Initial Problem

Start: evalwcet2start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: evalwcet2bb1in, evalwcet2bb2in, evalwcet2bb4in, evalwcet2bb5in, evalwcet2entryin, evalwcet2returnin, evalwcet2start, evalwcet2stop
Transitions:
t₇: evalwcet2bb1in(X₀, X₁) → evalwcet2bb2in(X₀, 1+X₁)
t₄: evalwcet2bb2in(X₀, X₁) → evalwcet2bb1in(X₀, X₁) :|: X₁ ≤ 9 ∧ 3 ≤ X₀
t₅: evalwcet2bb2in(X₀, X₁) → evalwcet2bb4in(X₀, X₁) :|: X₀ ≤ 2
t₆: evalwcet2bb2in(X₀, X₁) → evalwcet2bb4in(X₀, X₁) :|: 10 ≤ X₁
t₈: evalwcet2bb4in(X₀, X₁) → evalwcet2bb5in(1+X₀, X₁)
t₂: evalwcet2bb5in(X₀, X₁) → evalwcet2bb2in(X₀, 0) :|: X₀ ≤ 4
t₃: evalwcet2bb5in(X₀, X₁) → evalwcet2returnin(X₀, X₁) :|: 5 ≤ X₀
t₁: evalwcet2entryin(X₀, X₁) → evalwcet2bb5in(X₀, X₁)
t₉: evalwcet2returnin(X₀, X₁) → evalwcet2stop(X₀, X₁)
t₀: evalwcet2start(X₀, X₁) → evalwcet2entryin(X₀, X₁)

Preprocessing

Found invariant 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 for location evalwcet2bb2in

Found invariant 5 ≤ X₀ for location evalwcet2returnin

Found invariant 0 ≤ X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 4 for location evalwcet2bb4in

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀+X₁ ≤ 13 ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀ for location evalwcet2bb1in

Found invariant 5 ≤ X₀ for location evalwcet2stop

Problem after Preprocessing

Start: evalwcet2start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: evalwcet2bb1in, evalwcet2bb2in, evalwcet2bb4in, evalwcet2bb5in, evalwcet2entryin, evalwcet2returnin, evalwcet2start, evalwcet2stop
Transitions:
t₇: evalwcet2bb1in(X₀, X₁) → evalwcet2bb2in(X₀, 1+X₁) :|: X₀+X₁ ≤ 13 ∧ X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₄: evalwcet2bb2in(X₀, X₁) → evalwcet2bb1in(X₀, X₁) :|: X₁ ≤ 9 ∧ 3 ≤ X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ 0 ≤ X₁
t₅: evalwcet2bb2in(X₀, X₁) → evalwcet2bb4in(X₀, X₁) :|: X₀ ≤ 2 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ 0 ≤ X₁
t₆: evalwcet2bb2in(X₀, X₁) → evalwcet2bb4in(X₀, X₁) :|: 10 ≤ X₁ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ 0 ≤ X₁
t₈: evalwcet2bb4in(X₀, X₁) → evalwcet2bb5in(1+X₀, X₁) :|: X₀ ≤ 4 ∧ X₀ ≤ 2+X₁ ∧ 0 ≤ X₁
t₂: evalwcet2bb5in(X₀, X₁) → evalwcet2bb2in(X₀, 0) :|: X₀ ≤ 4
t₃: evalwcet2bb5in(X₀, X₁) → evalwcet2returnin(X₀, X₁) :|: 5 ≤ X₀
t₁: evalwcet2entryin(X₀, X₁) → evalwcet2bb5in(X₀, X₁)
t₉: evalwcet2returnin(X₀, X₁) → evalwcet2stop(X₀, X₁) :|: 5 ≤ X₀
t₀: evalwcet2start(X₀, X₁) → evalwcet2entryin(X₀, X₁)

MPRF for transition t₂: evalwcet2bb5in(X₀, X₁) → evalwcet2bb2in(X₀, 0) :|: X₀ ≤ 4 of depth 1:

new bound:

X₀+5 {O(n)}

• evalwcet2bb1in: [4-X₀]
• evalwcet2bb2in: [4-X₀]
• evalwcet2bb4in: [4-X₀]
• evalwcet2bb5in: [5-X₀]

MPRF for transition t₅: evalwcet2bb2in(X₀, X₁) → evalwcet2bb4in(X₀, X₁) :|: X₀ ≤ 2 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀+5 {O(n)}

• evalwcet2bb1in: [5-X₀]
• evalwcet2bb2in: [5-X₀]
• evalwcet2bb4in: [4-X₀]
• evalwcet2bb5in: [5-X₀]

MPRF for transition t₆: evalwcet2bb2in(X₀, X₁) → evalwcet2bb4in(X₀, X₁) :|: 10 ≤ X₁ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀+5 {O(n)}

• evalwcet2bb1in: [5-X₀]
• evalwcet2bb2in: [5-X₀]
• evalwcet2bb4in: [4-X₀]
• evalwcet2bb5in: [5-X₀]

MPRF for transition t₈: evalwcet2bb4in(X₀, X₁) → evalwcet2bb5in(1+X₀, X₁) :|: X₀ ≤ 4 ∧ X₀ ≤ 2+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀+5 {O(n)}

• evalwcet2bb1in: [5-X₀]
• evalwcet2bb2in: [5-X₀]
• evalwcet2bb4in: [5-X₀]
• evalwcet2bb5in: [5-X₀]

MPRF for transition t₄: evalwcet2bb2in(X₀, X₁) → evalwcet2bb1in(X₀, X₁) :|: X₁ ≤ 9 ∧ 3 ≤ X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

10⋅X₀+60 {O(n)}

• evalwcet2bb1in: [9-X₁]
• evalwcet2bb2in: [10-X₁]
• evalwcet2bb4in: [-X₁]
• evalwcet2bb5in: [10]

MPRF for transition t₇: evalwcet2bb1in(X₀, X₁) → evalwcet2bb2in(X₀, 1+X₁) :|: X₀+X₁ ≤ 13 ∧ X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

10⋅X₀+60 {O(n)}

• evalwcet2bb1in: [10-X₁]
• evalwcet2bb2in: [10-X₁]
• evalwcet2bb4in: [-X₁]
• evalwcet2bb5in: [10]

All Bounds

Timebounds

Overall timebound:24⋅X₀+144 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+5 {O(n)}
t₃: 1 {O(1)}
t₄: 10⋅X₀+60 {O(n)}
t₅: X₀+5 {O(n)}
t₆: X₀+5 {O(n)}
t₇: 10⋅X₀+60 {O(n)}
t₈: X₀+5 {O(n)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 24⋅X₀+144 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+5 {O(n)}
t₃: 1 {O(1)}
t₄: 10⋅X₀+60 {O(n)}
t₅: X₀+5 {O(n)}
t₆: X₀+5 {O(n)}
t₇: 10⋅X₀+60 {O(n)}
t₈: X₀+5 {O(n)}
t₉: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: 2⋅X₀+9 {O(n)}
t₂, X₁: 0 {O(1)}
t₃, X₀: 3⋅X₀+9 {O(n)}
t₃, X₁: X₁+10 {O(n)}
t₄, X₀: 4 {O(1)}
t₄, X₁: 9 {O(1)}
t₅, X₀: 2⋅X₀+9 {O(n)}
t₅, X₁: 0 {O(1)}
t₆, X₀: 4 {O(1)}
t₆, X₁: 10 {O(1)}
t₇, X₀: 4 {O(1)}
t₇, X₁: 10 {O(1)}
t₈, X₀: 2⋅X₀+9 {O(n)}
t₈, X₁: 10 {O(1)}
t₉, X₀: 3⋅X₀+9 {O(n)}
t₉, X₁: X₁+10 {O(n)}