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) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(0, 100, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Eliminate variables {X₂,X₃} that do not contribute to the problem

Found invariant 1 ≤ 0 for location l5

Found invariant X₁ ≤ 100+X₀ ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant X₁ ≤ 100+X₀ ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3

Cut unsatisfiable transition t₁₃: l1→l4

Cut unsatisfiable transition t₁₆: l4→l5

Cut unreachable locations [l4; l5] from the program graph

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₁: l0(X₀, X₁) → l2(X₀, X₁)
t₁₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < X₁ ∧ X₁ ≤ 100+X₀ ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₄: l2(X₀, X₁) → l1(0, 100)
t₁₅: l3(X₀, X₁) → l1(X₀+1, X₁+1) :|: X₁ ≤ 100+X₀ ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ 0 ≤ X₀

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

Chain transitions t₁₄: l2→l1 and t₁₂: l1→l3 to t₃₉: l2→l3

Analysing control-flow refined program

Found invariant X₁ ≤ 100+X₀ ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 100+X₀ ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ 0 ≤ 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 X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___3

Found invariant X₁ ≤ 100+X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 100+X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___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}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}

Costbounds

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

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₄, X₀: 0 {O(1)}
t₁₄, X₁: 100 {O(1)}