Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
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) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₁, X₃, X₄) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, 2, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, (X₁)², X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₂
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂-1, X₃, X₄)
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)

Preprocessing

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

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l6

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l7

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₃ ∧ 0 ≤ X₁ for location l1

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

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁
t₁₉: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁
t₂₀: l2(X₀, X₁, X₂, X₃) → l1(X₃, 2, X₂, X₃)
t₂₁: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, (X₁)², X₂, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₂: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₃: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₄: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂-1, X₃) :|: X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₅: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0

MPRF for transition t₁₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃ {O(n)}

MPRF for transition t₂₁: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, Temp_Int₁₅₂, X₂, X₃) :|: 0 ≤ Temp_Int₁₅₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

Chain transitions t₂₄: l5→l4 and t₂₃: l4→l6 to t₅₇: l5→l6

Chain transitions t₁₉: l1→l4 and t₂₃: l4→l6 to t₅₈: l1→l6

Chain transitions t₁₉: l1→l4 and t₂₂: l4→l5 to t₅₉: l1→l5

Chain transitions t₂₄: l5→l4 and t₂₂: l4→l5 to t₆₀: l5→l5

Analysing control-flow refined program

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l6

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l7

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₃ ∧ 0 ≤ X₁ for location l1

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

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 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 X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l5___1

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l6

Found invariant X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___2

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l7

Found invariant X₀ ≤ X₃ ∧ 0 ≤ X₁ for location l1

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

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l5___3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: X₃ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₃ {O(n)}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: inf {Infinity}
t₂₅: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: X₃ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₃ {O(n)}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: inf {Infinity}
t₂₅: 1 {O(1)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: X₃ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₀: 2⋅X₃ {O(n)}
t₁₉, X₃: 2⋅X₃ {O(n)}
t₂₀, X₀: X₃ {O(n)}
t₂₀, X₁: 2 {O(1)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₁, X₀: X₃ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₂, X₀: 2⋅X₃ {O(n)}
t₂₂, X₃: 2⋅X₃ {O(n)}
t₂₃, X₀: 4⋅X₃ {O(n)}
t₂₃, X₂: 0 {O(1)}
t₂₃, X₃: 4⋅X₃ {O(n)}
t₂₄, X₀: 2⋅X₃ {O(n)}
t₂₄, X₃: 2⋅X₃ {O(n)}
t₂₅, X₀: 4⋅X₃ {O(n)}
t₂₅, X₂: 0 {O(1)}
t₂₅, X₃: 4⋅X₃ {O(n)}