Initial Problem

Start: eval0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval0, eval1
Transitions:
t₀: eval0(X₀, X₁, X₂) → eval1(X₀, X₁, X₂) :|: 1 ≤ X₀
t₁: eval1(X₀, X₁, X₂) → eval1(X₀, X₀+X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂
t₂: eval1(X₀, X₁, X₂) → eval1(X₀, X₁, X₁-X₀) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂

Preprocessing

Found invariant 1 ≤ X₀ for location eval1

Problem after Preprocessing

Start: eval0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval0, eval1
Transitions:
t₀: eval0(X₀, X₁, X₂) → eval1(X₀, X₁, X₂) :|: 1 ≤ X₀
t₁: eval1(X₀, X₁, X₂) → eval1(X₀, X₀+X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂
t₂: eval1(X₀, X₁, X₂) → eval1(X₀, X₁, X₁-X₀) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂

MPRF for transition t₁: eval1(X₀, X₁, X₂) → eval1(X₀, X₀+X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂ of depth 1:

new bound:

X₀+X₁ {O(n)}

• eval1: [X₀-X₁]

MPRF for transition t₂: eval1(X₀, X₁, X₂) → eval1(X₀, X₁, X₁-X₀) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂ of depth 1:

new bound:

X₀+X₂ {O(n)}

• eval1: [X₂-X₀]

All Bounds

Timebounds

Overall timebound:2⋅X₀+X₁+X₂+1 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+X₁ {O(n)}
t₂: X₀+X₂ {O(n)}

Costbounds

Overall costbound: 2⋅X₀+X₁+X₂+1 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+X₁ {O(n)}
t₂: X₀+X₂ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2⋅X₀⋅X₀+2⋅X₀⋅X₁+2⋅X₀+X₁ {O(n^2)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2⋅X₀⋅X₀+2⋅X₀⋅X₁+2⋅X₀+2⋅X₁ {O(n^2)}
t₂, X₂: 2⋅X₀⋅X₀+2⋅X₀⋅X₁+2⋅X₁+4⋅X₀ {O(n^2)}