Certification Problem

Input (TPDB TRS_Standard/Kaliszyk_19/arith)

The rewrite relation of the following TRS is considered.

There are 108 ruless (increase limit for explicit display).

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Rule Removal

Using the
prec(NUMERAL) = 0 stat(NUMERAL) = mul
prec(0) = 5 stat(0) = mul
prec(BIT0) = 4 stat(BIT0) = lex
prec(SUC) = 6 stat(SUC) = lex
prec(BIT1) = 1 stat(BIT1) = mul
prec(PRE) = 7 stat(PRE) = lex
prec(if) = 2 stat(if) = mul
prec(eq) = 7 stat(eq) = lex
prec(plus) = 8 stat(plus) = lex
prec(mult) = 9 stat(mult) = lex
prec(exp) = 10 stat(exp) = lex
prec(EVEN) = 5 stat(EVEN) = lex
prec(T) = 5 stat(T) = mul
prec(F) = 3 stat(F) = mul
prec(ODD) = 11 stat(ODD) = lex
prec(le) = 12 stat(le) = lex
prec(lt) = 12 stat(lt) = lex
prec(ge) = 5 stat(ge) = lex
prec(gt) = 5 stat(gt) = lex
prec(minus) = 13 stat(minus) = lex

π(NUMERAL) = [1]
π(0) = []
π(BIT0) = [1]
π(SUC) = [1]
π(BIT1) = [1]
π(PRE) = [1]
π(if) = [1,2,3]
π(eq) = [1,2]
π(plus) = [1,2]
π(mult) = [1,2]
π(exp) = [2,1]
π(EVEN) = [1]
π(T) = []
π(F) = []
π(ODD) = [1]
π(le) = [2,1]
π(lt) = [2,1]
π(ge) = [2,1]
π(gt) = [2,1]
π(minus) = [2,1]

all of the following rules can be deleted.

There are 108 ruless (increase limit for explicit display).

1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.