Initial Problem

Start: start
Program_Vars: X₀
Temp_Vars: B, C, D, E, F
Locations: eval, start
Transitions:
t₀: eval(X₀) → eval(0) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ B ∧ B ≤ 0
t₁: eval(X₀) → eval(2⋅B) :|: X₀ ≤ 1+2⋅B ∧ 0 ≤ 1+B ∧ 1+2⋅B ≤ X₀ ∧ 0 ≤ B
t₂: eval(X₀) → eval(B) :|: 2⋅C ≤ 1 ∧ 2⋅D ≤ 1 ∧ 2⋅E ≤ 1 ∧ 2⋅F ≤ 1 ∧ X₀ ≤ 1 ∧ 1 ≤ 2⋅D ∧ 1 ≤ X₀ ∧ 2 ≤ 3⋅E ∧ 2 ≤ 3⋅F ∧ E ≤ B ∧ B ≤ F ∧ 0 ≤ C
t₃: eval(X₀) → eval(B) :|: 2⋅D ≤ 1+2⋅C ∧ 0 ≤ 1+2⋅D ∧ 1 ≤ 2⋅D ∧ 1+2⋅D ≤ 3⋅E ∧ 1+2⋅D ≤ 3⋅F ∧ E ≤ B ∧ B ≤ F ∧ C ≤ D ∧ X₀ ≤ 2⋅D ∧ E ≤ D ∧ F ≤ D ∧ 2⋅D ≤ X₀
t₄: start(X₀) → eval(X₀)

Preprocessing

Cut unsatisfiable transition [t₂: eval→eval]

Problem after Preprocessing

Start: start
Program_Vars: X₀
Temp_Vars: B, C, D, E, F
Locations: eval, start
Transitions:
t₀: eval(X₀) → eval(0) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ B ∧ B ≤ 0
t₁: eval(X₀) → eval(2⋅B) :|: X₀ ≤ 1+2⋅B ∧ 0 ≤ 1+B ∧ 1+2⋅B ≤ X₀ ∧ 0 ≤ B
t₃: eval(X₀) → eval(B) :|: 2⋅D ≤ 1+2⋅C ∧ 0 ≤ 1+2⋅D ∧ 1 ≤ 2⋅D ∧ 1+2⋅D ≤ 3⋅E ∧ 1+2⋅D ≤ 3⋅F ∧ E ≤ B ∧ B ≤ F ∧ C ≤ D ∧ X₀ ≤ 2⋅D ∧ E ≤ D ∧ F ≤ D ∧ 2⋅D ≤ X₀
t₄: start(X₀) → eval(X₀)

MPRF for transition t₀: eval(X₀) → eval(0) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ B ∧ B ≤ 0 of depth 1:

new bound:

4⋅X₀ {O(n)}

• eval: [4⋅X₀]

MPRF for transition t₁: eval(X₀) → eval(2⋅B) :|: X₀ ≤ 1+2⋅B ∧ 0 ≤ 1+B ∧ 1+2⋅B ≤ X₀ ∧ 0 ≤ B of depth 1:

new bound:

4⋅X₀ {O(n)}

• eval: [4⋅X₀]

MPRF for transition t₃: eval(X₀) → eval(B) :|: 2⋅D ≤ 1+2⋅C ∧ 0 ≤ 1+2⋅D ∧ 1 ≤ 2⋅D ∧ 1+2⋅D ≤ 3⋅E ∧ 1+2⋅D ≤ 3⋅F ∧ E ≤ B ∧ B ≤ F ∧ C ≤ D ∧ X₀ ≤ 2⋅D ∧ E ≤ D ∧ F ≤ D ∧ 2⋅D ≤ X₀ of depth 1:

new bound:

2⋅X₀+3 {O(n)}

• eval: [3+2⋅X₀]

All Bounds

Timebounds

Overall timebound:10⋅X₀+4 {O(n)}
t₀: 4⋅X₀ {O(n)}
t₁: 4⋅X₀ {O(n)}
t₃: 2⋅X₀+3 {O(n)}
t₄: 1 {O(1)}

Costbounds

Overall costbound: 10⋅X₀+4 {O(n)}
t₀: 4⋅X₀ {O(n)}
t₁: 4⋅X₀ {O(n)}
t₃: 2⋅X₀+3 {O(n)}
t₄: 1 {O(1)}

Sizebounds

t₀, X₀: 0 {O(1)}
t₁, X₀: X₀ {O(n)}
t₃, X₀: X₀ {O(n)}
t₄, X₀: X₀ {O(n)}