l4

Cut unreachable locations [l4; l5] from the program graph

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₄: l0(X₀) → l2(X₀)
t₁₅: l1(X₀) → l3(X₀) :|: X₀ < 100 ∧ 0 ≤ X₀
t₁₇: l2(X₀) → l1(0)
t₁₈: l3(X₀) → l1(X₀+1) :|: X₀ < 50 ∧ X₀ ≤ 99 ∧ 0 ≤ X₀
t₁₉: l3(X₀) → l1(X₀-1) :|: 50 ≤ X₀ ∧ X₀ ≤ 99 ∧ 0 ≤ X₀

Analysing control-flow refined program

Found invariant X₀ ≤ 50 ∧ 2 ≤ X₀ for location n_l1___6

Found invariant X₀ ≤ 98 ∧ 49 ≤ X₀ for location n_l1___4

Found invariant X₀ ≤ 98 ∧ 49 ≤ X₀ for location n_l3___3

Found invariant X₀ ≤ 99 ∧ 2 ≤ X₀ for location n_l3___5

Found invariant X₀ ≤ 50 ∧ 50 ≤ X₀ for location n_l1___2

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___8

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___9

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₀ ≤ 50 ∧ 50 ≤ X₀ for location n_l3___1

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___7

MPRF for transition t₅₅: n_l1___6(X₀) → n_l3___5(X₀) :|: 0 ≤ X₀ ∧ X₀ < 100 ∧ X₀ ≤ 99 ∧ 0 ≤ X₀ ∧ X₀ ≤ 99 ∧ 0 ≤ X₀ ∧ X₀ < 100 ∧ X₀ ≤ 50 ∧ 2 ≤ X₀ of depth 1:

new bound:

53 {O(1)}

MPRF:

n_l3___5 [50-X₀ ]
n_l1___6 [51-X₀ ]

MPRF for transition t₆₁: n_l3___5(X₀) → n_l1___6(X₀+1) :|: X₀ ≤ 99 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ < 50 ∧ X₀ ≤ 99 ∧ 2 ≤ X₀ of depth 1:

new bound:

102 {O(1)}

MPRF:

n_l3___5 [100-X₀ ]
n_l1___6 [100-X₀ ]

MPRF for transition t₅₉: n_l3___3(X₀) → n_l1___4(X₀-1) :|: X₀ ≤ 98 ∧ 49 ≤ X₀ ∧ 50 ≤ X₀ ∧ X₀ ≤ 99 ∧ X₀ ≤ 98 ∧ 49 ≤ X₀ of depth 1:

new bound:

7300 {O(1)}

MPRF:

n_l3___1 [50⋅X₀-2450 ]
n_l1___2 [50⋅X₀-2450 ]
n_l3___3 [50⋅X₀-2400 ]
n_l1___4 [50⋅X₀-2400 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}

Sizebounds

t₁₄, X₀: X₀ {O(n)}
t₁₅, X₀: 99 {O(1)}
t₁₇, X₀: 0 {O(1)}
t₁₈, X₀: 50 {O(1)}
t₁₉, X₀: 98 {O(1)}