YES
0 QTRS
↳1 QTRSRRRProof (⇔, 80 ms)
↳2 QTRS
↳3 RisEmptyProof (⇔, 0 ms)
↳4 YES
from(X) → cons(X, n__from(n__s(X)))
2ndspos(0, Z) → rnil
2ndspos(s(N), cons(X, n__cons(Y, Z))) → rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z)))
2ndsneg(0, Z) → rnil
2ndsneg(s(N), cons(X, n__cons(Y, Z))) → rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z)))
pi(X) → 2ndspos(X, from(0))
plus(0, Y) → Y
plus(s(X), Y) → s(plus(X, Y))
times(0, Y) → 0
times(s(X), Y) → plus(Y, times(X, Y))
square(X) → times(X, X)
from(X) → n__from(X)
s(X) → n__s(X)
cons(X1, X2) → n__cons(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__cons(X1, X2)) → cons(activate(X1), X2)
activate(X) → X
pi1 > [2ndspos2, 2ndsneg2] > activate1 > from1 > cons2 > ncons2 > [rnil, rcons2]
pi1 > [2ndspos2, 2ndsneg2] > activate1 > from1 > nfrom1 > [rnil, rcons2]
pi1 > [2ndspos2, 2ndsneg2] > activate1 > from1 > ns1 > [rnil, rcons2]
pi1 > [2ndspos2, 2ndsneg2] > activate1 > s1 > ns1 > [rnil, rcons2]
pi1 > [2ndspos2, 2ndsneg2] > activate1 > s1 > posrecip1 > [rnil, rcons2]
pi1 > 0 > [rnil, rcons2]
square1 > times2 > plus2 > s1 > ns1 > [rnil, rcons2]
square1 > times2 > plus2 > s1 > posrecip1 > [rnil, rcons2]
from1: [1]
cons2: [2,1]
nfrom1: multiset
ns1: multiset
2ndspos2: [1,2]
0: multiset
rnil: multiset
s1: multiset
ncons2: multiset
rcons2: [1,2]
posrecip1: multiset
activate1: multiset
2ndsneg2: [1,2]
pi1: [1]
plus2: multiset
times2: [2,1]
square1: multiset
from(X) → cons(X, n__from(n__s(X)))
2ndspos(0, Z) → rnil
2ndspos(s(N), cons(X, n__cons(Y, Z))) → rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z)))
2ndsneg(0, Z) → rnil
2ndsneg(s(N), cons(X, n__cons(Y, Z))) → rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z)))
pi(X) → 2ndspos(X, from(0))
plus(0, Y) → Y
plus(s(X), Y) → s(plus(X, Y))
times(0, Y) → 0
times(s(X), Y) → plus(Y, times(X, Y))
square(X) → times(X, X)
from(X) → n__from(X)
s(X) → n__s(X)
cons(X1, X2) → n__cons(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__cons(X1, X2)) → cons(activate(X1), X2)
activate(X) → X