0 CpxTRS
↳1 RcToIrcProof (BOTH BOUNDS(ID, ID), 4 ms)
↳2 CpxTRS
↳3 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID), 0 ms)
↳4 CdtProblem
↳5 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID), 0 ms)
↳6 CdtProblem
↳7 SIsEmptyProof (BOTH BOUNDS(ID, ID), 0 ms)
↳8 BOUNDS(1, 1)
2nd(cons1(X, cons(Y, Z))) → Y
2nd(cons(X, X1)) → 2nd(cons1(X, activate(X1)))
from(X) → cons(X, n__from(s(X)))
from(X) → n__from(X)
activate(n__from(X)) → from(X)
activate(X) → X
The duplicating contexts are:
from([])
The defined contexts are:
2nd(cons1(x0, []))
[] just represents basic- or constructor-terms in the following defined contexts:
2nd(cons1(x0, []))
As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
2nd(cons1(X, cons(Y, Z))) → Y
2nd(cons(X, X1)) → 2nd(cons1(X, activate(X1)))
from(X) → cons(X, n__from(s(X)))
from(X) → n__from(X)
activate(n__from(X)) → from(X)
activate(X) → X
Tuples:
2nd(cons1(z0, cons(z1, z2))) → z1
2nd(cons(z0, z1)) → 2nd(cons1(z0, activate(z1)))
from(z0) → cons(z0, n__from(s(z0)))
from(z0) → n__from(z0)
activate(n__from(z0)) → from(z0)
activate(z0) → z0
S tuples:
2ND(cons1(z0, cons(z1, z2))) → c
2ND(cons(z0, z1)) → c1(2ND(cons1(z0, activate(z1))), ACTIVATE(z1))
FROM(z0) → c2
FROM(z0) → c3
ACTIVATE(n__from(z0)) → c4(FROM(z0))
ACTIVATE(z0) → c5
K tuples:none
2ND(cons1(z0, cons(z1, z2))) → c
2ND(cons(z0, z1)) → c1(2ND(cons1(z0, activate(z1))), ACTIVATE(z1))
FROM(z0) → c2
FROM(z0) → c3
ACTIVATE(n__from(z0)) → c4(FROM(z0))
ACTIVATE(z0) → c5
2nd, from, activate
2ND, FROM, ACTIVATE
c, c1, c2, c3, c4, c5
2ND(cons(z0, z1)) → c1(2ND(cons1(z0, activate(z1))), ACTIVATE(z1))
2ND(cons1(z0, cons(z1, z2))) → c
FROM(z0) → c3
FROM(z0) → c2
ACTIVATE(n__from(z0)) → c4(FROM(z0))
ACTIVATE(z0) → c5
Tuples:none
2nd(cons1(z0, cons(z1, z2))) → z1
2nd(cons(z0, z1)) → 2nd(cons1(z0, activate(z1)))
from(z0) → cons(z0, n__from(s(z0)))
from(z0) → n__from(z0)
activate(n__from(z0)) → from(z0)
activate(z0) → z0
2nd, from, activate