Dead-path-elimination (DPE) is a key ingredient of the business process execution language for web services (BPEL4WS). In this paper, we introduce a small language called the BPE-calculus which contains those constructs of BPEL4WS that are most relevant to DPE. We present three models for the BPE-calculus: one without DPE, one with DPE, and one with our proposed modification of DPE. We formulate a condition and show that it is sufficient and necessary for (modified) DPE being free of (unintended) side effects. More precisely, we prove the following two properties. First of all, if the condition is satisfied, then the behaviour of a BPE-process is the same in the model without DPE and the model with (modified) DPE. Secondly, if the condition is not satisfied, then we can construct a BPE-process that behaves differently in the models. As a consequence, if the condition is satisfied, then DPE becomes an optimisation. In that case, programmers can ignore DPE and, hence, programming in BPEL4WS becomes simpler.

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