The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(1)).

(0) Obligation:

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

c → f
f → g

Rewrite Strategy: INNERMOST

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

c → f
f → g

Tuples:

C → c1(F)

S tuples:

C → c1(F)

K tuples:none
Defined Rule Symbols:

c, f

Defined Pair Symbols:

C

Compound Symbols:

c1

(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 1 trailing nodes:

C → c1(F)

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

c → f
f → g

Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

c, f

Defined Pair Symbols:none

Compound Symbols:none

(5) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(6) BOUNDS(O(1), O(1))