Initial Problem

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

Preprocessing

Found invariant 0 ≤ X₁ for location l1

Problem after Preprocessing

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

MPRF for transition t₂: l1(X₀, X₁) → l1(C, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l1 [X₁+1 ]

Analysing control-flow refined program

Found invariant 0 ≤ X₁ for location l1

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

MPRF for transition t₃₆: l1(X₀, X₁) → n_l1___1(X₀-1, X₁) :|: 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

n_l1___1 [X₁ ]
l1 [X₁+1 ]

MPRF for transition t₃₇: l1(X₀, X₁) → l1(NoDet0, X₁-1) :|: 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

n_l1___1 [X₁ ]
l1 [X₁+1 ]

MPRF for transition t₃₅: n_l1___1(X₀, X₁) → l1(NoDet0, X₁-1) :|: 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

n_l1___1 [X₁+1 ]
l1 [X₁+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁: 1 {O(1)}
t₀: inf {Infinity}
t₂: X₁+1 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
t₁: 1 {O(1)}
t₀: inf {Infinity}
t₂: X₁+1 {O(n)}

Sizebounds

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