Initial Problem

Start: f1
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: f0, f1, f2
Transitions:
t₁: f0(X₀, X₁, X₂) → f0(X₀+X₂, X₁, X₂-1) :|: 1 ≤ X₀
t₀: f0(X₀, X₁, X₂) → f2(X₀, D, X₂) :|: X₀ ≤ 0
t₂: f1(X₀, X₁, X₂) → f0(X₀, X₁, X₂)

Preprocessing

Eliminate variables [D; X₁] that do not contribute to the problem

Found invariant X₀ ≤ 0 for location f2

Problem after Preprocessing

Start: f1
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f1, f2
Transitions:
t₅: f0(X₀, X₁) → f0(X₀+X₁, X₁-1) :|: 1 ≤ X₀
t₆: f0(X₀, X₁) → f2(X₀, X₁) :|: X₀ ≤ 0
t₇: f1(X₀, X₁) → f0(X₀, X₁)

MPRF for transition t₅: f0(X₀, X₁) → f0(X₀+X₁, X₁-1) :|: 1 ≤ X₀ of depth 2:

new bound:

8⋅X₀+8⋅X₁+9 {O(n)}

• f0: [1+X₁; X₀]

All Bounds

Timebounds

Overall timebound:8⋅X₀+8⋅X₁+11 {O(n)}
t₅: 8⋅X₀+8⋅X₁+9 {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}

Costbounds

Overall costbound: 8⋅X₀+8⋅X₁+11 {O(n)}
t₅: 8⋅X₀+8⋅X₁+9 {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}

Sizebounds

t₅, X₀: 144⋅X₀⋅X₁+64⋅X₀⋅X₀+80⋅X₁⋅X₁+153⋅X₀+172⋅X₁+90 {O(n^2)}
t₅, X₁: 8⋅X₀+9⋅X₁+9 {O(n)}
t₆, X₀: 144⋅X₀⋅X₁+64⋅X₀⋅X₀+80⋅X₁⋅X₁+154⋅X₀+172⋅X₁+90 {O(n^2)}
t₆, X₁: 10⋅X₁+8⋅X₀+9 {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}