Initial Problem

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

Preprocessing

Problem after Preprocessing

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

MPRF for transition t₀: eval(X₀, X₁) → eval(X₀-1, C) :|: 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

• eval: [1+X₀]

Found invariant 0 ≤ 1+X₁ for location eval_v1

Found invariant 0 ≤ 1+X₀ for location eval_v2

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ for location eval_v3

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₀, X₀: X₀+1 {O(n)}
t₁, X₀: X₀+1 {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}