Initial Problem

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

Preprocessing

Problem after Preprocessing

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

Analysing control-flow refined program

Found invariant 0 ≤ 1+X₁ for location n_l1___2

Found invariant 0 ≤ 1+X₀ for location n_l1___3

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ for location n_l1___1

Found invariant 0 ≤ 1+X₁ for location n_l1___2

Found invariant 0 ≤ 1+X₀ for location n_l1___3

Found invariant 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ for location n_l1___1

Time-Bound by TWN-Loops:

TWN-Loops: t₅₂ 4⋅X₁+12 {O(n)}

TWN-Loops:

entry: t₅₆: l1(X₀, X₁) → n_l1___2(X₀, X₁-1) :|: 0 ≤ X₁
results in twn-loop: twn:Inv: [0 ≤ 1+X₁] , (X₀,X₁) -> (X₀,X₁-1) :|: 0 ≤ 1+X₁ ∧ 0 ≤ X₁
order: [X₁]
closed-form:
X₁: X₁ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

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

Stabilization-Threshold for: 0 ≤ X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 0 ≤ 1+X₁
alphas_abs: 1+X₁
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₅₆:
X₁: X₁+1 {O(n)}
Runtime-bound of t₅₆: 1 {O(1)}
Results in: 4⋅X₁+12 {O(n)}

4⋅X₁+12 {O(n)}

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₀, X₀: 2⋅X₀+1 {O(n)}
t₁, X₀: 2⋅X₀+1 {O(n)}