simplification rules for iff
#1, ?x_0 ↔ ?x_0 ↦ true
#1, false ↔ ?x_0 ↦ ¬?x_0
#1, ?x_0 ↔ false ↦ ¬?x_0
#1, true ↔ ?x_0 ↦ ?x_0
#1, ?x_0 ↔ true ↦ ?x_0
#0, false ↔ true ↦ false
#0, true ↔ false ↦ false
#1, ¬?x_0 ↔ ?x_0 ↦ false
#1, ?x_0 ↔ ¬?x_0 ↦ false
#2, ?x_0 - ?x_1 ≤ ?x_0 ↦ true
#1, 0 ≤ ?x_0 ↦ true
#1, succ ?x_0 ≤ ?x_0 ↦ false
#1, pred ?x_0 ≤ ?x_0 ↦ true
#1, ?x_0 ≤ succ ?x_0 ↦ true
#1, ?x_0 ∧ ?x_0 ↦ ?x_0
#1, ?x_0 ∧ ¬?x_0 ↦ false
#1, ¬?x_0 ∧ ?x_0 ↦ false
#1, false ∧ ?x_0 ↦ false
#1, ?x_0 ∧ false ↦ false
#1, true ∧ ?x_0 ↦ ?x_0
#1, ?x_0 ∧ true ↦ ?x_0
#3 perm, ?x_0 ∧ ?x_1 ∧ ?x_2 ↦ ?x_1 ∧ ?x_0 ∧ ?x_2
#3, (?x_0 ∧ ?x_1) ∧ ?x_2 ↦ ?x_0 ∧ ?x_1 ∧ ?x_2
#2 perm, ?x_0 ∧ ?x_1 ↦ ?x_1 ∧ ?x_0
#2, ?x_1 == ?x_1 ↦ true
#2, ?x_0 - ?x_1 < succ ?x_0 ↦ true
#1, ?x_0 < 0 ↦ false
#1, ?x_0 < succ ?x_0 ↦ true
#1, 0 < succ ?x_0 ↦ true
#1, ?x_0 ∨ ?x_0 ↦ ?x_0
#1, false ∨ ?x_0 ↦ ?x_0
#1, ?x_0 ∨ false ↦ ?x_0
#1, true ∨ ?x_0 ↦ true
#1, ?x_0 ∨ true ↦ true
#3 perm, ?x_0 ∨ ?x_1 ∨ ?x_2 ↦ ?x_1 ∨ ?x_0 ∨ ?x_2
#3, (?x_0 ∨ ?x_1) ∨ ?x_2 ↦ ?x_0 ∨ ?x_1 ∨ ?x_2
#2 perm, ?x_0 ∨ ?x_1 ↦ ?x_1 ∨ ?x_0
#2, ?x_1 = ?x_1 ↦ true
#4, ite ?x_0 ?x_1 ?x_2 ↦ (?x_0 → ?x_1) ∧ (¬?x_0 → ?x_2)
#0, ¬true ↦ false
#2, ¬?x_1 = ?x_1 ↦ false
#0, ¬false ↦ true
#1, false → ?x_0 ↦ true
#1, true → ?x_0 ↦ ?x_0
#1, ?x_0 → true ↦ true
#1, ?x_0 → ?x_0 ↦ true
#3, ?x_0 → ?x_1 ∧ ?x_2 ↦ (?x_0 → ?x_1) ∧ (?x_0 → ?x_2)
#3, ?x_0 ∨ ?x_1 → ?x_2 ↦ (?x_0 → ?x_2) ∧ (?x_1 → ?x_2)
#3, ?x_0 ∧ ?x_1 → ?x_2 ↦ ?x_0 → ?x_1 → ?x_2
simplification rules for eq
#1, g ?x_0 ↦ f ?x_0 + 1
#2, g ?x_0 ↦ 1
#2, f ?x_0 ↦ 0
#3, ite false ?x_1 ?x_2 ↦ ?x_2
#3, ite true ?x_1 ?x_2 ↦ ?x_1
#4, ite ?x_0 ?x_3 ?x_3 ↦ ?x_3
#1, 0 - ?x_0 ↦ 0
#2, succ ?x_0 - succ ?x_1 ↦ ?x_0 - ?x_1