simplification rules for iff
#2, ?M_1 - ?M_2 ≤ ?M_1 ↦ true
#1, 0 ≤ ?M_1 ↦ true
#1, succ ?M_1 ≤ ?M_1 ↦ false
#1, pred ?M_1 ≤ ?M_1 ↦ true
#1, ?M_1 ≤ succ ?M_1 ↦ true
#2, ?M_1 - ?M_2 < succ ?M_1 ↦ true
#1, ?M_1 < 0 ↦ false
#1, ?M_1 < succ ?M_1 ↦ true
#1, 0 < succ ?M_1 ↦ true
simplification rules for eq
#1, g ?M_1 ↦ f ?M_1 + 1
#2, g ?M_3 ↦ 1
#2, f ?M_1 ↦ 0
#4, ite ?M_1 ?M_4 ?M_4 ↦ ?M_4
#1, 0 - ?M_1 ↦ 0
#2, succ ?M_1 - succ ?M_2 ↦ ?M_1 - ?M_2