(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
admit(x, nil) → nil
admit(x, .(u, .(v, .(w, z)))) → cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z)))))
cond(true, y) → y
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
[admit2, w] > nil
[admit2, w] > [.2, =2, sum3, carry3] > cond2
Status:
admit2: [2,1]
nil: multiset
.2: [2,1]
w: multiset
cond2: multiset
=2: [1,2]
sum3: [3,1,2]
carry3: [3,1,2]
true: multiset
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
admit(x, nil) → nil
admit(x, .(u, .(v, .(w, z)))) → cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z)))))
cond(true, y) → y
(2) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(3) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) YES