Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁+(X₂)³, X₂+1) :|: 0 < X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂) → l2(X₀, X₁-1, X₂) :|: 0 < X₁

Preprocessing

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁+(X₂)³, X₂+1) :|: 0 < X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂) → l2(X₀, X₁-1, X₂) :|: 0 < X₁ ∧ X₀ ≤ 0

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁+Temp_Int₆₈, X₂+1) :|: 0 < X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

Analysing control-flow refined program

Found invariant X₀ ≤ 0 for location l2

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₂: X₀+X₂ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₂: 2⋅X₂+X₀ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₂: 2⋅X₂+X₀ {O(n)}