Initial Problem

Start: f999
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2, f999
Transitions:
t₃: f1(X₀, X₁) → f1(1+X₀, X₁-1) :|: 1 ≤ X₁
t₀: f1(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₀
t₄: f2(X₀, X₁) → f1(1+X₀, X₁-1) :|: 1 ≤ X₁
t₁: f2(X₀, X₁) → f2(X₀-1, 1+X₁) :|: 1 ≤ X₀
t₂: f999(X₀, X₁) → f1(1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0

Preprocessing

Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f1

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f2

Problem after Preprocessing

Start: f999
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2, f999
Transitions:
t₃: f1(X₀, X₁) → f1(1+X₀, X₁-1) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₀: f1(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₄: f2(X₀, X₁) → f1(1+X₀, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₁: f2(X₀, X₁) → f2(X₀-1, 1+X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂: f999(X₀, X₁) → f1(1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0

MPRF for transition t₀: f1(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

• f1: [X₀+X₁]
• f2: [X₀+X₁]

MPRF for transition t₄: f2(X₀, X₁) → f1(1+X₀, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

• f1: [X₀+X₁]
• f2: [1+X₀+X₁]

Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f1

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f1_v1

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f2

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f2_v1

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)}