(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(a, empty) → g(a, empty)
f(a, cons(x, k)) → f(cons(x, a), k)
g(empty, d) → d
g(cons(x, k), d) → g(k, cons(x, d))
Rewrite Strategy: FULL
(1) CpxTrsToCpxRelTrsProof (BOTH BOUNDS(ID, ID) transformation)
Transformed TRS to relative TRS where S is empty.
(2) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
f(a, empty) → g(a, empty)
f(a, cons(x, k)) → f(cons(x, a), k)
g(empty, d) → d
g(cons(x, k), d) → g(k, cons(x, d))
S is empty.
Rewrite Strategy: FULL
(3) SlicingProof (LOWER BOUND(ID) transformation)
Sliced the following arguments:
cons/0
(4) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
f(a, empty) → g(a, empty)
f(a, cons(k)) → f(cons(a), k)
g(empty, d) → d
g(cons(k), d) → g(k, cons(d))
S is empty.
Rewrite Strategy: FULL
(5) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
f(a, cons(k)) →+ f(cons(a), k)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [k / cons(k)].
The result substitution is [a / cons(a)].
(6) BOUNDS(n^1, INF)