(0) Obligation:

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

*(*(x, y), z) → *(x, *(y, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, +(y, f(z))) → *(g(x, z), +(y, y))

Rewrite Strategy: FULL

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
*(x, +(f(z3204_0), f(z))) →+ *(g(g(x, z), z3204_0), +(f(z3204_0), f(z3204_0)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [ ].
The result substitution is [x / g(g(x, z), z3204_0), z / z3204_0].