Initial Problem

Start: start
Program_Vars: X₀, X₁
Temp_Vars: C, D, E
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁) → eval(D, X₁) :|: D ≤ 1+E ∧ 1+X₀+X₁ ≤ 3⋅C ∧ 1+C ≤ D ∧ 1+X₀+X₁ ≤ 3⋅E ∧ 1+X₀ ≤ X₁ ∧ 2⋅C ≤ X₀+X₁ ∧ 2⋅E ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁
t₁: eval(X₀, X₁) → eval(X₀, D) :|: 1+X₀+X₁ ≤ 3⋅C ∧ 1+X₀+X₁ ≤ 3⋅E ∧ 1+X₀ ≤ X₁ ∧ C ≤ D ∧ 2⋅C ≤ X₀+X₁ ∧ D ≤ E ∧ 2⋅E ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁
t₂: start(X₀, X₁) → eval(X₀, X₁)

Preprocessing

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁
Temp_Vars: C, D, E
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁) → eval(D, X₁) :|: D ≤ 1+E ∧ 1+X₀+X₁ ≤ 3⋅C ∧ 1+C ≤ D ∧ 1+X₀+X₁ ≤ 3⋅E ∧ 1+X₀ ≤ X₁ ∧ 2⋅C ≤ X₀+X₁ ∧ 2⋅E ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁
t₁: eval(X₀, X₁) → eval(X₀, D) :|: 1+X₀+X₁ ≤ 3⋅C ∧ 1+X₀+X₁ ≤ 3⋅E ∧ 1+X₀ ≤ X₁ ∧ C ≤ D ∧ 2⋅C ≤ X₀+X₁ ∧ D ≤ E ∧ 2⋅E ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁
t₂: start(X₀, X₁) → eval(X₀, X₁)

MPRF for transition t₁: eval(X₀, X₁) → eval(X₀, D) :|: 1+X₀+X₁ ≤ 3⋅C ∧ 1+X₀+X₁ ≤ 3⋅E ∧ 1+X₀ ≤ X₁ ∧ C ≤ D ∧ 2⋅C ≤ X₀+X₁ ∧ D ≤ E ∧ 2⋅E ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

• eval: [1+2⋅X₁]

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_v1

Found invariant 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_v2

Found invariant 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location eval_v3

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

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