Initial Problem

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

Preprocessing

Problem after Preprocessing

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

Solv. Size Bound: t₁: l1→l1 for X₀

cycle: [t₁: l1→l1; t₂: l1→l1]
loop: (1 ≤ X₀ ∧ 1 ≤ X₁ ∨ 1 ≤ X₀ ∧ X₁+1 ≤ 0,(X₀,X₁) -> (X₀+X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₁: l1→l1 and X₀: inf {Infinity}

MPRF for transition t₂: l1(X₀, X₁) → l1(X₀+X₁, X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ 0 of depth 1:

new bound:

X₀ {O(n)}

Solv. Size Bound - Lifting for t₁: l1→l1 and X₀: inf {Infinity}

Analysing control-flow refined program

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___2

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

MPRF for transition t₅₇: n_l1___1(X₀, X₁) → n_l1___1(X₀+X₁, X₁) :|: 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

Solv. Size Bound: t₅₈: n_l1___2→n_l1___2 for X₀

cycle: [t₅₈: n_l1___2→n_l1___2]
loop: (1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁,(X₀,X₁) -> (X₀+X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₅₈: n_l1___2→n_l1___2 and X₀: inf {Infinity}

Solv. Size Bound - Lifting for t₅₈: n_l1___2→n_l1___2 and X₀: inf {Infinity}

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: inf {Infinity}
t₂: X₀ {O(n)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: X₀ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: 2⋅X₁+X₀ {O(n)}
t₂, X₁: X₁ {O(n)}