### (0) Obligation:

Runtime Complexity TRS:

The TRS R consists of the following rules:

*(X, +(Y, 1)) → +(*(X, +(Y, *(1, 0))), X)

*(X, 1) → X

*(X, 0) → X

*(X, 0) → 0

Rewrite Strategy: FULL

### (1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:

The rewrite sequence

*(X, +(Y, 1)) →^{+} +(*(X, +(Y, 1)), X)

gives rise to a decreasing loop by considering the right hand sides subterm at position [0].

The pumping substitution is [ ].

The result substitution is [ ].

### (2) BOUNDS(INF, INF)