Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < X₁
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₁₁: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: 0 < X₂ ∧ 0 < X₃
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₃: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₁ < X₀
t₈: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₀ ≤ X₁
t₉: l4(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁-X₀, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ < X₀
t₁₀: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-X₀, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁

Preprocessing

Cut unsatisfiable transition t₈: l4→l1

Cut unsatisfiable transition t₉: l4→l1

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁ for location l1

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁
t₁₁: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: 0 < X₂ ∧ 0 < X₃
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₃: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁
t₁₀: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-X₀, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁

Chain transitions t₁₀: l4→l1 and t₅: l1→l4 to t₁₁₃: l4→l4

Chain transitions t₇: l4→l1 and t₅: l1→l4 to t₁₁₄: l4→l4

Chain transitions t₇: l4→l1 and t₄: l1→l4 to t₁₁₅: l4→l4

Chain transitions t₁₀: l4→l1 and t₄: l1→l4 to t₁₁₆: l4→l4

Chain transitions t₁: l3→l1 and t₄: l1→l4 to t₁₁₇: l3→l4

Chain transitions t₁: l3→l1 and t₅: l1→l4 to t₁₁₈: l3→l4

Chain transitions t₁: l3→l1 and t₆: l1→l2 to t₁₁₉: l3→l2

Chain transitions t₇: l4→l1 and t₆: l1→l2 to t₁₂₀: l4→l2

Chain transitions t₁₀: l4→l1 and t₆: l1→l2 to t₁₂₁: l4→l2

Analysing control-flow refined program

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁ for location l1

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁ for location l4

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ for location n_l4___6

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀+X₁ for location n_l1___4

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ for location n_l4___3

Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___2

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___5

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ for location n_l1___1

MPRF for transition t₂₉₆: n_l1___1(X₀, X₁, X₂, X₃) → n_l4___5(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF for transition t₃₀₄: n_l4___5(X₀, X₁, X₂, X₃) → n_l1___1(X₀-X₁, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {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}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₁, X₂: 5⋅X₂ {O(n)}
t₁₁, X₃: 5⋅X₃ {O(n)}