YES
0 QTRS
↳1 QTRSRRRProof (⇔, 0 ms)
↳2 QTRS
↳3 RisEmptyProof (⇔, 0 ms)
↳4 YES
fib(0) → 0
fib(s(0)) → s(0)
fib(s(s(x))) → +(fib(s(x)), fib(x))
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
POL(+(x1, x2)) = x1 + x2
POL(0) = 2
POL(fib(x1)) = 1 + 2·x1
POL(s(x1)) = 1 + 2·x1
fib(0) → 0
fib(s(0)) → s(0)
fib(s(s(x))) → +(fib(s(x)), fib(x))