KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location eval_Loopus2011_ex1_.critedge_in

Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₁ for location eval_Loopus2011_ex1_stop

Found invariant 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_Loopus2011_ex1_bb5_in

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 0 ≤ X₁ for location eval_Loopus2011_ex1_bb2_in

Found invariant 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location eval_Loopus2011_ex1_2

Found invariant 0 ≤ X₁ for location eval_Loopus2011_ex1_bb1_in

Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₁ for location eval_Loopus2011_ex1_bb6_in

Problem after Preprocessing

Start: eval_Loopus2011_ex1_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: eval_Loopus2011_ex1_.critedge_in, eval_Loopus2011_ex1_2, eval_Loopus2011_ex1_3, eval_Loopus2011_ex1_bb0_in, eval_Loopus2011_ex1_bb1_in, eval_Loopus2011_ex1_bb2_in, eval_Loopus2011_ex1_bb3_in, eval_Loopus2011_ex1_bb4_in, eval_Loopus2011_ex1_bb5_in, eval_Loopus2011_ex1_bb6_in, eval_Loopus2011_ex1_start, eval_Loopus2011_ex1_stop
Transitions:
t₁₃: eval_Loopus2011_ex1_.critedge_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb1_in(X₀, X₂-1, X₂, X₃, X₄) :|: 1 ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃
t₁₄: eval_Loopus2011_ex1_.critedge_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb1_in(X₀, X₂, X₂, X₃, X₄) :|: X₃ ≤ 0 ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃
t₉: eval_Loopus2011_ex1_2(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_3(nondef.0, X₁, X₂, X₃, X₄) :|: 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃
t₁₁: eval_Loopus2011_ex1_3(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃
t₁₀: eval_Loopus2011_ex1_3(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃
t₁: eval_Loopus2011_ex1_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb1_in(X₀, 0, X₂, X₃, X₄)
t₂: eval_Loopus2011_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₄ ∧ 0 ≤ X₁
t₃: eval_Loopus2011_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb6_in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₁ ∧ 0 ≤ X₁
t₄: eval_Loopus2011_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb3_in(X₀, X₁, 1+X₁, 0, X₄) :|: 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 0 ≤ X₁
t₆: eval_Loopus2011_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃
t₅: eval_Loopus2011_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃
t₇: eval_Loopus2011_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_2(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃
t₁₂: eval_Loopus2011_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb3_in(X₀, X₁, 1+X₂, 1+X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃
t₁₅: eval_Loopus2011_ex1_bb6_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_stop(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₁ ∧ X₄ ≤ X₁
t₀: eval_Loopus2011_ex1_start(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb0_in(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₂: eval_Loopus2011_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₄ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_2: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_3: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb1_in: [X₄-X₁]
• eval_Loopus2011_ex1_bb2_in: [X₄-1-X₁]
• eval_Loopus2011_ex1_bb3_in: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb4_in: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb5_in: [X₃+X₄-X₂]

MPRF for transition t₄: eval_Loopus2011_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb3_in(X₀, X₁, 1+X₁, 0, X₄) :|: 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_2: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_3: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb1_in: [X₄-X₁]
• eval_Loopus2011_ex1_bb2_in: [X₄-X₁]
• eval_Loopus2011_ex1_bb3_in: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb4_in: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb5_in: [X₃+X₄-X₂]

MPRF for transition t₅: eval_Loopus2011_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ of depth 1:

new bound:

3⋅X₄+4 {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [X₃+3⋅X₄-3-2⋅X₂]
• eval_Loopus2011_ex1_2: [X₃+3⋅X₄-3-2⋅X₂]
• eval_Loopus2011_ex1_3: [X₃+3⋅X₄-3-2⋅X₂]
• eval_Loopus2011_ex1_bb1_in: [3⋅X₄-4-2⋅X₁]
• eval_Loopus2011_ex1_bb2_in: [3⋅X₄-4-2⋅X₁]
• eval_Loopus2011_ex1_bb3_in: [X₃+3⋅X₄-2-2⋅X₂]
• eval_Loopus2011_ex1_bb4_in: [X₃+3⋅X₄-3-2⋅X₂]
• eval_Loopus2011_ex1_bb5_in: [X₃+3⋅X₄-3-2⋅X₂]

MPRF for transition t₆: eval_Loopus2011_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [X₃+X₄-X₂]
• eval_Loopus2011_ex1_2: [1+X₃+X₄-X₂]
• eval_Loopus2011_ex1_3: [1+X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb1_in: [X₄-X₁]
• eval_Loopus2011_ex1_bb2_in: [X₄-X₁]
• eval_Loopus2011_ex1_bb3_in: [1+X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb4_in: [1+X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb5_in: [1+X₃+X₄-X₂]

MPRF for transition t₇: eval_Loopus2011_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_2(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₄+3 {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [X₃+2⋅X₄-2-2⋅X₂]
• eval_Loopus2011_ex1_2: [X₃+2⋅X₄-2-2⋅X₂]
• eval_Loopus2011_ex1_3: [X₃+2⋅X₄-2-2⋅X₂]
• eval_Loopus2011_ex1_bb1_in: [2⋅X₄-3-2⋅X₁]
• eval_Loopus2011_ex1_bb2_in: [2⋅X₄-3-2⋅X₁]
• eval_Loopus2011_ex1_bb3_in: [X₃+2⋅X₄-1-2⋅X₂]
• eval_Loopus2011_ex1_bb4_in: [X₃+2⋅X₄-1-2⋅X₂]
• eval_Loopus2011_ex1_bb5_in: [X₃+2⋅X₄-2-2⋅X₂]

MPRF for transition t₉: eval_Loopus2011_ex1_2(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_3(nondef.0, X₁, X₂, X₃, X₄) :|: 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₄+3 {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [X₃+2⋅X₄-2-2⋅X₂]
• eval_Loopus2011_ex1_2: [X₃+2⋅X₄-1-2⋅X₂]
• eval_Loopus2011_ex1_3: [X₃+2⋅X₄-2-2⋅X₂]
• eval_Loopus2011_ex1_bb1_in: [2⋅X₄-3-2⋅X₁]
• eval_Loopus2011_ex1_bb2_in: [2⋅X₄-3-2⋅X₁]
• eval_Loopus2011_ex1_bb3_in: [X₃+2⋅X₄-1-2⋅X₂]
• eval_Loopus2011_ex1_bb4_in: [X₃+2⋅X₄-1-2⋅X₂]
• eval_Loopus2011_ex1_bb5_in: [X₃+2⋅X₄-2-2⋅X₂]

MPRF for transition t₁₀: eval_Loopus2011_ex1_3(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [2+X₄-X₂]
• eval_Loopus2011_ex1_2: [2+X₄-X₂]
• eval_Loopus2011_ex1_3: [2+X₄-X₂]
• eval_Loopus2011_ex1_bb1_in: [1+X₄-X₁]
• eval_Loopus2011_ex1_bb2_in: [1+X₄-X₁]
• eval_Loopus2011_ex1_bb3_in: [2+X₄-X₂]
• eval_Loopus2011_ex1_bb4_in: [2+X₄-X₂]
• eval_Loopus2011_ex1_bb5_in: [1+X₄-X₂]

MPRF for transition t₁₁: eval_Loopus2011_ex1_3(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₄+3 {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [X₃+2⋅X₄-3-X₂]
• eval_Loopus2011_ex1_2: [X₃+2⋅X₄-2-X₂]
• eval_Loopus2011_ex1_3: [X₃+2⋅X₄-2-X₂]
• eval_Loopus2011_ex1_bb1_in: [2⋅X₄-3-X₁]
• eval_Loopus2011_ex1_bb2_in: [2⋅X₄-3-X₁]
• eval_Loopus2011_ex1_bb3_in: [X₃+2⋅X₄-2-X₂]
• eval_Loopus2011_ex1_bb4_in: [X₃+2⋅X₄-2-X₂]
• eval_Loopus2011_ex1_bb5_in: [X₃+2⋅X₄-2-X₂]

MPRF for transition t₁₂: eval_Loopus2011_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb3_in(X₀, X₁, 1+X₂, 1+X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [X₄-X₂]
• eval_Loopus2011_ex1_2: [X₄-X₂]
• eval_Loopus2011_ex1_3: [X₄-X₂]
• eval_Loopus2011_ex1_bb1_in: [X₄-1-X₁]
• eval_Loopus2011_ex1_bb2_in: [X₄-1-X₁]
• eval_Loopus2011_ex1_bb3_in: [X₄-X₂]
• eval_Loopus2011_ex1_bb4_in: [X₄-X₂]
• eval_Loopus2011_ex1_bb5_in: [X₄-X₂]

MPRF for transition t₁₃: eval_Loopus2011_ex1_.critedge_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb1_in(X₀, X₂-1, X₂, X₃, X₄) :|: 1 ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [1+X₃+X₄-X₂]
• eval_Loopus2011_ex1_2: [1+X₃+X₄-X₂]
• eval_Loopus2011_ex1_3: [1+X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb1_in: [X₄-X₁]
• eval_Loopus2011_ex1_bb2_in: [X₄-X₁]
• eval_Loopus2011_ex1_bb3_in: [1+X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb4_in: [1+X₃+X₄-X₂]
• eval_Loopus2011_ex1_bb5_in: [1+X₃+X₄-X₂]

MPRF for transition t₁₄: eval_Loopus2011_ex1_.critedge_in(X₀, X₁, X₂, X₃, X₄) → eval_Loopus2011_ex1_bb1_in(X₀, X₂, X₂, X₃, X₄) :|: X₃ ≤ 0 ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₄+1 {O(n)}

MPRF:

• eval_Loopus2011_ex1_.critedge_in: [2⋅X₄-X₂]
• eval_Loopus2011_ex1_2: [2⋅X₄-X₂]
• eval_Loopus2011_ex1_3: [2⋅X₄-X₂]
• eval_Loopus2011_ex1_bb1_in: [2⋅X₄-1-X₁]
• eval_Loopus2011_ex1_bb2_in: [2⋅X₄-1-X₁]
• eval_Loopus2011_ex1_bb3_in: [2⋅X₄-X₂]
• eval_Loopus2011_ex1_bb4_in: [2⋅X₄-X₂]
• eval_Loopus2011_ex1_bb5_in: [2⋅X₄-X₂]

All Bounds

Timebounds

Overall timebound:17⋅X₄+20 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: 3⋅X₄+4 {O(n)}
t₆: X₄ {O(n)}
t₇: 2⋅X₄+3 {O(n)}
t₉: 2⋅X₄+3 {O(n)}
t₁₀: X₄+1 {O(n)}
t₁₁: 2⋅X₄+3 {O(n)}
t₁₂: X₄+1 {O(n)}
t₁₃: X₄ {O(n)}
t₁₄: 2⋅X₄+1 {O(n)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 17⋅X₄+20 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: 3⋅X₄+4 {O(n)}
t₆: X₄ {O(n)}
t₇: 2⋅X₄+3 {O(n)}
t₉: 2⋅X₄+3 {O(n)}
t₁₀: X₄+1 {O(n)}
t₁₁: 2⋅X₄+3 {O(n)}
t₁₂: X₄+1 {O(n)}
t₁₃: X₄ {O(n)}
t₁₄: 2⋅X₄+1 {O(n)}
t₁₅: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 0 {O(1)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₁: 2⋅X₄+1 {O(n)}
t₂, X₂: 8⋅X₄+X₂+4 {O(n)}
t₂, X₃: 2⋅X₄+X₃+2 {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₁: 2⋅X₄+1 {O(n)}
t₃, X₂: 4⋅X₄+X₂+2 {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₁: 2⋅X₄+1 {O(n)}
t₄, X₂: 2⋅X₄+1 {O(n)}
t₄, X₃: 0 {O(1)}
t₄, X₄: X₄ {O(n)}
t₅, X₁: 2⋅X₄+1 {O(n)}
t₅, X₂: 2⋅X₄+1 {O(n)}
t₅, X₃: X₄+1 {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₁: 4⋅X₄+2 {O(n)}
t₆, X₂: 2⋅X₄+1 {O(n)}
t₆, X₃: X₄+1 {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₁: 2⋅X₄+1 {O(n)}
t₇, X₂: 2⋅X₄+1 {O(n)}
t₇, X₃: X₄+1 {O(n)}
t₇, X₄: X₄ {O(n)}
t₉, X₁: 2⋅X₄+1 {O(n)}
t₉, X₂: 2⋅X₄+1 {O(n)}
t₉, X₃: X₄+1 {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₁: 2⋅X₄+1 {O(n)}
t₁₀, X₂: 2⋅X₄+1 {O(n)}
t₁₀, X₃: X₄+1 {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₁, X₁: 2⋅X₄+1 {O(n)}
t₁₁, X₂: 2⋅X₄+1 {O(n)}
t₁₁, X₃: X₄+1 {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₂, X₁: 2⋅X₄+1 {O(n)}
t₁₂, X₂: 2⋅X₄+1 {O(n)}
t₁₂, X₃: X₄+1 {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₁: 2⋅X₄+1 {O(n)}
t₁₃, X₂: 4⋅X₄+2 {O(n)}
t₁₃, X₃: 2⋅X₄+2 {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₁: 2⋅X₄+1 {O(n)}
t₁₄, X₂: 4⋅X₄+2 {O(n)}
t₁₄, X₃: 0 {O(1)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₁: 2⋅X₄+1 {O(n)}
t₁₅, X₂: 4⋅X₄+X₂+2 {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: 2⋅X₄ {O(n)}