KoAT2 Proof Output

Initial Problem

Start: eval_exmini_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_exmini_bb0_in, eval_exmini_bb1_in, eval_exmini_bb2_in, eval_exmini_bb3_in, eval_exmini_start, eval_exmini_stop
Transitions:
t₁: eval_exmini_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb1_in(X₃, X₄, X₅, X₃, X₄, X₅)
t₂: eval_exmini_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂
t₃: eval_exmini_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 101 ≤ X₀
t₄: eval_exmini_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₁
t₅: eval_exmini_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb1_in(X₁, 1+X₀, X₂-1, X₃, X₄, X₅)
t₆: eval_exmini_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_exmini_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant X₂ ≤ X₅ for location eval_exmini_bb3_in

Found invariant X₂ ≤ X₅ for location eval_exmini_stop

Found invariant X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100 for location eval_exmini_bb2_in

Found invariant X₂ ≤ X₅ for location eval_exmini_bb1_in

Problem after Preprocessing

Start: eval_exmini_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_exmini_bb0_in, eval_exmini_bb1_in, eval_exmini_bb2_in, eval_exmini_bb3_in, eval_exmini_start, eval_exmini_stop
Transitions:
t₁: eval_exmini_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb1_in(X₃, X₄, X₅, X₃, X₄, X₅)
t₂: eval_exmini_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₅
t₃: eval_exmini_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 101 ≤ X₀ ∧ X₂ ≤ X₅
t₄: eval_exmini_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₁ ∧ X₂ ≤ X₅
t₅: eval_exmini_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb1_in(X₁, 1+X₀, X₂-1, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₂ ≤ X₅
t₆: eval_exmini_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₅
t₀: eval_exmini_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₂: eval_exmini_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₅ of depth 1:

new bound:

X₃+X₄+X₅+101 {O(n)}

MPRF:

• eval_exmini_bb1_in: [101+X₅-X₀-X₁]
• eval_exmini_bb2_in: [100+X₅-X₀-X₁]

MPRF for transition t₅: eval_exmini_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_exmini_bb1_in(X₁, 1+X₀, X₂-1, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₂ ≤ X₅ of depth 1:

new bound:

X₃+X₄+X₅+101 {O(n)}

MPRF:

• eval_exmini_bb1_in: [101+X₅-X₀-X₁]
• eval_exmini_bb2_in: [101+X₅-X₀-X₁]

All Bounds

Timebounds

Overall timebound:2⋅X₃+2⋅X₄+2⋅X₅+207 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+X₄+X₅+101 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₃+X₄+X₅+101 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+2⋅X₄+2⋅X₅+207 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+X₄+X₅+101 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₃+X₄+X₅+101 {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₅ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 3⋅X₃+3⋅X₄+X₅+104 {O(n)}
t₂, X₁: 3⋅X₃+3⋅X₄+X₅+104 {O(n)}
t₂, X₂: 2⋅X₅+X₃+X₄+102 {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 2⋅X₅+3⋅X₄+4⋅X₃+4 {O(n)}
t₃, X₁: 2⋅X₅+3⋅X₃+4⋅X₄+4 {O(n)}
t₃, X₂: 4⋅X₅+X₃+X₄+2 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 2⋅X₅+3⋅X₄+4⋅X₃+4 {O(n)}
t₄, X₁: 2⋅X₅+3⋅X₃+4⋅X₄+4 {O(n)}
t₄, X₂: 4⋅X₅+X₃+X₄+2 {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₅, X₀: 2⋅X₅+3⋅X₃+3⋅X₄+4 {O(n)}
t₅, X₁: 2⋅X₅+3⋅X₃+3⋅X₄+4 {O(n)}
t₅, X₂: 3⋅X₅+X₃+X₄+2 {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₆, X₀: 4⋅X₅+6⋅X₄+8⋅X₃+8 {O(n)}
t₆, X₁: 4⋅X₅+6⋅X₃+8⋅X₄+8 {O(n)}
t₆, X₂: 2⋅X₃+2⋅X₄+8⋅X₅+4 {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}
t₆, X₅: 4⋅X₅ {O(n)}