Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀+X₁, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₂: l1(X₀, X₁) → l1(X₀+X₁, X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ 0

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀+X₁, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₂: l1(X₀, X₁) → l1(X₀+X₁, X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ 0

Analysing control-flow refined program

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___2

Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ for location n_l1___1

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___2

Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ for location n_l1___1

Time-Bound by TWN-Loops:

TWN-Loops: t₄₆ 4⋅X₀+6⋅X₁+7 {O(n)}

TWN-Loops:

entry: t₄₈: l1(X₀, X₁) → n_l1___1(X₀+X₁, X₁) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ 0
results in twn-loop: twn:Inv: [1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀] , (X₀,X₁) -> (X₀+X₁,X₁) :|: 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ 0
order: [X₁; X₀]
closed-form:
X₁: X₁
X₀: X₀ + [[n != 0]] * X₁ * n^1

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₄₈:
X₀: X₀+X₁ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₄₈: 1 {O(1)}
Results in: 4⋅X₀+6⋅X₁+7 {O(n)}

4⋅X₀+6⋅X₁+7 {O(n)}

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___2

Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: 2⋅X₁+X₀ {O(n)}
t₂, X₁: X₁ {O(n)}