Initial Problem

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: f0, f2
Transitions:
t₁: f0(X₀, X₁) → f2(C, X₁-1) :|: 1 ≤ X₁
t₀: f2(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₀
t₂: f2(X₀, X₁) → f2(C, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0

Preprocessing

Found invariant 0 ≤ X₁ for location f2

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: f0, f2
Transitions:
t₁: f0(X₀, X₁) → f2(C, X₁-1) :|: 1 ≤ X₁
t₀: f2(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₁
t₂: f2(X₀, X₁) → f2(C, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁

MPRF for transition t₂: f2(X₀, X₁) → f2(C, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

• f2: [1+X₁]

Found invariant 0 ≤ X₁ for location f2

Found invariant 0 ≤ X₁ for location f2_v1

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f2_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: inf {Infinity}
t₁: 1 {O(1)}
t₂: X₁+1 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
t₀: inf {Infinity}
t₁: 1 {O(1)}
t₂: X₁+1 {O(n)}

Sizebounds

t₀, X₁: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₁: X₁ {O(n)}