Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₄: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₁+1 ≤ X₀
t₁: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₀+1 ≤ X₁ ∧ X₁+1 ≤ X₀
t₂: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₁+1 ≤ X₀ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀+1 ≤ X₁ ∧ X₀ ≤ X₁

Preprocessing

Cut unsatisfiable transition t₁: l1→l1

Cut unsatisfiable transition t₂: l1→l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₄: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₁+1 ≤ X₀
t₃: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀+1 ≤ X₁ ∧ X₀ ≤ X₁

Time-Bound by TWN-Loops:

TWN-Loops: t₀ 2⋅X₀+2⋅X₁+4 {O(n)}

TWN-Loops:

entry: t₄: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₁+1) :|: X₁+1 ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₄:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₄: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+4 {O(n)}

2⋅X₀+2⋅X₁+4 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₃ 4⋅X₀+4⋅X₁+6 {O(n)}

TWN-Loops:

entry: t₄: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀+1,X₁) :|: X₀+1 ≤ X₁ ∧ X₀ ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < X₁ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₄:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₄: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+6 {O(n)}

4⋅X₀+4⋅X₁+6 {O(n)}

All Bounds

Timebounds

Overall timebound:6⋅X₀+6⋅X₁+11 {O(n)}
t₄: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+4 {O(n)}
t₃: 4⋅X₀+4⋅X₁+6 {O(n)}

Costbounds

Overall costbound: 6⋅X₀+6⋅X₁+11 {O(n)}
t₄: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+4 {O(n)}
t₃: 4⋅X₀+4⋅X₁+6 {O(n)}

Sizebounds

t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: 2⋅X₀+3⋅X₁+4 {O(n)}
t₃, X₀: 4⋅X₁+5⋅X₀+6 {O(n)}
t₃, X₁: X₁ {O(n)}