Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(0, X₁)
t₁: l1(X₀, X₁) → l1(C+1, X₁) :|: X₀ ≤ 5 ∧ 5 ≤ X₀
t₂: l1(X₀, X₁) → l1(X₀+1, X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 4
t₃: l1(X₀, X₁) → l1(X₀+1, X₀) :|: X₀ ≤ 9 ∧ 6 ≤ X₀
t₄: l1(X₀, X₁) → l2(X₀, X₁) :|: 10 ≤ X₀

Preprocessing

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

Found invariant 10 ≤ X₀ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₁₅: l0(X₀) → l1(0)
t₁₆: l1(X₀) → l1(C+1) :|: X₀ ≤ 5 ∧ 5 ≤ X₀
t₁₇: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 9 ∧ X₀ ≤ 4
t₁₈: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 9 ∧ 6 ≤ X₀
t₁₉: l1(X₀) → l2(X₀) :|: 10 ≤ X₀

Analysing control-flow refined program

Cut unsatisfiable transition t₁₉: l1→l2

Cut unsatisfiable transition t₁₄₅: n_l1___3→l2

Cut unsatisfiable transition t₁₄₆: n_l1___4→l2

Found invariant 10 ≤ X₀ for location l2

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___4

Found invariant X₀ ≤ 5 for location n_l1___3

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

Found invariant X₀ ≤ 10 ∧ 7 ≤ X₀ for location n_l1___1

MPRF for transition t₁₂₃: n_l1___1(X₀) → n_l1___1(X₀+1) :|: 6 ≤ X₀ ∧ 7 ≤ X₀ ∧ X₀ ≤ 10 ∧ 6 ≤ X₀ ∧ X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 7 ≤ X₀ of depth 1:

new bound:

21 {O(1)}

MPRF:

n_l1___1 [11-X₀ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}

Sizebounds

t₁₅, X₀: 0 {O(1)}
t₁₈, X₀: 10 {O(1)}