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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₁
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

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

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

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

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ for location l3

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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁

MPRF for transition t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃ {O(n)}

Chain transitions t₅: l3→l1 and t₄: l1→l4 to t₄₉: l3→l4

Chain transitions t₁: l2→l1 and t₄: l1→l4 to t₅₀: l2→l4

Chain transitions t₁: l2→l1 and t₃: l1→l3 to t₅₁: l2→l3

Chain transitions t₅: l3→l1 and t₃: l1→l3 to t₅₂: l3→l3

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₅₃: l2→l3

Chain transitions t₅: l3→l1 and t₂: l1→l3 to t₅₄: l3→l3

Analysing control-flow refined program

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

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

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

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ for location l3

MPRF for transition t₅₂: l3(X₀, X₁, X₂, X₃) -{2}> l3(X₀-1, 1+X₁, X₂, X₃) :|: 2+X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ X₀ ≤ 1+X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ of depth 1:

new bound:

2⋅X₂+2⋅X₃ {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₁₅₄: n_l1___5→l4

Found invariant 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 3+X₀ ≤ X₁ for location n_l3___4

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6

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

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

Found invariant 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 3+X₀ ≤ X₁ for location n_l1___5

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

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

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

Found invariant 3+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___1

Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l3___7

MPRF for transition t₁₃₈: n_l1___3(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF for transition t₁₄₃: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁+1, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ X₁ < X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 3+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₂+X₃+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}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: X₂+X₃ {O(n)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: X₂+X₃ {O(n)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: 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, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₃ {O(n)}