Initial Problem
Start: l0
Program_Vars: X₀
Temp_Vars: B, C, D, E, F
Locations: l0, l1
Transitions:
t₄: l0(X₀) → l1(X₀)
t₀: l1(X₀) → l1(0) :|: 0 ≤ 2⋅B ∧ 2⋅B ≤ 0 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₁: l1(X₀) → l1(2⋅B) :|: 0 ≤ 2⋅B ∧ 0 ≤ 2+2⋅B ∧ X₀ ≤ 1+2⋅B ∧ 1+2⋅B ≤ X₀
t₂: l1(X₀) → l1(B) :|: 2⋅C ≤ 1 ∧ 0 ≤ 2⋅C ∧ 1 ≤ 2⋅D ∧ 2⋅D ≤ 1 ∧ 2⋅E ≤ 1 ∧ 2 ≤ 3⋅E ∧ E ≤ B ∧ 2⋅F ≤ 1 ∧ 2 ≤ 3⋅F ∧ B ≤ F ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₃: l1(X₀) → l1(B) :|: 1 ≤ 2⋅D ∧ 0 ≤ 1+2⋅D ∧ 2⋅C ≤ 2⋅D ∧ 2⋅D ≤ 1+2⋅C ∧ 2⋅E ≤ 2⋅D ∧ 2⋅D+1 ≤ 3⋅E ∧ E ≤ B ∧ 2⋅F ≤ 2⋅D ∧ 2⋅D+1 ≤ 3⋅F ∧ B ≤ F ∧ X₀ ≤ 2⋅D ∧ 2⋅D ≤ X₀
Preprocessing
Cut unsatisfiable transition t₂: l1→l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀
Temp_Vars: B, C, D, E, F
Locations: l0, l1
Transitions:
t₄: l0(X₀) → l1(X₀)
t₀: l1(X₀) → l1(0) :|: 0 ≤ 2⋅B ∧ 2⋅B ≤ 0 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₁: l1(X₀) → l1(2⋅B) :|: 0 ≤ 2⋅B ∧ 0 ≤ 2+2⋅B ∧ X₀ ≤ 1+2⋅B ∧ 1+2⋅B ≤ X₀
t₃: l1(X₀) → l1(B) :|: 1 ≤ 2⋅D ∧ 0 ≤ 1+2⋅D ∧ 2⋅C ≤ 2⋅D ∧ 2⋅D ≤ 1+2⋅C ∧ 2⋅E ≤ 2⋅D ∧ 2⋅D+1 ≤ 3⋅E ∧ E ≤ B ∧ 2⋅F ≤ 2⋅D ∧ 2⋅D+1 ≤ 3⋅F ∧ B ≤ F ∧ X₀ ≤ 2⋅D ∧ 2⋅D ≤ X₀
MPRF for transition t₀: l1(X₀) → l1(0) :|: 0 ≤ 2⋅B ∧ 2⋅B ≤ 0 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:
new bound:
4⋅X₀ {O(n)}
MPRF:
l1 [4⋅X₀ ]
MPRF for transition t₁: l1(X₀) → l1(2⋅B) :|: 0 ≤ 2⋅B ∧ 0 ≤ 2+2⋅B ∧ X₀ ≤ 1+2⋅B ∧ 1+2⋅B ≤ X₀ of depth 1:
new bound:
2⋅X₀ {O(n)}
MPRF:
l1 [2⋅X₀ ]
MPRF for transition t₃: l1(X₀) → l1(B) :|: 1 ≤ 2⋅D ∧ 0 ≤ 1+2⋅D ∧ 2⋅C ≤ 2⋅D ∧ 2⋅D ≤ 1+2⋅C ∧ 2⋅E ≤ 2⋅D ∧ 2⋅D+1 ≤ 3⋅E ∧ E ≤ B ∧ 2⋅F ≤ 2⋅D ∧ 2⋅D+1 ≤ 3⋅F ∧ B ≤ F ∧ X₀ ≤ 2⋅D ∧ 2⋅D ≤ X₀ of depth 1:
new bound:
2⋅X₀ {O(n)}
MPRF:
l1 [2⋅X₀ ]
All Bounds
Timebounds
Overall timebound:8⋅X₀+1 {O(n)}
t₄: 1 {O(1)}
t₀: 4⋅X₀ {O(n)}
t₁: 2⋅X₀ {O(n)}
t₃: 2⋅X₀ {O(n)}
Costbounds
Overall costbound: 8⋅X₀+1 {O(n)}
t₄: 1 {O(1)}
t₀: 4⋅X₀ {O(n)}
t₁: 2⋅X₀ {O(n)}
t₃: 2⋅X₀ {O(n)}
Sizebounds
t₄, X₀: X₀ {O(n)}
t₀, X₀: 0 {O(1)}
t₁, X₀: 2⋅X₀ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}