Initial Problem
Start: eval_Loopus2015_ex1_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: eval_Loopus2015_ex1_2, eval_Loopus2015_ex1_3, eval_Loopus2015_ex1_bb0_in, eval_Loopus2015_ex1_bb1_in, eval_Loopus2015_ex1_bb2_in, eval_Loopus2015_ex1_bb3_in, eval_Loopus2015_ex1_bb4_in, eval_Loopus2015_ex1_bb5_in, eval_Loopus2015_ex1_start, eval_Loopus2015_ex1_stop
Transitions:
t₆: eval_Loopus2015_ex1_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_3(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆)
t₈: eval_Loopus2015_ex1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₁, X₀) :|: X₂ ≤ 0
t₇: eval_Loopus2015_ex1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₁, X₅, X₆) :|: 1 ≤ X₂
t₁: eval_Loopus2015_ex1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, 0, X₃)
t₂: eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆
t₃: eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 0
t₄: eval_Loopus2015_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_2(X₆-1, 1+X₅, X₂, X₃, X₄, X₅, X₆)
t₁₀: eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, 0, X₀) :|: X₄ ≤ 0
t₉: eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₄
t₁₁: eval_Loopus2015_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄-1, X₅, X₆)
t₁₂: eval_Loopus2015_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₀: eval_Loopus2015_ex1_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
Preprocessing
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ 1+X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₁+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₁ ≤ 1+X₅ ∧ 0 ≤ X₀+X₅ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_Loopus2015_ex1_3
Found invariant X₆ ≤ X₃ ∧ 0 ≤ X₅ for location eval_Loopus2015_ex1_bb1_in
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ 1+X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₁+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₁ ≤ 1+X₅ ∧ 0 ≤ X₀+X₅ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_Loopus2015_ex1_2
Found invariant X₆ ≤ 0 ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅ for location eval_Loopus2015_ex1_stop
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ 1+X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₁ ≤ 1+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_Loopus2015_ex1_bb3_in
Found invariant X₆ ≤ 0 ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅ for location eval_Loopus2015_ex1_bb5_in
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ 1+X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₁ ≤ 1+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_Loopus2015_ex1_bb4_in
Found invariant X₆ ≤ X₃ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃ for location eval_Loopus2015_ex1_bb2_in
Problem after Preprocessing
Start: eval_Loopus2015_ex1_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: eval_Loopus2015_ex1_2, eval_Loopus2015_ex1_3, eval_Loopus2015_ex1_bb0_in, eval_Loopus2015_ex1_bb1_in, eval_Loopus2015_ex1_bb2_in, eval_Loopus2015_ex1_bb3_in, eval_Loopus2015_ex1_bb4_in, eval_Loopus2015_ex1_bb5_in, eval_Loopus2015_ex1_start, eval_Loopus2015_ex1_stop
Transitions:
t₆: eval_Loopus2015_ex1_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_3(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅
t₈: eval_Loopus2015_ex1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₁, X₀) :|: X₂ ≤ 0 ∧ X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅
t₇: eval_Loopus2015_ex1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₁, X₅, X₆) :|: 1 ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅
t₁: eval_Loopus2015_ex1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, 0, X₃)
t₂: eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅
t₃: eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 0 ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅
t₄: eval_Loopus2015_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_2(X₆-1, 1+X₅, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅
t₁₀: eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, 0, X₀) :|: X₄ ≤ 0 ∧ X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₉: eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₄ ∧ X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₁₁: eval_Loopus2015_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄-1, X₅, X₆) :|: X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅
t₁₂: eval_Loopus2015_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₃ ∧ 0 ≤ X₅ ∧ X₆ ≤ X₅ ∧ X₆ ≤ 0
t₀: eval_Loopus2015_ex1_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
MPRF for transition t₂: eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF:
• eval_Loopus2015_ex1_2: [X₆]
• eval_Loopus2015_ex1_3: [X₆]
• eval_Loopus2015_ex1_bb1_in: [1+X₆]
• eval_Loopus2015_ex1_bb2_in: [X₆]
• eval_Loopus2015_ex1_bb3_in: [X₆]
• eval_Loopus2015_ex1_bb4_in: [X₆]
MPRF for transition t₄: eval_Loopus2015_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_2(X₆-1, 1+X₅, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
• eval_Loopus2015_ex1_2: [X₆-1]
• eval_Loopus2015_ex1_3: [X₀]
• eval_Loopus2015_ex1_bb1_in: [X₆]
• eval_Loopus2015_ex1_bb2_in: [X₆]
• eval_Loopus2015_ex1_bb3_in: [X₀]
• eval_Loopus2015_ex1_bb4_in: [X₀]
MPRF for transition t₆: eval_Loopus2015_ex1_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_3(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
• eval_Loopus2015_ex1_2: [1+X₀]
• eval_Loopus2015_ex1_3: [X₀]
• eval_Loopus2015_ex1_bb1_in: [X₆]
• eval_Loopus2015_ex1_bb2_in: [X₆]
• eval_Loopus2015_ex1_bb3_in: [X₀]
• eval_Loopus2015_ex1_bb4_in: [X₀]
MPRF for transition t₇: eval_Loopus2015_ex1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₁, X₅, X₆) :|: 1 ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
• eval_Loopus2015_ex1_2: [2⋅X₆-1-X₀]
• eval_Loopus2015_ex1_3: [X₆]
• eval_Loopus2015_ex1_bb1_in: [X₆]
• eval_Loopus2015_ex1_bb2_in: [X₆]
• eval_Loopus2015_ex1_bb3_in: [X₀]
• eval_Loopus2015_ex1_bb4_in: [X₀]
MPRF for transition t₈: eval_Loopus2015_ex1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₁, X₀) :|: X₂ ≤ 0 ∧ X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
• eval_Loopus2015_ex1_2: [1+X₀]
• eval_Loopus2015_ex1_3: [1+X₀]
• eval_Loopus2015_ex1_bb1_in: [X₆]
• eval_Loopus2015_ex1_bb2_in: [X₆]
• eval_Loopus2015_ex1_bb3_in: [X₀]
• eval_Loopus2015_ex1_bb4_in: [X₀]
MPRF for transition t₉: eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₄ ∧ X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₃+2 {O(n)}
MPRF:
• eval_Loopus2015_ex1_2: [1+X₁+X₆]
• eval_Loopus2015_ex1_3: [1+X₁+X₆]
• eval_Loopus2015_ex1_bb1_in: [2+X₅+X₆]
• eval_Loopus2015_ex1_bb2_in: [2+X₅+X₆]
• eval_Loopus2015_ex1_bb3_in: [2+X₀+X₄]
• eval_Loopus2015_ex1_bb4_in: [1+X₀+X₄]
MPRF for transition t₁₀: eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, 0, X₀) :|: X₄ ≤ 0 ∧ X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₃+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:
new bound:
2⋅X₃+1 {O(n)}
MPRF:
• eval_Loopus2015_ex1_2: [X₀+X₃]
• eval_Loopus2015_ex1_3: [X₀+X₃]
• eval_Loopus2015_ex1_bb1_in: [X₃+X₆-1]
• eval_Loopus2015_ex1_bb2_in: [X₃+X₆-1]
• eval_Loopus2015_ex1_bb3_in: [X₀+X₃]
• eval_Loopus2015_ex1_bb4_in: [X₀+X₃]
MPRF for transition t₁₁: eval_Loopus2015_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄-1, X₅, X₆) :|: X₆ ≤ 1+X₀ ∧ X₁ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₁ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
• eval_Loopus2015_ex1_2: [1+X₀+X₅]
• eval_Loopus2015_ex1_3: [1+X₀+X₅]
• eval_Loopus2015_ex1_bb1_in: [X₅+X₆]
• eval_Loopus2015_ex1_bb2_in: [X₅+X₆]
• eval_Loopus2015_ex1_bb3_in: [X₀+X₄]
• eval_Loopus2015_ex1_bb4_in: [X₀+X₄]
All Bounds
Timebounds
Overall timebound:9⋅X₃+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₃ {O(n)}
t₆: X₃ {O(n)}
t₇: X₃ {O(n)}
t₈: X₃ {O(n)}
t₉: X₃+2 {O(n)}
t₁₀: 2⋅X₃+1 {O(n)}
t₁₁: X₃ {O(n)}
t₁₂: 1 {O(1)}
Costbounds
Overall costbound: 9⋅X₃+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₃ {O(n)}
t₆: X₃ {O(n)}
t₇: X₃ {O(n)}
t₈: X₃ {O(n)}
t₉: X₃+2 {O(n)}
t₁₀: 2⋅X₃+1 {O(n)}
t₁₁: X₃ {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: X₄ {O(n)}
t₁, X₅: 0 {O(1)}
t₁, X₆: X₃ {O(n)}
t₂, X₀: 2⋅X₃+X₀ {O(n)}
t₂, X₁: 2⋅X₃+X₁ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₃ {O(n)}
t₂, X₆: X₃ {O(n)}
t₃, X₀: 2⋅X₃+X₀ {O(n)}
t₃, X₁: 2⋅X₃+X₁ {O(n)}
t₃, X₃: 3⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: X₃ {O(n)}
t₃, X₆: 3⋅X₃ {O(n)}
t₄, X₀: X₃ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₃ {O(n)}
t₄, X₆: X₃ {O(n)}
t₆, X₀: X₃ {O(n)}
t₆, X₁: X₃ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₃ {O(n)}
t₆, X₆: X₃ {O(n)}
t₇, X₀: X₃ {O(n)}
t₇, X₁: X₃ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₃ {O(n)}
t₇, X₅: X₃ {O(n)}
t₇, X₆: X₃ {O(n)}
t₈, X₀: X₃ {O(n)}
t₈, X₁: X₃ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₃ {O(n)}
t₈, X₆: X₃ {O(n)}
t₉, X₀: X₃ {O(n)}
t₉, X₁: X₃ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₃ {O(n)}
t₉, X₅: X₃ {O(n)}
t₉, X₆: X₃ {O(n)}
t₁₀, X₀: X₃ {O(n)}
t₁₀, X₁: X₃ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: 0 {O(1)}
t₁₀, X₅: 0 {O(1)}
t₁₀, X₆: X₃ {O(n)}
t₁₁, X₀: X₃ {O(n)}
t₁₁, X₁: X₃ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₃ {O(n)}
t₁₁, X₅: X₃ {O(n)}
t₁₁, X₆: X₃ {O(n)}
t₁₂, X₀: 2⋅X₃+X₀ {O(n)}
t₁₂, X₁: 2⋅X₃+X₁ {O(n)}
t₁₂, X₃: 3⋅X₃ {O(n)}
t₁₂, X₄: 2⋅X₄ {O(n)}
t₁₂, X₅: X₃ {O(n)}
t₁₂, X₆: 3⋅X₃ {O(n)}