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) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ 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) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁

MPRF for transition t₀: l1(X₀, X₁) → l1(X₀-1, C) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

Analysing control-flow refined program

Found invariant 0 ≤ X₀ for location n_l1___2

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

MPRF for transition t₃₂: n_l1___1(X₀, X₁) → n_l1___2(X₀-1, NoDet0) :|: 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+1 ]

MPRF for transition t₃₃: n_l1___2(X₀, X₁) → n_l1___1(X₀, X₁-1) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

n_l1___1 [X₀ ]
n_l1___2 [X₀+1 ]

MPRF for transition t₃₄: n_l1___2(X₀, X₁) → n_l1___2(X₀-1, NoDet0) :|: 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

n_l1___1 [X₀ ]
n_l1___2 [X₀+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂: 1 {O(1)}
t₀: X₀ {O(n)}
t₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₂: 1 {O(1)}
t₀: X₀ {O(n)}
t₁: inf {Infinity}

Sizebounds

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