Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁) → l2(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀, 2⋅X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁+1 ≤ X₀
t₂: l1(X₀, X₁) → l2(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₀: l2(X₀, X₁) → l1(X₀, 1) :|: 0 ≤ X₀

Preprocessing

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁) → l2(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀, 2⋅X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁+1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂: l1(X₀, X₁) → l2(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₀: l2(X₀, X₁) → l1(X₀, 1) :|: 0 ≤ X₀

Analysing control-flow refined program

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___4

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___2

Found invariant X₁ ≤ 1 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l2___3

Found invariant X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___5

Found invariant X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₉₁: n_l2___3(X₀, X₁) → n_l1___1(X₀, 1) :|: X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ 1 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 1+X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₈₅: n_l1___1(X₀, X₁) → n_l2___3(X₀-1, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₃: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
t₀: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₃: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
t₀: inf {Infinity}

Sizebounds

t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₁, X₀: X₀+1 {O(n)}
t₂, X₀: X₀+1 {O(n)}
t₀, X₀: X₀+1 {O(n)}
t₀, X₁: 1 {O(1)}