The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(2^n, INF).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

a__f(b, X, c) → a__f(X, a__c, X)
a__c → b
mark(f(X1, X2, X3)) → a__f(X1, mark(X2), X3)
mark(c) → a__c
mark(b) → b
a__f(X1, X2, X3) → f(X1, X2, X3)
a__c → c

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(2ⁿ):
The rewrite sequence
mark(f(b, X2, c)) →⁺ a__f(mark(X2), a__c, mark(X2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
The pumping substitution is [X2 / f(b, X2, c)].
The result substitution is [ ].

The rewrite sequence
mark(f(b, X2, c)) →⁺ a__f(mark(X2), a__c, mark(X2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [2].
The pumping substitution is [X2 / f(b, X2, c)].
The result substitution is [ ].

(2) BOUNDS(2^n, INF)