Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: X₂+X₃ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₂+X₃
t₅: l4(X₀, X₁, X₂, X₃) → l1(2⋅X₀+X₁, X₁-1, X₂, X₃)
Preprocessing
Found invariant X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 for location l1
Found invariant X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ 1 ≤ X₀ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: X₂+X₃ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₂+X₃
t₅: l4(X₀, X₁, X₂, X₃) → l1(2⋅X₀+X₁, X₁-1, X₂, X₃) :|: X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ 1 ≤ X₀
Chain transitions t₅: l4→l1 and t₃: l1→l4 to t₄₂: l4→l4
Chain transitions t₁: l3→l1 and t₃: l1→l4 to t₄₃: l3→l4
Chain transitions t₁: l3→l1 and t₄: l1→l2 to t₄₄: l3→l2
Chain transitions t₅: l4→l1 and t₄: l1→l2 to t₄₅: l4→l2
Analysing control-flow refined program
Found invariant X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 for location l1
Found invariant 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 2+X₁+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ for location l4
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 2+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l4___3
Found invariant 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 3+X₁+X₃ ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ 1+X₁+X₂ ≤ 0 ∧ 1 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ for location n_l1___2
Found invariant 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 3+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁+X₂ ≤ 0 ∧ 1 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l4___1
Found invariant X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0 for location l1
TWN: t₉₁: n_l1___2→n_l4___1
cycle: [t₉₁: n_l1___2→n_l4___1; t₉₃: n_l4___1→n_l1___2]
loop: (1+X₁ ≤ X₃ ∧ 3+X₁ ≤ X₀ ∧ 0 < X₀ ∧ 3+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 0 < X₀,(X₀,X₁,X₃) -> (2⋅X₀+X₁,X₁-1,X₃)
order: [X₁; X₀; X₃]
closed-form:
X₁: X₁ + [[n != 0]] * -1 * n^1
X₀: X₀ * 2^n + [[n != 0]] * X₁ * 2^n + [[n != 0]] * -X₁ + [[n != 0, n != 1]] * -1 * 2^n + [[n != 0, n != 1]] * n^1 + [[n != 0, n != 1]]
X₃: X₃
Termination: true
Formula:
0 < 1 ∧ 1 < X₀+X₁
∨ 1 < X₀+X₁ ∧ 0 < 1 ∧ 0 < 2 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 < X₀+X₁ ∧ 0 < 1 ∧ 2+2⋅X₁ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0
∨ 1 < X₀+X₁ ∧ 0 < 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0 ∧ 2+2⋅X₁ ≤ 0 ∧ 0 ≤ 2+2⋅X₁
∨ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < X₀+X₁
∨ 1 < X₀+X₁ ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 2 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 < X₀+X₁ ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2+2⋅X₁ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0
∨ 1 < X₀+X₁ ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0 ∧ 2+2⋅X₁ ≤ 0 ∧ 0 ≤ 2+2⋅X₁
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 < X₀+X₁
∨ 1 < X₀+X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 0 < 2 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 < X₀+X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 2+2⋅X₁ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0
∨ 1 < X₀+X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0 ∧ 2+2⋅X₁ ≤ 0 ∧ 0 ≤ 2+2⋅X₁
∨ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < 1 ∧ 1 < X₀+X₁
∨ 0 < 1 ∧ 0 < 2 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 0 < 1 ∧ 2+2⋅X₁ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0
∨ 0 < 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0 ∧ 2+2⋅X₁ ≤ 0 ∧ 0 ≤ 2+2⋅X₁
∨ 0 < 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < X₀+X₁
∨ 0 < 1 ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 2 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 0 < 1 ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2+2⋅X₁ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0
∨ 0 < 1 ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0 ∧ 2+2⋅X₁ ≤ 0 ∧ 0 ≤ 2+2⋅X₁
∨ 0 < 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 < X₀+X₁
∨ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 0 < 2 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 2+2⋅X₁ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0
∨ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0 ∧ 2+2⋅X₁ ≤ 0 ∧ 0 ≤ 2+2⋅X₁
∨ X₁ < 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1 < X₀+X₁
∨ X₁ < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 < 2 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ X₁ < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 2+2⋅X₁ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0
∨ X₁ < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0 ∧ 2+2⋅X₁ ≤ 0 ∧ 0 ≤ 2+2⋅X₁
∨ X₁ < 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < X₀+X₁
∨ X₁ < 1 ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 2 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ X₁ < 1 ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2+2⋅X₁ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0
∨ X₁ < 1 ∧ 1+X₁ < X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0 ∧ 2+2⋅X₁ ≤ 0 ∧ 0 ≤ 2+2⋅X₁
∨ X₁ < 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 < X₀+X₁
∨ X₁ < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 0 < 2 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ X₁ < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 2+2⋅X₁ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0
∨ X₁ < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ 2 ∧ 2 ≤ 0 ∧ 2+2⋅X₁ ≤ 0 ∧ 0 ≤ 2+2⋅X₁
Stabilization-Threshold for: 0 < X₀
alphas_abs: 1+X₁
M: 5
N: 2
Bound: 2⋅X₁+8 {O(n)}
Stabilization-Threshold for: 1+X₁ ≤ X₃
alphas_abs: 1+X₁+X₃
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₃+4 {O(n)}
Stabilization-Threshold for: 3+X₁ ≤ X₀
alphas_abs: 2+2⋅X₁
M: 5
N: 2
Bound: 4⋅X₁+10 {O(n)}
TWN - Lifting for t₉₁: n_l1___2→n_l4___1 of 2⋅X₃+8⋅X₁+24 {O(n)}
relevant size-bounds w.r.t. t₉₄:
X₁: X₃+1 {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₉₄: 1 {O(1)}
Results in: 10⋅X₃+32 {O(n)}
TWN: t₉₃: n_l4___1→n_l1___2
TWN - Lifting for t₉₃: n_l4___1→n_l1___2 of 2⋅X₃+8⋅X₁+24 {O(n)}
relevant size-bounds w.r.t. t₉₄:
X₁: X₃+1 {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₉₄: 1 {O(1)}
Results in: 10⋅X₃+32 {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
Infinite
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l5, n_l1___2, n_l4___1, n_l4___3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0
t₉₂: l1(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ 0 < X₀ ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: X₂+X₃ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₂+X₃
t₉₈: n_l1___2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 3+X₁+X₃ ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ 1+X₁+X₂ ≤ 0 ∧ 1 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀
t₉₁: n_l1___2(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ 3+X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 3+X₁+X₃ ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ 1+X₁+X₂ ≤ 0 ∧ 1 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀
t₉₃: n_l4___1(X₀, X₁, X₂, X₃) → n_l1___2(2⋅X₀+X₁, X₁-1, X₂, X₃) :|: 3+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 0 < X₀ ∧ X₂+X₃ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 3+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁+X₂ ≤ 0 ∧ 1 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1 ≤ X₀
t₉₄: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___2(2⋅X₀+X₁, X₁-1, X₂, X₃) :|: X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 2+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ X₀
CFR: Improvement to new bound with the following program:
new bound:
20⋅X₃+64 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l5, n_l1___2, n_l4___1, n_l4___3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0
t₉₂: l1(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ 0 < X₀ ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: X₂+X₃ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₂+X₃
t₉₈: n_l1___2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 3+X₁+X₃ ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ 1+X₁+X₂ ≤ 0 ∧ 1 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀
t₉₁: n_l1___2(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ 3+X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 3+X₁+X₃ ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ 1+X₁+X₂ ≤ 0 ∧ 1 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀
t₉₃: n_l4___1(X₀, X₁, X₂, X₃) → n_l1___2(2⋅X₀+X₁, X₁-1, X₂, X₃) :|: 3+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 0 < X₀ ∧ X₂+X₃ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 3+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁+X₂ ≤ 0 ∧ 1 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1 ≤ X₀
t₉₄: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___2(2⋅X₀+X₁, X₁-1, X₂, X₃) :|: X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 2+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:20⋅X₃+72 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₉₁: 10⋅X₃+32 {O(n)}
t₉₂: 1 {O(1)}
t₉₃: 10⋅X₃+32 {O(n)}
t₉₄: 1 {O(1)}
t₉₈: 1 {O(1)}
Costbounds
Overall costbound: 20⋅X₃+72 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₉₁: 10⋅X₃+32 {O(n)}
t₉₂: 1 {O(1)}
t₉₃: 10⋅X₃+32 {O(n)}
t₉₄: 1 {O(1)}
t₉₈: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₆, X₀: 1089⋅2^(10⋅X₃+32)+110⋅2^(10⋅X₃+32)⋅X₃⋅X₃+2^(10⋅X₃+32)⋅694⋅X₃+X₀+X₂+X₃ {O(EXP)}
t₆, X₁: 13⋅X₃+X₁+34 {O(n)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₉₁, X₀: 1089⋅2^(10⋅X₃+32)+110⋅2^(10⋅X₃+32)⋅X₃⋅X₃+2^(10⋅X₃+32)⋅694⋅X₃ {O(EXP)}
t₉₁, X₁: 11⋅X₃+33 {O(n)}
t₉₁, X₂: X₂ {O(n)}
t₉₁, X₃: X₃ {O(n)}
t₉₂, X₀: X₂ {O(n)}
t₉₂, X₁: X₃ {O(n)}
t₉₂, X₂: X₂ {O(n)}
t₉₂, X₃: X₃ {O(n)}
t₉₃, X₀: 1089⋅2^(10⋅X₃+32)+110⋅2^(10⋅X₃+32)⋅X₃⋅X₃+2^(10⋅X₃+32)⋅694⋅X₃ {O(EXP)}
t₉₃, X₁: 11⋅X₃+33 {O(n)}
t₉₃, X₂: X₂ {O(n)}
t₉₃, X₃: X₃ {O(n)}
t₉₄, X₀: X₃ {O(n)}
t₉₄, X₁: X₃+1 {O(n)}
t₉₄, X₂: X₂ {O(n)}
t₉₄, X₃: X₃ {O(n)}
t₉₈, X₀: 1089⋅2^(10⋅X₃+32)+110⋅2^(10⋅X₃+32)⋅X₃⋅X₃+2^(10⋅X₃+32)⋅694⋅X₃+X₃ {O(EXP)}
t₉₈, X₁: 12⋅X₃+34 {O(n)}
t₉₈, X₂: 2⋅X₂ {O(n)}
t₉₈, X₃: 2⋅X₃ {O(n)}