KoAT2 Proof Output

Initial Problem

Start: eval_jama_ex6_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_jama_ex6_bb0_in, eval_jama_ex6_bb1_in, eval_jama_ex6_bb2_in, eval_jama_ex6_bb3_in, eval_jama_ex6_bb4_in, eval_jama_ex6_bb5_in, eval_jama_ex6_bb6_in, eval_jama_ex6_bb7_in, eval_jama_ex6_bb8_in, eval_jama_ex6_start, eval_jama_ex6_stop
Transitions:
t₁: eval_jama_ex6_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, X₀, X₅, X₆)
t₂: eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, X₂, X₆) :|: X₄ ≤ X₁
t₃: eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₄
t₄: eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ X₃
t₅: eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₃ ≤ X₅
t₆: eval_jama_ex6_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₄-X₅)
t₇: eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄+X₅
t₈: eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄+X₅ ≤ X₆
t₉: eval_jama_ex6_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆)
t₁₀: eval_jama_ex6_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆)
t₁₁: eval_jama_ex6_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆)
t₁₂: eval_jama_ex6_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₀: eval_jama_ex6_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb5_in

Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb7_in

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb6_in

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location eval_jama_ex6_bb8_in

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location eval_jama_ex6_stop

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb3_in

Found invariant X₀ ≤ X₄ for location eval_jama_ex6_bb1_in

Found invariant X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb2_in

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb4_in

Problem after Preprocessing

Start: eval_jama_ex6_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_jama_ex6_bb0_in, eval_jama_ex6_bb1_in, eval_jama_ex6_bb2_in, eval_jama_ex6_bb3_in, eval_jama_ex6_bb4_in, eval_jama_ex6_bb5_in, eval_jama_ex6_bb6_in, eval_jama_ex6_bb7_in, eval_jama_ex6_bb8_in, eval_jama_ex6_start, eval_jama_ex6_stop
Transitions:
t₁: eval_jama_ex6_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, X₀, X₅, X₆)
t₂: eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, X₂, X₆) :|: X₄ ≤ X₁ ∧ X₀ ≤ X₄
t₃: eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄
t₄: eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ X₃ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₅
t₅: eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₃ ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₅
t₆: eval_jama_ex6_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₄-X₅) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃
t₇: eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄+X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃
t₈: eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄+X₅ ≤ X₆ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃
t₉: eval_jama_ex6_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃
t₁₀: eval_jama_ex6_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃
t₁₁: eval_jama_ex6_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: 1+X₃ ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₅
t₁₂: eval_jama_ex6_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄
t₀: eval_jama_ex6_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₂: eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, X₂, X₆) :|: X₄ ≤ X₁ ∧ X₀ ≤ X₄ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• eval_jama_ex6_bb1_in: [1+X₁-X₄]
• eval_jama_ex6_bb2_in: [X₁-X₄]
• eval_jama_ex6_bb3_in: [X₁-X₄]
• eval_jama_ex6_bb4_in: [X₁-X₄]
• eval_jama_ex6_bb5_in: [X₁-X₄]
• eval_jama_ex6_bb6_in: [X₁-X₄]
• eval_jama_ex6_bb7_in: [X₁-X₄]

MPRF for transition t₅: eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₃ ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₅ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• eval_jama_ex6_bb1_in: [1+X₁-X₄]
• eval_jama_ex6_bb2_in: [1+X₁-X₄]
• eval_jama_ex6_bb3_in: [1+X₁-X₄]
• eval_jama_ex6_bb4_in: [1+X₁-X₄]
• eval_jama_ex6_bb5_in: [1+X₁-X₄]
• eval_jama_ex6_bb6_in: [1+X₁-X₄]
• eval_jama_ex6_bb7_in: [X₁-X₄]

MPRF for transition t₁₁: eval_jama_ex6_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb1_in(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: 1+X₃ ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₅ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

MPRF for transition t₄: eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ X₃ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₅ of depth 1:

new bound:

X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}

MPRF:

• eval_jama_ex6_bb1_in: [1+X₃-X₂]
• eval_jama_ex6_bb2_in: [1+X₃-X₅]
• eval_jama_ex6_bb3_in: [X₃-X₅]
• eval_jama_ex6_bb4_in: [X₃-X₅]
• eval_jama_ex6_bb5_in: [X₃-X₅]
• eval_jama_ex6_bb6_in: [X₃-X₅]
• eval_jama_ex6_bb7_in: [X₃-X₅]

MPRF for transition t₆: eval_jama_ex6_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₄-X₅) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃ of depth 1:

new bound:

X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}

MPRF:

• eval_jama_ex6_bb1_in: [1+X₃-X₂]
• eval_jama_ex6_bb2_in: [1+X₃-X₅]
• eval_jama_ex6_bb3_in: [1+X₃-X₅]
• eval_jama_ex6_bb4_in: [X₃-X₅]
• eval_jama_ex6_bb5_in: [X₃-X₅]
• eval_jama_ex6_bb6_in: [X₃-X₅]
• eval_jama_ex6_bb7_in: [X₃-X₅]

MPRF for transition t₈: eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄+X₅ ≤ X₆ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃ of depth 1:

new bound:

4⋅X₀⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₂+4⋅X₁⋅X₃+8⋅X₂+8⋅X₃+X₀+X₁+2 {O(n^2)}

MPRF:

• eval_jama_ex6_bb1_in: [1+4⋅X₃-4⋅X₂]
• eval_jama_ex6_bb2_in: [1+4⋅X₃-3⋅X₂-X₅]
• eval_jama_ex6_bb3_in: [1+4⋅X₃-3⋅X₂-X₅]
• eval_jama_ex6_bb4_in: [1+4⋅X₃-3⋅X₂-X₅]
• eval_jama_ex6_bb5_in: [1+4⋅X₃-3⋅X₂-X₅]
• eval_jama_ex6_bb6_in: [4⋅X₃-3⋅X₂-X₅]
• eval_jama_ex6_bb7_in: [4⋅X₃-3⋅X₂-X₅]

MPRF for transition t₁₀: eval_jama_ex6_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb2_in(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃ of depth 1:

new bound:

X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}

MPRF:

• eval_jama_ex6_bb1_in: [1+X₃-X₂]
• eval_jama_ex6_bb2_in: [1+X₃-X₅]
• eval_jama_ex6_bb3_in: [1+X₃-X₅]
• eval_jama_ex6_bb4_in: [1+X₃-X₅]
• eval_jama_ex6_bb5_in: [1+X₃-X₅]
• eval_jama_ex6_bb6_in: [1+X₃-X₅]
• eval_jama_ex6_bb7_in: [X₃-X₅]

MPRF for transition t₇: eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄+X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃ of depth 1:

new bound:

2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}

MPRF:

• eval_jama_ex6_bb1_in: [1+2⋅X₃]
• eval_jama_ex6_bb2_in: [1+2⋅X₃]
• eval_jama_ex6_bb3_in: [1+2⋅X₃]
• eval_jama_ex6_bb4_in: [1+X₃+X₄-X₆]
• eval_jama_ex6_bb5_in: [X₃+X₄-X₆]
• eval_jama_ex6_bb6_in: [1+X₃+X₄-X₆]
• eval_jama_ex6_bb7_in: [1+2⋅X₃]

TWN: t₉: eval_jama_ex6_bb5_in→eval_jama_ex6_bb4_in

cycle: [t₉: eval_jama_ex6_bb5_in→eval_jama_ex6_bb4_in; t₇: eval_jama_ex6_bb4_in→eval_jama_ex6_bb5_in]
original loop: (X₆ ≤ X₄+X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃,(X₀,X₁,X₂,X₃,X₄,X₅,X₆) -> (X₀,X₁,X₂,X₃,X₄,X₅,1+X₆))
transformed loop: (X₆ ≤ X₄+X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃,(X₀,X₁,X₂,X₃,X₄,X₅,X₆) -> (X₀,X₁,X₂,X₃,X₄,X₅,1+X₆))
loop: (X₆ ≤ X₄+X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃,(X₀,X₁,X₂,X₃,X₄,X₅,X₆) -> (X₀,X₁,X₂,X₃,X₄,X₅,1+X₆))
order: [X₆; X₅; X₄; X₃; X₂; X₁; X₀]
closed-form:

X₆: X₆ + [[n != 0]]⋅n^1
X₅: X₅
X₄: X₄
X₃: X₃
X₂: X₂
X₁: X₁
X₀: X₀

Termination: true
Formula:

0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₆ ≤ X₄+X₅ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃ ∧ X₆ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₆
∨ 1 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃

Stabilization-Threshold for: X₆ ≤ X₄+X₅

alphas_abs: 1+X₄+X₅+X₆
M: 0
N: 1
Bound: 2⋅X₄+2⋅X₅+2⋅X₆+4 {O(n)}

TWN - Lifting for [7: eval_jama_ex6_bb4_in->eval_jama_ex6_bb5_in; 9: eval_jama_ex6_bb5_in->eval_jama_ex6_bb4_in] of 2⋅X₄+2⋅X₅+2⋅X₆+6 {O(n)}

relevant size-bounds w.r.t. t₆: eval_jama_ex6_bb3_in→eval_jama_ex6_bb4_in:
X₄: 2⋅X₀+X₁+1 {O(n)}
X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
X₆: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₁+2⋅X₃+3⋅X₀+4⋅X₂+3 {O(n^2)}
Runtime-bound of t₆: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
Results in: 16⋅X₀⋅X₁⋅X₂⋅X₃+4⋅X₀⋅X₀⋅X₂⋅X₂+4⋅X₀⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₁⋅X₂⋅X₂+4⋅X₁⋅X₁⋅X₃⋅X₃+8⋅X₀⋅X₀⋅X₂⋅X₃+8⋅X₀⋅X₁⋅X₂⋅X₂+8⋅X₀⋅X₁⋅X₃⋅X₃+8⋅X₁⋅X₁⋅X₂⋅X₃+12⋅X₁⋅X₁⋅X₂+12⋅X₁⋅X₁⋅X₃+16⋅X₀⋅X₀⋅X₂+16⋅X₀⋅X₀⋅X₃+16⋅X₀⋅X₃⋅X₃+16⋅X₁⋅X₃⋅X₃+24⋅X₀⋅X₂⋅X₂+24⋅X₁⋅X₂⋅X₂+28⋅X₀⋅X₁⋅X₂+28⋅X₀⋅X₁⋅X₃+40⋅X₀⋅X₂⋅X₃+40⋅X₁⋅X₂⋅X₃+12⋅X₀⋅X₀+16⋅X₃⋅X₃+20⋅X₀⋅X₁+32⋅X₂⋅X₂+48⋅X₂⋅X₃+50⋅X₁⋅X₃+58⋅X₀⋅X₃+58⋅X₁⋅X₂+66⋅X₀⋅X₂+8⋅X₁⋅X₁+34⋅X₁+42⋅X₀+52⋅X₃+68⋅X₂+36 {O(n^4)}

knowledge_propagation leads to new time bound 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)} for transition t₉: eval_jama_ex6_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_jama_ex6_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃

Found invariant 1+X₄ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 1+X₃ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb2_in_v2

Found invariant X₅ ≤ 1+X₃ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb2_in_v1

Found invariant X₀ ≤ X₄ for location eval_jama_ex6_bb1_in

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb5_in_v2

Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb7_in

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb4_in_v2

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb6_in_v1

Found invariant X₅ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb3_in_v2

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location eval_jama_ex6_bb8_in

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location eval_jama_ex6_stop

Found invariant 1+X₄ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb3_in_v3

Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb2_in

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb6_in_v2

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb4_in_v1

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb5_in_v1

Found invariant X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location eval_jama_ex6_bb3_in_v1

All Bounds

Timebounds

Overall timebound:4⋅X₀⋅X₂⋅X₃+4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₂⋅X₃+4⋅X₁⋅X₃⋅X₃+13⋅X₀⋅X₃+13⋅X₁⋅X₃+8⋅X₂⋅X₃+8⋅X₃⋅X₃+9⋅X₀⋅X₂+9⋅X₁⋅X₂+18⋅X₂+30⋅X₃+9⋅X₀+9⋅X₁+21 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₅: X₀+X₁+1 {O(n)}
t₆: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₇: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}
t₈: 4⋅X₀⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₂+4⋅X₁⋅X₃+8⋅X₂+8⋅X₃+X₀+X₁+2 {O(n^2)}
t₉: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}
t₁₀: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₁₁: X₀+X₁+1 {O(n)}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₀⋅X₂⋅X₃+4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₂⋅X₃+4⋅X₁⋅X₃⋅X₃+13⋅X₀⋅X₃+13⋅X₁⋅X₃+8⋅X₂⋅X₃+8⋅X₃⋅X₃+9⋅X₀⋅X₂+9⋅X₁⋅X₂+18⋅X₂+30⋅X₃+9⋅X₀+9⋅X₁+21 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₅: X₀+X₁+1 {O(n)}
t₆: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₇: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}
t₈: 4⋅X₀⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₂+4⋅X₁⋅X₃+8⋅X₂+8⋅X₃+X₀+X₁+2 {O(n^2)}
t₉: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}
t₁₀: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₁₁: X₀+X₁+1 {O(n)}
t₁₂: 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)}
t₀, X₆: X₆ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₀ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: 2⋅X₀+X₁+1 {O(n)}
t₂, X₅: 2⋅X₂ {O(n)}
t₂, X₆: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+X₆+9 {O(n^3)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 3⋅X₀+X₁+1 {O(n)}
t₃, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+6⋅X₂+X₀+X₁+X₅+2 {O(n^2)}
t₃, X₆: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+2⋅X₆+5⋅X₁+7⋅X₀+9 {O(n^3)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: 2⋅X₀+X₁+1 {O(n)}
t₄, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₄, X₆: 4⋅X₀⋅X₂⋅X₃+4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₂⋅X₃+4⋅X₁⋅X₃⋅X₃+10⋅X₀⋅X₃+10⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+8⋅X₂⋅X₃+8⋅X₃⋅X₃+10⋅X₁+14⋅X₀+20⋅X₂+24⋅X₃+X₆+18 {O(n^3)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: 2⋅X₀+X₁+1 {O(n)}
t₅, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+6⋅X₂+X₀+X₁+2 {O(n^2)}
t₅, X₆: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+X₆+9 {O(n^3)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: 2⋅X₀+X₁+1 {O(n)}
t₆, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₆, X₆: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₁+2⋅X₃+3⋅X₀+4⋅X₂+3 {O(n^2)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: 2⋅X₀+X₁+1 {O(n)}
t₇, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₇, X₆: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+10⋅X₃+3⋅X₁+4⋅X₀+6⋅X₂+6 {O(n^3)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: 2⋅X₀+X₁+1 {O(n)}
t₈, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₈, X₆: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+9 {O(n^3)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: 2⋅X₀+X₁+1 {O(n)}
t₉, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₉, X₆: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+10⋅X₃+3⋅X₁+4⋅X₀+6⋅X₂+6 {O(n^3)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: 2⋅X₀+X₁+1 {O(n)}
t₁₀, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₁₀, X₆: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+9 {O(n^3)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: 2⋅X₀+X₁+1 {O(n)}
t₁₁, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+6⋅X₂+X₀+X₁+2 {O(n^2)}
t₁₁, X₆: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+X₆+9 {O(n^3)}
t₁₂, X₀: 2⋅X₀ {O(n)}
t₁₂, X₁: 2⋅X₁ {O(n)}
t₁₂, X₂: 2⋅X₂ {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₂, X₄: 3⋅X₀+X₁+1 {O(n)}
t₁₂, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+6⋅X₂+X₀+X₁+X₅+2 {O(n^2)}
t₁₂, X₆: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+2⋅X₆+5⋅X₁+7⋅X₀+9 {O(n^3)}