Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁) → l1(1, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁
t₀: l1(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀
t₄: l2(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁
t₁: l2(X₀, X₁) → l2(X₀-1, X₁+1) :|: 1 ≤ X₀

Preprocessing

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2

Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁) → l1(1, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₀: l1(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l2(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁: l2(X₀, X₁) → l2(X₀-1, X₁+1) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

MPRF for transition t₀: l1(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₄: l2(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

Analysing control-flow refined program

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___1

Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

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

MPRF for transition t₄₈: l2(X₀, X₁) → n_l2___1(X₀-1, X₁+1) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₅₁: n_l2___1(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₆₄: l1(X₀, X₁) → n_l1___1(X₀+1, X₁-1) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF for transition t₆₅: l1(X₀, X₁) → n_l1___1(X₀+1, X₁-1) :|: X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₆₈: n_l1___1(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: X₁+1 {O(n)}
t₁: inf {Infinity}
t₂: 1 {O(1)}
t₃: inf {Infinity}
t₄: X₁+1 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
t₀: X₁+1 {O(n)}
t₁: inf {Infinity}
t₂: 1 {O(1)}
t₃: inf {Infinity}
t₄: X₁+1 {O(n)}

Sizebounds

t₂, X₀: 1 {O(1)}
t₂, X₁: X₁ {O(n)}