Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 7 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 7
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₀+1, X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables {X₄} that do not contribute to the problem

Found invariant X₀ ≤ 6 for location l5

Found invariant X₀ ≤ 6 for location l4

Found invariant 7 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₁: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 7 ≤ X₀
t₁₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 7
t₁₄: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₁₅: l3(X₀, X₁, X₂, X₃) → l1(X₁, X₀+1, X₂, X₃) :|: 7 ≤ X₀
t₁₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 6

Chain transitions t₁₅: l3→l1 and t₁₃: l1→l4 to t₃₅: l3→l4

Chain transitions t₁₄: l2→l1 and t₁₃: l1→l4 to t₃₆: l2→l4

Chain transitions t₁₄: l2→l1 and t₁₂: l1→l3 to t₃₇: l2→l3

Chain transitions t₁₅: l3→l1 and t₁₂: l1→l3 to t₃₈: l3→l3

Analysing control-flow refined program

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 6 for location l5

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 6 for location l4

Found invariant 7 ≤ X₂ ∧ 14 ≤ X₀+X₂ ∧ 7 ≤ 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

Cut unsatisfiable transition t₈₈: n_l1___1→l4

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 7 ≤ X₂ ∧ 14 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 7 ≤ X₀ for location n_l3___4

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 7 ≤ X₂ ∧ 15 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 8 ≤ X₁ for location n_l1___3

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 6 for location l5

Found invariant 7 ≤ X₃ ∧ 14 ≤ X₂+X₃ ∧ 15 ≤ X₁+X₃ ∧ 14 ≤ X₀+X₃ ∧ 7 ≤ X₂ ∧ 15 ≤ X₁+X₂ ∧ 14 ≤ X₀+X₂ ∧ 8 ≤ X₁ ∧ 15 ≤ X₀+X₁ ∧ 7 ≤ X₀ for location n_l3___2

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 6 for location l4

Found invariant 7 ≤ X₃ ∧ 14 ≤ X₂+X₃ ∧ 15 ≤ X₁+X₃ ∧ 15 ≤ X₀+X₃ ∧ 7 ≤ X₂ ∧ 15 ≤ X₁+X₂ ∧ 15 ≤ X₀+X₂ ∧ 8 ≤ X₁ ∧ 16 ≤ X₀+X₁ ∧ 8 ≤ X₀ for location n_l1___1

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₃, X₃: 2⋅X₃ {O(n)}
t₁₄, X₀: X₂ {O(n)}
t₁₄, X₁: X₃ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}