Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₄
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(1, X₆, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(-1, X₆, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 1
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁+X₀, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁-X₀, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 1
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Eliminate variables {X₃,X₅} that do not contribute to the problem

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 for location l5

Found invariant X₀ ≤ 1 for location l1

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 for location l4

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ 1 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₅: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₁₆: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ X₀ ≤ 1
t₁₇: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁ ∧ X₀ ≤ 1
t₁₈: l2(X₀, X₁, X₂, X₃, X₄) → l1(1, X₄, X₂, X₃, X₄) :|: 1 ≤ X₂
t₁₉: l2(X₀, X₁, X₂, X₃, X₄) → l1(-1, X₄, X₂, X₃, X₄) :|: X₂ < 1
t₂₀: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁+X₀, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1
t₂₁: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁-X₀, X₂, X₃, X₄) :|: X₂ < 1 ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1
t₂₂: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ X₀ ≤ 1

Chain transitions t₂₁: l3→l1 and t₁₇: l1→l4 to t₆₃: l3→l4

Chain transitions t₂₀: l3→l1 and t₁₇: l1→l4 to t₆₄: l3→l4

Chain transitions t₂₀: l3→l1 and t₁₆: l1→l3 to t₆₅: l3→l3

Chain transitions t₂₁: l3→l1 and t₁₆: l1→l3 to t₆₆: l3→l3

Chain transitions t₁₉: l2→l1 and t₁₆: l1→l3 to t₆₇: l2→l3

Chain transitions t₁₉: l2→l1 and t₁₇: l1→l4 to t₆₈: l2→l4

Chain transitions t₁₈: l2→l1 and t₁₆: l1→l3 to t₆₉: l2→l3

Chain transitions t₁₈: l2→l1 and t₁₇: l1→l4 to t₇₀: l2→l4

Analysing control-flow refined program

Found invariant X₄ ≤ 1+X₁ ∧ 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l5

Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l1

Found invariant X₄ ≤ 1+X₁ ∧ X₃ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l4

Found invariant X₄ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___4

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___3

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 for location l5

Found invariant 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___2

Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l1

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l4

Found invariant X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location n_l3___1

MPRF for transition t₁₇₇: n_l1___3(X₀, X₁, X₂, X₃, X₄) → n_l3___2(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀+X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃+X₄+2 {O(n)}

MPRF for transition t₁₈₁: n_l3___2(X₀, X₁, X₂, X₃, X₄) → n_l1___3(X₀, X₀+X₁, X₂, X₃, X₄) :|: X₁ ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₀ ≤ 1 ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃+X₄+2 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: 1 {O(1)}

Sizebounds

t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₆, X₀: 2 {O(1)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₇, X₀: 6 {O(1)}
t₁₇, X₂: 6⋅X₂ {O(n)}
t₁₇, X₃: 6⋅X₃ {O(n)}
t₁₇, X₄: 6⋅X₄ {O(n)}
t₁₈, X₀: 1 {O(1)}
t₁₈, X₁: X₄ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₉, X₀: 1 {O(1)}
t₁₉, X₁: X₄ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₂₀, X₀: 2 {O(1)}
t₂₀, X₂: 2⋅X₂ {O(n)}
t₂₀, X₃: 2⋅X₃ {O(n)}
t₂₀, X₄: 2⋅X₄ {O(n)}
t₂₁, X₀: 2 {O(1)}
t₂₁, X₂: 2⋅X₂ {O(n)}
t₂₁, X₃: 2⋅X₃ {O(n)}
t₂₁, X₄: 2⋅X₄ {O(n)}
t₂₂, X₀: 6 {O(1)}
t₂₂, X₂: 6⋅X₂ {O(n)}
t₂₂, X₃: 6⋅X₃ {O(n)}
t₂₂, X₄: 6⋅X₄ {O(n)}