Initial Problem

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

Preprocessing

Eliminate variables {D,X₁} that do not contribute to the problem

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀, X₂) → l1(X₀, X₂)
t₉: l1(X₀, X₂) → l1(X₀+X₂, X₂-1) :|: 1 ≤ X₀
t₈: l1(X₀, X₂) → l2(X₀, X₂) :|: X₀ ≤ 0

MPRF for transition t₉: l1(X₀, X₂) → l1(X₀+X₂, X₂-1) :|: 1 ≤ X₀ of depth 2:

new bound:

8⋅X₀+8⋅X₂+9 {O(n)}

MPRF:

l1 [X₂+1 ; X₀ ]

All Bounds

Timebounds

Overall timebound:8⋅X₀+8⋅X₂+11 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 8⋅X₀+8⋅X₂+9 {O(n)}

Costbounds

Overall costbound: 8⋅X₀+8⋅X₂+11 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 8⋅X₀+8⋅X₂+9 {O(n)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₇, X₂: X₂ {O(n)}
t₈, X₀: 144⋅X₀⋅X₂+64⋅X₀⋅X₀+80⋅X₂⋅X₂+154⋅X₀+172⋅X₂+90 {O(n^2)}
t₈, X₂: 10⋅X₂+8⋅X₀+9 {O(n)}
t₉, X₀: 144⋅X₀⋅X₂+64⋅X₀⋅X₀+80⋅X₂⋅X₂+153⋅X₀+172⋅X₂+90 {O(n^2)}
t₉, X₂: 8⋅X₀+9⋅X₂+9 {O(n)}